Comparing Various Fractal Models for Analysing Vegetation Cover Types at Different Resolutions with the Change in Altitude and Season
Comparing Various Fractal Models for Analysing Vegetation Cover Types at Different Resolutions with the change in Altitude and Season
Chandan Nayak January, 2008
Comparing Various Fractal Models for Analysing Vegetation Cover Types at Different Resolutions with the change in Altitude and Season
by
Chandan Nayak
Thesis submitted to the International Institute for Geo-information Science and Earth Observation in partial fulfilment of the requirements for the degree of Master of Science in Geo-information Science and Earth Observation, Specialisation: (Geoinformatics)
Thesis Assessment Board
Chairman : Prof. Dr. Ir. A. (Alfred) Stein, ITC External Examiner: Dr. R. D. Garg, IIT, Roorkee IIRS member : Dr. Sameer Saran IIRS member : Dr. C Jeganathan IIRS member : Vandita Srivastava.
Thesis supervisors IIRS : Vandita Srivastava ITC : Prof. Dr. Ir. A. (Alfred) Stein
iirs
INTERNATIONAL INSTITUTE FOR GEO-INFORMATION SCIENCE AND EARTH OBSERVATION ENSCHEDE, THE NETHERLANDS & INDIAN INSTITUTE OF REMOTE SENSING, NATIONAL REMOTE SENSING AGENCY (NRSA), DEPARTMENT OF SPACE, DEHRADUN, INDIA
Disclaimer
This document describes work undertaken as part of a programme of study at the International Institute for Geo-information Science and Earth Observation. All views and opinions expressed therein remain the sole responsibility of the author, and do not necessarily represent those of the institute.
Dedicated to my beloved Ma, For making me the person I am.
COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
Abstract
In the last quarter century, fractal geometry has strived to become a useful tool for modeling natural phenomenon. As remote sensing images tend to be spatially complicated, fractal analysis, the study of complicated phenomenon is used as an alternative to Euclidean concepts for a more accurate representation of the nature of complexity in natural boundaries and surfaces. Fractal dimension (FD) is the central construct of fractal geometry used to describe the geometric complexity of natural phenomenon. The objective of the present study was to compare three fractal models: Isarithm, Variogram and Triangular Prism Surface Area method (TPSAM), for differentiating the vegetation types found in the study area at different resolution with the change in altitude and season. Remote sensing data of different spatial resolution from different sensors like LISS III, LISS IV and ASTER were used to compute FD using the integrated software package ICAMS (Image Characterization and Modeling System). Both local (moving window based) and global (whole image or major subset) approaches were used wherever it could be implemented. Mean FD values from the different methods for every vegetation type were calculated for different subset areas representing Sal, Planted, Mixed broad leaf and Mountain vegetations. This was done for green, red, infra-red band of the sensors and NDVI. It was seen that Variogram method was the better method in differentiating the vegetation type found in the study area with 250 by 250m subset. Other methods, Isarithm and TPSAM, did not give satisfactory results and had comparatively poor performance in terms of standard deviation and R2 values of the FD calculated. It was also found that NDVI and IR bands are the optimal bands which could appreciably distinguish the vegetation types. 23.5m of LISS III was judged to be the best resolution when coupled with Variogram method. Fractal measurements can be used, albeit cautiously, to remote sensing images for discriminating vegetation types, taking other factors into consideration. This could also serve as a metadata for content –based data mining from these imagery.
Keywords: Fractal dimension, Isarithm, Variogram, Triangular prism, ICAMS
i COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
Acknowledgements
My first and foremost gratitude is expressed to Prof Alfred Stein, the one person who kept my confidence and spirit high throughout the 6 months of thesis work. Every mail from Prof Stein, whether of appreciation or criticism has contributed to do justice to the thesis in one respect or other. His professional yet friendly and humorous ways of communication has helped in the successful completion of thesis with ease and comfort. I extend my thanks to Ms Vandita Srivastava for being my first supervisor. Her suggestions from time to time made me stay focused in the right direction to achieve the objective of the study.
I am greatly indebted to IIRS and ITC for allowing me to take up the M.Sc course. The fellowship provided by ITC is appreciated without bounds. Thanks are due in this context to Dr V.K. Dadhwal, Dean, IIRS for providing all the necessary facilities required for the research work. His expert opinion and technical guidance have proved to be precious all through the course.
Dr C. Jeganathan, a true teacher, friend and guide….. Jegan sir deserves my sincere respect and gratitude for his support and motivation from the very beginning of the course to the end. A model scientist, few have the mettle like him to inspire his students.
I am immensely thankful to Mr Amit Kulkarni, Ph.D student, Louisiana State University for responding to my mails and taking initiative to provide the ICAMS software without which the research would be nowhere. Acknowledgement is due to Dr. Nina Lam, Professor, Louisiana State University, for giving her permission to use the software.
I cannot forget to mention Mr P.L.N. Raju, In-charge, Geo-informatics Division, for the help extended in course of the research, especially to acquire satellite data from NRSA. I express my thanks to Ms. Minakshi Kumar, Scientist “SE”, PRSD, Dr S.K Saha, Head of the Department, ASD and Dr Sarnam Singh, Scientist “SE”, FED, IIRS for the time they have spared to provide data and technical help. A word of gratitude is expressed to Dr Valentijn Tolpekin and Dr Nicholas Hamm for their suggestions during the mid–term evaluation. I also thank MSc. W. H. Bakker, Geoinformation Processing Department, ITC for his guidance during the conceptualization of this research.
My friend and roomie for the last one and a half years, Mr Gurdeep Singh cannot be missed out in this section. The light moments we have shared during long nights of hard work throughout the research will always stay in memory. I thank each one of my batchmates, Chand sir, Gopal sir, Duminda, Sashi, Sandeep, Jhumur, Rupinder, Gurpreet, Sumona and Pravesh for being there to have fun and frolic at IIRS and ITC. Vidya, Nidhi, Saurav, Aditi, Smita, Tushar, and all in the PGD batch of Geo- informatics and Geo- hazards, 2006-07 are lovingly remembered. My special thanks goes to Ambika for her constant support and help when indeed it mattered the most.
I thank my dear baba for encouraging my venture to take up the MSc Geo-informatics course. His love and support are my strengths without which I would not have reached this far.
ii COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
Last but not the least; I thank the Royal Govt. of Netherlands for allowing the trip to Netherlands and giving an opportunity to experience the Dutch culture and customs.
Chandan Nayak Dehra Dun, India January 2008.
iii COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
Table of contents
Abstract…………………………………………………………………………………………………i Acknowledgement……………………………………………………………………………………...ii List of figures…………………………………………………………………………………………..vi List of tables…………………………………………………………………………………………...vii 1. Introduction ...... 1 1.1. Use of Fractals in Remote Sensing:...... 1 1.2. Problem definition:...... 2 1.3. Research objective...... 3 1.3.1. Main objective...... 3 1.3.2. Sub-Objectives ...... 4 1.4. Research Questions ...... 4 1.5. Methodology ...... 4 1.6. Chapter schema ...... 5 2. Fractal Geometry and Fractal Models ...... 6 2.1. Background ...... 6 2.2. Natural fractals - statistical self-similarity...... 7 2.3. Fractals in remote sensing of land-cover...... 7 2.4. Fractal models ...... 8 2.4.1. Isarithm method...... 10 2.4.2. Triangular Prism Surface Area method...... 11 2.4.3. Variogram method...... 13 3. Materials and methods...... 16 3.1. Study area and field investigation ...... 16 3.1.1. Location of study area ...... 16 3.1.2. Reasons for selecting the study area...... 16 3.1.3. Vegetation in the study area ...... 17 3.1.4. Field visit...... 18 3.2. Image data ...... 20 LISS IV ...... 20 ASTER ...... 20 LISS III...... 20 3.3. Data generation...... 21 Detailed methodology: ...... 21 3.4. Software used ...... 25 4. Results & Discussions...... 26 4.1. Selection of optimal spectral band(s) for differentiating different vegetation types...... 27 4.2. Change of FD with spatial resolution:...... 31 4.3. Change of FD with seasons...... 38 4.4. Change of FD with altitude:...... 43 4.5. Comparison: ...... 45 4.5.1. Optimal band selection...... 45 4.5.2. Fractal dimension and spatial resolution: ...... 47 4.5.3. Fractal dimension and change in season: ...... 48
iv COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
4.5.4. Fractal dimension and altitude...... 49 5. Conclusions and recommendations ...... 50 5.1. Conclusions ...... 50 5.2. Limitations of the study...... 51 5.3. Future recommendations ...... 52 6. References ...... 53 Appendix – 1 ...... 55 ICAMS interface and fractal image...... 55 Appendix – 2 ...... 57 Plots of change of FD with Spatial resolution and Spectral bands: ...... 57 Appendix – 3 ...... 59 Plots of variation of FD with the change in altitude: ...... 59 Appendix – 4 ...... 62 Plots of change of FD with spectral bands for different vegetation types ...... 62 Appendix – 5 ...... 65 Plots of Local fractal approach for optimal band selection...... 65 Appendix – 6 ...... 68 FD values calculated with different methods...... 68 Appendix – 7 ...... 75 Field photographs...... 75
v COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
List of figures
Figure 1-1: Methodology flow chart ...... 4 Figure 2-1: Estimation of FD using isarithm method ...... 10 Figure 2-2: Pictorial representation of the Triangular prism surface area method...... 12 Figure 2-3: The log-log plot of variance and distance as used in variogram method ...... 14 Figure 3-1: Location and extent of study areas...... 16 Figure 3-2: Altitudinal distribution of forests in western Himalayas...... 17 Figure 3-3: Image showing field points and elevation values in Haldwani...... 18 Figure 3-4 DEM showing field points in Haldwani ...... 19 Figure 3-5: Detailed methodology flow chart ...... 22 Figure 3-6: Some selected subsets of vegetations ...... 24 Figure 4-1: Plot of Local Variogram method, ASTER October...... 29 Figure 4-2: Plot of Local Variogram method, LISS III November...... 29 Figure 4-3: Change of FD with spectral bands ...... 30 Figure 4-4: Variation of range of FD with spatial resolution Sal (NDVI example)...... 33 Figure 4-5: Variation of range of FD with spatial resolution Plantations (NDVI example)...... 34 Figure 4-6: Variation of range of FD with spatial resolution MBL (NDVI example)...... 36 Figure 4-7: Variation of range of FD with spatial resolution, MV (NDVI example) ...... 37 Figure 4-8: Variation of FD with the change in season in Sal ...... 39 Figure 4-9: Variation of FD with the change in season in plantation ...... 40 Figure 4-10: Variation of FD with the change in season in MBL...... 41 Figure 4-11: Variation of FD with the change in season in MV...... 42 Figure 4-12: Effect of change of FD with Altitude, Sal LISS III...... 44 Figure 4-13: Effect of Change of FD with Altitude, MBL LISS III ...... 44 Figure 4-14: Effect of Change of FD with Altitude, MV LISS III ...... 45 Figure 4-15: Comparison of IR plots for local fractal approach, Haldwani and Dehradun...... 45 Figure 4-16: Comparison of NDVI plots for local fractal approach, Haldwani and Dehradun...... 46 Figure 4-17 : Plot of variation of FD with spatial resolution, DDN ...... 47 Figure 4-18: Plot of change of FD with the variation of spectral bands and season, DDN ...... 48
vi COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
List of tables
Table 2-1: Summary of methods for computing fractal dimension...... 14 Table 3-1: Spectral characteristics of LISS IV...... 20 Table 3-2: Spectral characteristics of ASTER...... 20 Table 3-3: Spectral characteristics of LISS III...... 21 Table 4-1: Details of subsets used for local and global fractal approaches...... 27 Table 4-2: Suitable bands and corresponding R2 values of Global approach...... 29 Table 4-3: Change of FD with spatial resolution; ex: sal (season 1, 250m by 250m subset) ...... 32 Table 4-4: R-square values for sal forests ...... 32 Table 4-5: Change of FD with spatial resolution; ex: plantation (season 1, 250m by 250m subset).....33 Table 4-6: R-square values for plantations...... 34 Table 4-7: Change of FD with spatial resolution; ex: mixed broad leaf (season 1, 250m by 250m subset)...... 35 Table 4-8: R- square values for mixed broad leaf forests...... 35 Table 4-9: Change of FD with spatial resolution; eg: mountain vegetation (season 1, 250m by 250m subset) ...... 36 Table 4-10: R- square values for mountain vegetations...... 37 Table 4-11: Change of FD with Seasons with different methods; Sal (250m by 250m subsets)...... 39 Table 4-12: Change of FD with Seasons with different methods; plantations (250m by 250m subsets) ...... 40 Table 4-13: Change of FD with Seasons with different methods; mixed broad leaf (250m by 250m subsets)...... 41 Table 4-14: Change of FD with Seasons with different methods; MV (250m by 250m subsets) ...... 42 Table 4-15: Optimum bands of Dehradun (DDN) and Haldwani (HALD); (Aster) ...... 46 Table 4-16: Global R- square values of Dehradun (DDN) and Haldwani (HALD); (Aster) ...... 47 Table 4-17: Change of FD with Season; Dehradun Sal ( 250m by 250m subset) ...... 48
vii COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
1. Introduction
Earth’s vegetation plays a major role in forming the composition and characteristic of the land surface. Information about the vegetation cover is an indirect indicator of land-use, and is highly relevant for environmental studies. Proper environmental planning and management in today’s environmentally insecure world demands accurate classification of various vegetation types along with many other factors, making it immensely valuable to the human society.
Mapping of landscape processes like vegetation, land-cover/land-use, soil survey, geological mapping are traditionally done based on hierarchical systems. Depending on the objective, diagnostic features or criteria are chosen. The data required also depends on the objective of the study, though different studies may be using the same data or different ones. Data as of satellite remote sensing provides an important source of land-cover information and it has gained popularity nowadays owing to the wide choice of bands, in and beyond the visible spectrum in which the digital images can be obtained. This opens new avenues for vegetation and soil survey as well as for landscape analysis (Jong, 1994). Several methods are available to describe the variation on the earth surface, all treating the environmental variables as a set of patterns occurring at specific scales. It is known, however, that the processes on the earth surface which are responsible in determining its shape and form occur at different scales; varying from large-scale geological processes, small-scale slope formation, large forests to small agriculture holdings. So it may be of interest to use these different scales when studying the variability of landscapes. Quantifying the complexity between scale and resolution is a challenging task even if several tools and means are available, such as univariate and multivariate statistics, spatial autocorrelation indices like Moran’s I and Geary’s C, and local variance measures within a moving window. These provide some understanding of such interaction but they also have their limitations of assumptions and limits of certainty.(Emerson et al., 1999).
1.1. Use of Fractals in Remote Sensing: Physicist John A. Wheeler once said that “no one is considered scientifically literate today who does not know what a Gaussian distribution is, or meaning or scope of the concept of entropy. It is possible to believe that no one will be considered scientifically literate tomorrow who is not equally familiar with fractals” (Batty, 1985. cited in (Lam, 1990)). The statement appears to be quite true as fractal analysis is said to be one of the four most significant scientific concepts of the 20th century, with a significant impact similar to that of the general theory of relativity, development of the double-helix model of DNA and quantum mechanics (Clarke and Schweizer, 1991 cited in(Jaggi et al., 1993)).
In the context of complexity, i.e. between scale and resolution, the concept of fractal geometry can be a step forward to describe this complex form of natural phenomena. Fractals in the sense of fractal geometry have the property of self similarity, i.e. the behaviour of a system is spatially scale- independent, resulting in comparability between measurements at different scales (Emerson et al., 1999; Read and Lam, 2002). Since its introduction by Mandelbrot in 1975, fractal geometry and its
1 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
scale independent nature have attracted in particular the earth scientists, who observe and study landscape features at various scales. Satellite imagery with improving spectral and spatial resolution reveals more of landscape features at finer resolutions and wider spectral range. Relevance and usefulness of fractal geometry to solving remote sensing problems of exploitation of data, spanning a large order of magnitude of scale ( cartographic, geographic, operational and measurement)(Emerson et al., 1999; Lovejoy et al., 2001) can be attributed to the fact that remotely sensed images are spectrally and spatially complex but also exhibit similarities at different spatial scales. The fractal dimension (FD now onwards) is a central concept of fractal geometry. It can be viewed as a measure of irregularity of spatial arrangements of physical processes. Fractals, self-similarity and FD are the key concepts of fractal geometry on which most of the applications on remote sensing are done. In remote sensing FD is used to measure the roughness or the textural complexity of land surfaces. Major application of fractal geometry and FD in the field of remote sensing include characterization of overall spatial complexity of an image, using textural information for image classification, describing the geometric complexity of the shape of feature classes in a classified image and to examine the behaviour of environmental phenomenon due to scaling (Sun et al., 2006) The FD of remote sensing data yields quantitative insight into spatial complexity and information. Remote sensing images acquired from different sensors at varying spatial and spectral resolutions may thus be comparable using fractal measurements. The FD can then be interpreted and compared with other measures of spatial complexity to understand the significance of spatial relationships within the data.(Jaggi et al., 1993)
1.2. Problem definition: In Euclidean geometry, dimensions are integers or whole numbers and the topological dimension remain constant no matter how irregular the line or surface may be. Natural surfaces, however, do not usually have a simple Euclidean shape. The idea of using FD is then promising because it captures elements that are lost in traditional geometry. For example, a high spatial complexity of a line or a surface corresponds to a high FD. Hence, FD for lines ranges from 1 to almost 2, and for surfaces from 2 to almost 3. If the FD of fractal surfaces (i.e. complex topologically 2D objects) increases, the surface occupies more of the 3D space.(Parrinello and Vaughan, 2002; Read and Lam, 2002; Sun et al., 2006). Moreover the problem then is not only to quantify the complex inter-relationship but also to efficiently handle and process data. In fact, calculations on such objects place a heavy demand on the data processing and storage capabilities of hardware and software. Solving this problem requires using data efficiently which means using the data at appropriate scale and resolution to characterize phenomenon. This will help accurately provide answer of the questions being asked about characterizing the natural phenomenon studied through remote sensing.(Emerson et al., 1999). This would be particularly helpful in the studies of forests where shape and size play an important role. From the air, natural forests have boundaries similar to islands. Boundaries between forests and meadows are fractal in nature due to their elevation difference. Even inside the forests large patches of vegetation are formed by joining satellite patches. Different species have different characteristics and thus different texture, and thus can have difference in their FD. This study deals with different fractal models and the derivation of FD from them. Observing the change of FD with changes in resolution, we could aim to see the change across different spatial and spectral resolutions and correlate them with environmental variables for achieving a better understanding. For example, at one particular scale FD may change with vegetation type. We could
2 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
then study this relationship, i.e. quantify and interpret it, taking changes in altitude and season into consideration. As the type of vegetation changes with the change in altitude, it would then be of interest to see the changes in the FD and the relation with altitude.
Different fractal models exist and three of them, viz., Isarithm, Triangular Prism Surface Area and Variogram method will be used in this study. Isarithm method is based on the idea that the complexity of isarithm or contour lines may be used to approximate the complexity of a surface. Starting with the method, a matrix of z-elevations (or DN values), and an isarithm interval is selected and isarithm lines are constructed on the surface. Lengths are calculated, for each isarithm line, in terms of the number of boundary cells over a number of step sizes, log (number of boundary cells) is regressed against log (step sizes). The slope of the regression line is used to derive the FD of the isarithm line and is repeated for every isarithm line and averaged to find the FD of the surface (Sun et al., 2006). Triangular Prism Surface Area method estimates lumped D values from topographic surfaces or remotely sensed images. This method takes elevation values (DN) at the corners of squares i.e. the centre of a pixel, interpolates the centre value of the square by averaging, divides the square into 4 triangles and then computes the surface areas of the imaginary prism. This is repeated for different square sizes and spacing. The calculation stops when the size of the square is too big to fit an image. The Variogram method is one of the widely used methods to compute FD. In this method, the mean of the squared elevation (or DN) difference or variance is calculated for different distances, and D is calculated from the slope of the regression between the log of variance and distance so that FD = 3 – slope/2. Variogram method is easy to use because it can be used to both regular and irregular data and is more reliable than isarithm method.(Sun et al., 2006). Using different fractal models at different resolution would generate different results and validation of these results requires some time- tested references.
This study also aims to compare the results of the present study area with that of another area so as to reveal the relation of different variables used in the study. Therefore the fractal approach may meet the criteria of an easier and quicker method of assessing spatial pattern from remotely sensed images. The most obvious validation method would be ground truth collection, which will involve identification of vegetation species at different locations and altitude. The information acquired during the field will be used in demarcating vegetation patches in the remote sensing images. These patches will then be used to generate subset of suitable dimensions to carry out their fractal analysis and validate the results.
1.3. Research objective The study compares different fractal models and analyzes their results to come up with an answer which can provide the end–users, using this technique, about the optimal method, spatial resolution and spectral band which can be used to differentiate different vegetation type found in the study area. This will help not only to save time and effort but also help reduce the complications of large data handling and processing.
1.3.1. Main objective
The main objective of the study is to compare various fractal models for analyzing the vegetation cover types at different resolutions.
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1.3.2. Sub-Objectives • To identify appropriate spectral bands and spatial resolutions of remote sensing images to calculate the fractal dimension of different vegetation types. • To calculate fractal dimension using various fractal models, for selected spatial resolutions and spectral bands in a given remote sensing image. • To explore the relation between fractal indices calculated for vegetation cover types and elevation at different spatial resolutions. • To find out the best parameters for variables in the study which would help in discriminating various vegetation types using calculated fractal dimension. • To validate the results of differentiation using ground data collection.
1.4. Research Questions The research questions to be addressed are:
• Which fractal model is best suited to differentiate the vegetation types in the area? • How does the fractal dimension change with spatial resolution and spectral bands for different vegetations with the change in season and altitude? • Can we differentiate various types of vegetation found in the study area with the help of fractal dimensions obtained?
1.5. Methodology
Image 1 Image 2 Image 3 Resolution 1 Resolution 2 Resolution 3
Band selection
Compute FD
Isarithm, TPSAM, Variogram Compare results
Analysis Field data
Differentiate Optimal Effective Vegetation Spectral bands fractal model types
Figure 1-1: Methodology flow chart
4 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
A broad overview of the methodology is given in the figure above, for more detailed information the reader is directed to chapter 3. The study deals mainly with multi-resolution seasonal data. Raw data acquired from different sources were pre-processed and converted into formats that were recognized by different software packages used in the study. Four different vegetation types: sal, plantations, mixed broad leaf and mountain vegetations were first identified through visual interpretation, local knowledge, expertise and field verification and area subsets of different sizes were generated according to their spatial extent. FD were calculated for all the bands available and NDVI images. Analysis was carried out using relation formed by different variables – spectral bands, spatial resolution, altitude, seasons, methods and vegetations. The results were then tabulated and inference made according to the results they gave.
1.6. Chapter schema This thesis is divided into 5 chapters. Chapter 1 gives the rationale for the present study with a set of objectives and questions to be attempted. Theory and understanding of different fractal models are summarized in chapter 2. Chapter 3 details about the methodology followed in this study, while the results and discussions are penned down in chapter 4. Finally the thesis is concluded with chapter 5.
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2. Fractal Geometry and Fractal Models
The term fractal (from Latin fractus - irregular, fragmented) applies to objects in space or fluctuations in time that possess a form of self-similarity and cannot be described within a single absolute scale of measurement. Fractals are a family of mathematical functions proposed to describe natural objects with irregular shapes. They are irregular and recurrent in space or time, with themes repeated like the layers of an onion or a cauliflower at different levels or scales. Fragments of a fractal object or sequence are exact or statistical copies of the whole and can be made to match the whole by shifting and stretching (Klonowski, 2000)
2.1. Background Fractal geometry was coined and popularized by Mandelbrot (Mandelbrot, 1982)to describe and characterize highly complex forms of natural phenomenon such as coastlines and landscapes, and since then it has gained much support in the field of image analysis. Although Mandelbrot’s idea was to describe self-similar geometric figures but the recent researches in earth and environmental sciences have pushed the use of fractals into the territory of metadata representation, environmental monitoring, change detection, and landscape and feature characterization.(Bisoi and Mishra, 2001; Sun et al., 2006; Zhou and Lam, 2005)
Fractals have two basic characteristics suitable for modeling the topography of the Earth’s surface: self-similarity and randomness. An important property of fractal geometry is that true fractals display self-similarity, i.e. the shape of a fractal object remains independent of scale at which it is measured, thus measurement made at different scales are comparable (Read and Lam, 2002; Weng, 2003). Dimension can be said to be a function of the observer’s location. If we consider the dimension of a ball of strings, then from very far away it looks like a dot (dimension = 0), closer it is solid (dimension = 3), very close it is a twisted tread (dimension = 1). So here in fractal geometry, dimension brings observer in to the story. An ideal fractal curve or surface has constant dimension, which quantifies subjective notions concerning how densely the fractal occupies the traditional Euclidean space in which it is embedded (Kolibal and Monde, 1998), over all the scales i.e. the form of the curve or surface is invariant with respect to the scale. We can say, however, that it should not be possible to determine the scale of a fractal from its form, i.e. its shape or appearance (Goodchild, 1980). As self- similarity refers to the fact that earth’s morphology appears similar across a range of scales but the concept of self-similarity also contains randomness, because the resemblance of the earth’s morphology at different scales is statistical and not exact (Malinverno,1995, cited in (Weng, 2003). Self-affinity is defined as a union of non-overlapping subset that can linearly map into the whole set. A fractal that includes randomness is said to be self-affine and needs to be scaled as scaling is not uniform in all coordinates but invariant under transformation that scale different coordinates by different amount (Parrinello and Vaughan, 2002). The dimension is called ‘fractal’ as it can have fractional or non-integer value. The concept of fractional dimension was first formulated by Hausdorff and Besicovitch. Mandelbrot called it fractal
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dimension and defined fractal as “a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension (Klonowski, 2000; Lam, 1990) Mathematically fractal dimension for strictly self-similar surface can be derived by:
FD = LogN / Log (1 / r ) Equation 2-1
Where 1/r is a similarity ratio or the degree of self-similarity and N is the number of step sizes or an object of N parts scaled down by a ratio ‘r’. In traditional or Euclidean geometry, the topological dimensions are 1, 2 and 3 for a curve, plane and volume respectively. Conventionally, we consider integer dimensions which are exponents of length, i.e., surface = length2 or volume = length3. The exponent is the dimension. This topological dimension remains constant no matter how irregular the curve or area may be. In this context a straight as well as a crooked line will have the same topological dimension of 1 and hence the line’s regularity or irregularity cannot be discriminated by mere topology. Information about an irregular surface is lost in this type of representation. On the other hand dimension in fractal geometry is treated as a range i.e. a FD of a curve may be any value between 1 and 2 and from 2 to 3 for a surface, depending on the complexity. Fractal geometry allows for there to be measures which change in a non-integer or fractional way when the unit of measurements changes. As fractal dimension is directly related to an object’s complexity, a smooth line having originally FD = 1 will approach FD = 2 when it becomes complex enough to occupy the whole space of a plane. This also holds true for a plane having FD = 2 approach a 3-dimensional volume with increasing complexity. An object will fill more space when it becomes increasingly irregular and have higher value of FD. (Lam, 1990; Sun et al., 2006)
2.2. Natural fractals - statistical self-similarity The notion of self-similarity is the basic property of fractal objects. A mathematical fractal has an infinite number of identical versions of itself and can be made by the iteration of a certain rule. In principle, a theoretical or mathematically generated fractal is self-similar over an infinite range of scales, while natural fractals have a limited range of self-similarity. The similarity method for calculating fractal dimension works for a mathematical fractal, which is composed of. It is not completely true for natural objects. Such objects show only statistical self-similarity. In non-fractals, however, the size always stays the same, no matter of applied magnification. Unlike mathematical fractals, natural objects do not always display exact self-similarity, therefore the fractal dimension for natural objects can only be found out empirically and not analytically.
2.3. Fractals in remote sensing of land-cover Remotely sensed images are not only spectrally and spatially complex, but often exhibit certain similarities at different spatial scales and the relevance and use of fractal geometry comes in solving these remote sensing problems (Sun et al., 2006). The use of FD as a texture measure to segment and classify remote sensing images have been tried and tested. Fractal techniques are well suited for the analysis of texture in remote sensing images as the environmental feature that are captured in the images are often complex and fragmented. It can be supposed that different kind of terrain can have different texture or roughness and can be expressed in terms of different FD. While computing the fractal dimension, an image is considered to be a 3D surface where the complexity of the surface is
7 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
expressed as its variability over space and it is a function of its vertical variability of pixel values (Qiu et al., 1999). It has been suggested by (Pentland 1984, Keller et. al. 1987) cited in (Sun et al., 2006) that local variation in FD can be used as texture measures to segment images. This is based on the idea that different land-cover types have characteristic texture or roughness and can have different FD values. Therefore a local fractal analysis of images can reveal information on patterns of vegetation and rock outcrops much better than pixel-per-pixel procedures (Jong and Burrough, 1995). In their study De Jong and Burrough ((Jong and Burrough, 1995)) proposed a ‘local D- algorithm’ for Triangular Prism Surface Area method (TPSAM) which gave results as a new image file with the FD values. This new layer was used in classification procedure. They used their proposed method to classify six types of Mediterranean vegetation with Landsat TM and GER images. Although they were able to distinguish 5 out of 6 vegetation types, in their study area, with the Landsat image but the results were not satisfactory with the GER images for their poor image quality. They concluded that though FD values for TM images reflected different land cover types but they alone are not enough to classify the imagery. Roach and Fung (Roach and Fung, 1994) applied two techniques, the power spectrum method and fractional Brownian motion (fBm) method, for quantifying fractal scaling characteristics to texture within spectrally-classified segments of Landsat TM and MEIS images of a logging area in South-East British Columbia. From their study they concluded that fractal geometry can be a useful tool in the study of remote sensing forestry texture but a ‘blind’ application of fractal techniques to non-fractal anisotropic textures can result in characteristic fractal plots which can be falsely interpreted as fractal. Lam, (Lam, 1990) used two methods, isarithm and variogram, to measure the spatial complexity of three Landsat TM images consisting of three different land-cover types of coastal Louisiana. She found that the calculated fractal dimension of these TM surfaces were higher than real-world terrain. Read and Lam (Read and Lam, 2002) compared performances of selected pattern recognition methods for characterizing different land-cover types using unclassified Landsat TM data of lowland site NE Costa Rica. They used fractal dimension, calculated from Isarithm and TPSAM, and other spatial auto- correlation and landscape indices to represent land-cover types of forest, agriculture, pasture and scrubs. They found that fractal dimension from TPSAM and Moran’s I index of spatial auto- correlation were useful for characterizing spatial complexity of imagery whereas the landscape indices failed.
2.4. Fractal models There are several proposed methods to compute the fractal dimension of natural objects, which use different ways to approximate N given in equation 2-1 but most of the methods have the following three common steps: • Measure the quantities of the object using different step sizes. • Plot log- log graph of measured quantities versus step sizes and fit a least square regression line through the data points. • Use the slope of regression line to derive the FD
Different computational methods, however, have their own practical, and theoretical limitations, or both. Past researches used fractals as a spatial measure for describing and analyzing remotely sensed imagery emphasizing more on spatial relationship between adjacent cells. Hence they are different from traditional spectral methods, which either perform pixel-by-pixel comparison between two images or matrix of from-to classes during classification (Kulkarni, 2004). Pixel-by-pixel classifier do
8 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
not take into account the spatial content of the pixels (Jong and Burrough, 1995) and therefore cannot exploit all the information in the data (Cihlar, 2000). Main problems that hinder the widespread use of fractals in remote sensing are the lack of standardized tools and algorithm details in research papers. (Sun et al., 2006) pointed out the lack of review papers which summarizes and evaluates different fractal methods and applications are widely scattered in the literature. A number of methods for calculation of fractal dimension have been developed for application in various spatial problems and variety of image processing and pattern recognition problem and several researchers have applied fractal techniques to describe image textures and used segmentation of various types of images (Sun et al., 2006), but most of the methods have their own limitations of assumption and certainty. Studies by several researchers (Lam et al., 2002; Sun et al., 2006; Tate, 1998) reveal the fact that different methods bring out significantly different FD values, for the same feature/ surface. Apart from method induced errors, factors such as input parameter values, quality of image data also influences the output FD value (Sun et al., 2006). Studies have been done comparing different fractal estimators. As cited in (Zhou and Lam, 2005), Klinkenberg and Goodchild (1992) tested seven methods on 55 real topographic data sets that yielded mixed results. (Tate, 1998) analyzed several estimators using nine simulated surfaces and also concluded that indeed different estimators gave different results. (Lam et al., 2002) used 25 simulated surfaces in three methods TPSAM, Isarithm and Variogram methods and found that Isarithm and TPSAM performed better than Variogram method. The methods have been well described and documented in (Goodchild, 1980; Jaggi et al., 1993; Kolibal and Monde, 1998), the detailed algorithm is given in (Jaggi et al., 1993). The software package, ICAMS, contains all these methods along with other spatial descriptors (Quattrochi et al., 1997) (Sun et al., 2006), in their review paper stated that most of the research till date has suggested that real remotely sensed images are not true fractals, which clearly contradicts the fundamental assumption underlying the theory of fractal descriptors. Some researchers (Lam et al., 2002) argued that this should not be taken as a drawback instead could be used positively. They pointed out that FD value which is stable over limited ranges of scale can be used to study the effect of scale changes on image properties. Emerson in (Emerson et al., 1999) pointed out that no one scale is optimal for different geographical processes, therefore further investigation is required to determine how the fractal dimension can be used as an indicator of the trade-off between scale, resolution and spatial extent of the input imagery. Some of the methods that are used in FD calculation are as follows: • TPSAM • Isarithm method • Variogram method • Differential Box counting method • Robust Fractal estimator • Power spectrum method etc.
From the above mentioned methods, the first three methods will be used in this study. The reason is that these three methods are extensively used in remote sensing images and are easily applicable Apart from this, these methods have their own advantages, like TPASM uses raster representation of elevation of the earth’s surface and is computationally simple method. Isarithm method can be used to estimate FD of non self-similar surfaces, it is robust, accurate and relatively lacks sensitivity to input parameters and returns good result for images with medium-ranged complexity. Variogram method is easy to use and can be applied to both regular and irregular data (Sun et al., 2006).
9 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
2.4.1. Isarithm method The isarithm or line-divider method calculates the fractal dimension using an extension of the one dimensional line-divider method (Jaggi et al., 1993). It uses the walking-divider logic by using different ‘step-sizes’, that represent the segments necessary to cross a curve, to calculate the fractal dimension. For an irregular curve, as the step sizes become smaller, the complexity and the length of the stepped representation of the curve increase. If the logarithm of the number of step or segments needed to traverse the curve for a range of step-sizes is plotted against the length of the curve, we get the D of the isarithm line from the slope of the regression line as: LogL = C + βLogr D = 1− β Equation 2-2 where, L is the length of the curve or the number of boundary cells, β is the slope of the regression line and C is a constant.
Figure 2-1: Estimation of FD using isarithm method Source: (Weng, 2003)
The figure above shows a self affine fractal with a nominal length of λ0 having discreet intervals of ‘r’ and a standard deviation of heights δ. Therefore the total length of the line α as a function of r is approximately
λ 1/ 2 α = 0 ()r 2 + δ 2 Equation 2-3 r
For a self affine fractal over distance r, the standard deviation of heights is
2−D ⎛ r ⎞ δ = b⎜ ⎟ Equation 2-4 ⎝ b ⎠
Where b is the crossover length, which is the horizontal sampling interval, above which the method breaks down. Replacing δ in equation 2 we get
10 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
2(1−D) 1/ 2 ⎡ ⎛ r ⎞ ⎤ α = λ0 ⎢1+ ⎜ ⎟ ⎥ Equation 2-5 ⎣⎢ ⎝ b ⎠ ⎦⎥
For r << b, log (α) versus log (r) has slope of 1-D. When r >> b, then α ≈ λ0. (Weng, 2003). The algorithm used in this study is elaborately given in (Jaggi et al., 1993).For remotely sensed images, this method uses contours of equal z values as the object of measurement for which the fractal dimension is estimated. Multiple passes are taken in the image using different isarithm values (iso- spectral reflectance curve). These values are generated by dividing the range of pixel values of the image into a number of equally spaced intervals with the following parameters given by the user: • Number of step sizes • Isarithm interval and • Direction of computation (row, column or both).
To calculate the fractal dimension, the image is divided into two regions – one with values equal to or greater than the isarithm and the other with values less than the isarithm value. The whole image is transformed into a binary set of 1 and 0 by setting ‘off’ the pixels below the threshold and setting ‘on’ the pixels above the threshold. By comparing every pixel, an edge is detected and counted whenever it contains a value different from the threshold. These boundary cells are then counted at different step sizes, pre-defined by the user. In the absence of boundary cells for a given step-size, the isarithm line is excluded from the analysis to avoid regression using fewer points than the given number of steps (Sun et al., 2006). The log of the number of edges is regressed against the log of step-sizes producing a fractal plot, which is used to calculate the FD using D = 1- β. This process is repeated for every isarithm line and the FD of the entire image is obtained by averaging the FD values of all the isarithm lines that have R2 ≥ 0.9. The slope of the regression line is always negative as when the step-sizes increases, the details in the line decreases and the length of the line decreases (Read and Lam, 2002). The isarithm method provides a measure of the pixel correlation which determines the distance over which fluctuation in one region of the image are correlated or affected by those in another region.
2.4.2. Triangular Prism Surface Area method The triangular prism surface area method is a computationally simple method, put forward by Clarke (1986) cited in (Sun et al., 2006), to calculate the dimension of topographic surface. It has been applied extensively to remote sensing images (Sun et al., 2006). It makes use of a raster representation of the elevation of the Earth’s surface as in a DEM. The image is seen as a grid of ‘x’ and ‘y’ coordinates and the value of the pixel is taken as the ‘z’ value, providing a vertical dimension for the cell. Taking the value of the pixels that constitute the four corners of the square (side of the square equals to the step size), the mean is calculated. A vertical line equal to the mean value is drawn from the centre of the square grid. Straight lines are drawn joining the top of each corner lines and with the centre line (figure 2-2). This defines the four triangular surfaces comprising the triangular prism. The area of the top of this prism is calculated using trigonometric formulae.
11 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
Figure 2-2: Pictorial representation of the Triangular prism surface area method Source : (Jong and Burrough, 1995; Sun et al., 2006)
This procedure is repeated for every step-size. Each succeeding computation takes a cell area which is exponentially larger than the previous one. This process continues till the whole image area is calculated as a single cell area. But doing this the image resolution diminishes and information is lost when individual pixel values are replaced by the mean at the centre. As this method needs square grids of different sizes, the square grid with the largest step is computed first. If, for example, an image is made entirely of the same digital number, then the resulting 3D structure would be a cuboid and would give a fractal dimension of 2.0. On the other hand if an image has entirely uncorrelated brightness value, then it would give a fractal dimension of 3.0. A typical image has a fractal dimension between 2 and 3.(Jaggi et al., 1993) TPSAM unlike the Isarithm method compares area with grid cell length. Considering the basic equation for defining a fractal curve as given in Mandelbrot (1967) [see (Lam et al., 2002)] N(d ) = Kδ −D Equation 2-6
L(d ) = N(δ )δ = Kδ 1−D Equation 2-7
Where: δ = step size; N(δ) = number of steps: L(δ) = length of the curve: and K = constant
For extending this definition of curve to area, the expression for fractal dimension of an object of area A and step size δ can be deduced as follows:
A(δ ) = N(δ )δ 2 = Kδ 2−D Equation 2-8
Rearranging the above equation in logarithmic form we get:
12 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
LogA = K + (2 − D)Logδ Equation 2-9
Where: β = (2-D), the slope of the regression: K = constant, therefore:
D = 2 − β Equation 2-10
The log of the total surface areas (sum of all triangular prisms) is plotted against the log of the step- size. Fractal dimension is calculated by taking the slope of the regression line and substituting it in equation 2-10. As total surface area decrease with the increase of step-size, the β of the regression line is negative hence the resultant D ranges from 2.0 to 3.0
2.4.3. Variogram method The Variogram method is a widely used technique for computing D of surfaces (Sun et al., 2006) This method is based upon the statistical Gaussian modeling of images (Jaggi et al., 1993)which states that given a fractal dimension, it is possible to use the fractional Brownian motion (fBm) modeling to create an image corresponding to the given fractal dimension. The Variogram method attempts to solve the inverse of the Gaussian modeling problem. It states that if an image is given, its fractal dimension can be calculated assuming that the surface under consideration is a fractional Brownian surface. The fractional Brownian motions says that there exists a distinct statistical relationship between two pixels and the variance of the difference in their pixel values or
Var(1,2) ∝ dis(1,2) 2H
Where, dis(1,2) is the distance between two pixels 1 and 2, H represents the ruggedness of the surface. H ranges between 0 and 1, where small value of H corresponds to rugged surface, while a larger value of H exhibits smoother surface. The fractal D of the fBm surface is calculated by:
D = 3 − H Equation 2-11
To calculate the fractal dimension, the log of the variance between all the pixel pairs is plotted against log of the distance between them as shown in the figure above. The distance is partitioned into clusters and the variance is calculated for each of the cluster formed. To each cluster, the difference and the square of the difference between the pixel values is added and repeated for all pixel pairs. Using this, the variance for all data pairs that fall in each of the cluster or distance interval is calculated by n 2 γ d = 1 z − z Equation 2-12 () ( 2n)∑[]i ()d +1 i=1 Where: n = total number of data pairs that fall in distance interval d, z = DN values or surface values (Lam et al., 2002)
D is estimated from the slope of the regression line as follows:
13 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
D = 3 − β / 2 Equation 2-13
Where β is the slope of the regression line.(Jaggi et al., 1993)
Figure 2-3: The log-log plot of variance and distance as used in variogram method Source: (Sun et al., 2006)
The Variogram method uses the Variogram function to estimate the fractal dimension. The Variogram function describes how variance in surface height between data points is related to the spatial distance between them. The only difference between the traditional Variogram and that used in fractal estimation is that distance and variance are portrayed in double-log form. So to derive the Variogram function for a surface, variance of all data pairs which fall into a specific distance interval are calculated (Lam et al., 2002)
The above mentioned three fractal dimension estimators represent a collection of easily applied techniques used for remote sensing images. These are two-dimensional fractal measurement techniques mostly used for analyzing image textures and surface roughness. Perimeters and outlines are one-dimensional also used for forest studies but are not considered because in this study we are more concerned with the features delineated in areas and surfaces, like texture and roughness, rather than those with boundaries of forests. The summary of the methods, their formula and relation used are tabulated below:
METHOD RELATION USED BASIC FORMULA ESTIMATE OF FD Isarithm Length of contour line α ∝ r1−D For each contour line, plot vs. step size log α(δ) versus log (δ), slope = (1-D) TPSAM Total area of the tops A(δ ) ∝ δ 2−D Plot log A(δ) versus of prisms vs. side log(δ), length of analysis slope = (2-D) windows D = 2 − β
Variogram Mean squared elevation Var(1,2) ∝ dis(1,2) 2H Plot log(var) vs log(dist) (or DN) difference vs. Slope = 2H distance D = 3 − β / 2 Table 2-1: Summary of methods for computing fractal dimension Refined and adapted from (Sun et al., 2006)
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The detailed flowchart for all the methods used in this study and the source code is given (Jaggi et al., 1993). The present study requires understanding of different fractal models and their response to different remote sensing datasets. Fractal dimension which is the central construct of any fractal model holds the same importance in this research. Here we are mostly concerned with natural fractals and the change of fractal dimension with the change of vegetation, resolution, spectral resolution, season as well as well altitude.
15 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
3. Materials and methods
This chapter briefly describes the different materials used in the study and the methodology followed in this study. The importance of study area is also described.
3.1. Study area and field investigation Uttarakhand is among the northern states of India and covers an area of about 53,500 km2. It incorporates the entire Himalayan part and the adjoining parts of the Indo – Gangetic Plain falling in the Haridwar and Udham Singh Nagar districts. Dehradun is the provisional capital of the state situated in district of Dehradun, while Haldwani is located in the district of Nainital (Kumar, 2005).
3.1.1. Location of study area
Figure 3-1: Location and extent of study areas.
3.1.2. Reasons for selecting the study area The study area is rich in forest cover and diversity of forest types. It was chosen as it had a large diversity of vegetation as well as a considerable elevation gradient. The chosen area has about 2225.17 Ha of land under plantation (2005-06), where different species of trees like teak, shisham and poplar are grown as plantation forests. To the north of Haldwani the study area approaches the Himalayas, gaining an elevation of more than 2000m within a distance of about 50km. This relatively small area is
16 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
thus convenient to address issues of elevation differences and corresponding changes in vegetation type as shown in the figure 3-1 below
Figure 3-2: Altitudinal distribution of forests in western Himalayas Source: (Negi, 2000)
3.1.3. Vegetation in the study area The study area is extremely rich in vegetation, which comprises mainly of forests. The following forest regions are found in this area spanning different altitudes (figure 3-2): 1. Sub-montane or Sub-tropical region forests – It is found in the elevation range from 500m to 1500m. The main vegetation of this area being dominated by Sal (Shorea robusta), Khair (Acacia catechu), Shisham (Dalbergia sissoo), Chir pine ( Pinus roxburghii) and varieties consisting of deciduous species. Out of all these species of this region, Sal and Chir pine is taken in the study as they are seldom intermixed and found at different altitudes. Sal – Sal is a small to medium sized tree. Crown is moderately developed and has fairly long trunk. Generally the bark is dirty green or ash grey. When young, the leaves are oblong or elliptical, dark green and dense but become glabrous and coriaceous when mature. Flowering occurs during April and May while fruiting takes place in the winter season. Although Sal exhibits concentrated leaf drop in summer but the simultaneous leafing-out never renders their population naked. However the canopy becomes markedly thin during the summers. Pine – Pine is a fairly large-sized tree with not so well developed crown. The tree attains a height of about 30-35m. Pine has brownish bark which is moderately thick. Leaves are in the form of needles, light green in colour and found in bundles of three. Flowering takes place between February and April and fruiting occurs in April- May of next year.
17 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
2. Montane or Temperate region forests: This region extends from an elevation of about 1500m to 3500m. The main forests occurring in this area are Oak forests (Quercus leucotricophora), Deodar (Cedrus deodara), Kail and Fir and Spruce forests. Among all these, Oak is chosen for the study as it is at a lower navigable altitude than other and easily accessible. Oak- Oak is found at an altitude of more than 2000m. It is generally a medium to large sized tree. Its bark is highly fissured, dark grey or blackish in colour. Leaves are oblong or lanceolate, are spinous and tooted in young trees. Flowering occurs in April to early June while fruiting occurs fifteen to seventeen months after (Negi, 2000; Singh and Singh, 1992).
3.1.4. Field visit In order to gain knowledge about the study area and its vegetation, a field visit was carried out from 1st October to 5th October 2007. The main objective of the field visit was to collect ground truth for the different vegetation types found in the area. The base camp for the first two days was at Tanda forest guest house; south of Haldwani while the remaining was at Nainital. Forest survey was done with the help of local forest officials. Tree species, GPS reading and age of the forest was noted where possible. Field work for Dehradun area was undertaken after the first field work and similar investigation and collection of ground truth was done. Figure 3-3 and 3-4.
Figure 3-3: Image showing field points and elevation values in Haldwani.
18 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
Figure 3-4 DEM showing field points in Haldwani
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3.2. Image data For studying the variation of fractal dimension with the change in spectral and spatial resolution along with the change in season, a variety of remotely sensed images, from different sensors, offering a range of spatial and spectral resolution, has been taken. We considered two different seasons for dealing with existing temporal variation. Images from the months of March-April and October- November are taken. LISS IV, ASTER and LISS III images, offering resolutions of 5.8m, 15m and 23.5m respectively were used.
LISS IV LISS (Linear Imaging Self Scanner) IV on board IRS-P6 (ResourseSat) is a multi spectral high resolution sensor with a spatial resolution of 5.8m. This sensor was chosen for its high resolution and easy availability in India. The spectral characteristic of the sensor is given in the table below. (www.nrsa.gov.in)
BAND WAVELENGTH RESOLUTION SWATH REVISIT WIDTH TIME 1 (green) 0.52 µm to 0.59 µm 5.8m 23.9 km 5 days 2 (red) 0.62 µm to 0.68 µm 5.8m 23.9 km 5 days 3 (NIR) 0.77 µm to 0.86 µm 5.8m 23.9 km 5 days Table 3-1: Spectral characteristics of LISS IV
ASTER The Advanced Spaceborne Thermal Emission and Reflection Radiometer obtains high-resolution (15 to 90 m2 pixel-1) images of the Earth in 14 different wavelengths of the electromagnetic spectrum, ranging from visible to thermal infrared light. ASTER is the only high spatial resolution instrument on the Terra platform. ASTER's ability to serve as a zoom lens for the other Terra instruments is particularly important for change detection, calibration/validation and land surface studies. Unlike the other instruments aboard Terra, ASTER does not collect data continuously; rather, it does it on an average of 8 minutes of data per orbit. All three ASTER telescopes (VNIR, SWIR, and TIR) can be pointed in the cross-track direction. (http://terra.nasa.gov/About/ASTER/about_aster.html)
BAND WAVELENGTH RESOLUTION SWATH REVISIT WIDTH TIME 1 (green) 0.52 µm to 0.60 µm 15m 60 km 16 days 2 (red) 0.63 µm to 0.69 µm 15m 60 km 16 days 3 (NIR) 0.76 µm to 0.86 µm 15m 60 km 16 days Table 3-2: Spectral characteristics of ASTER
LISS III Spatial resolution of 23.5 m of IRS-1D and IRS-P6 LISS-III multi spectral sensor is considered suitable for this study because of its easy availability in India at relatively low costs. IRS ID and IRS P6 carry a medium resolution LISS-III camera operating in three visible spectral bands (B2, B3, B4), which are suitable for vegetation monitoring
20 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
BAND WAVELENGTH RESOLUTION SWATH REVISIT WIDTH TIME 1 (green) 0.52 µm to 0.59 µm 23.5m 140km 24days 2 (red) 0.62 µm to 0.68 µm 23.5m 140km 24days 3 (NIR) 0.77 µm to 0.86 µm 23.5m 140km 24days 4 (SWIR) 1.55 µm to 1.70 µm 23.5m 140km 24days Table 3-3: Spectral characteristics of LISS III
3.3. Data generation Several sites comprising patches of a varying homogeneity were selected for each type of recognized forest cover in the study area. Subsets of different sizes are generated for each of the sites. Three subset sizes of 750m by 750 m, 500m by 500m and 250m by 250 m for Global fractal approach could be generated for Sal forests as they have large extents of homogeneous cover over the study area. For other vegetation types, like the planted forests south and south-west of Haldwani, the number and size of the subset had to be reduced because of limitations in extent and homogeneity of the forest plots. This also applies for forest cover in the mountainous regions of the Nainital and Bhowali areas, having similar complexities in terrain feature. A uniform subset size of 1 km by 1km was generated for Local fractal approach. Criteria for selection of subset size were based on resolution, size of the regions, and a minimum number of pixels. Smaller subset size than those chosen here would not cover sufficient spatial or textural information to characterize the forest cover type. A larger subset size, however, would not be suitable as it would incorporate information from other vegetation types, thus leading to ineffective analyses. Since it is not possible to have all subset sizes for all vegetation types, it would be inappropriate to use different subset sizes for different forest covers as their comparison would become meaningless. Maximum effort was put to keep the same area of the subsets for different forest cover type similar, but it was not possible for all.
NDVI (Normalized Difference Vegetation Index) is used as an indicator for vegetation vigour. It can be used to interpret urban, rural or vegetation/forest contrast and seasonal changes in vegetation patterns (Emerson et al., 1999). NDVI values are calculated for every image with similar subsets generated for all vegetation patches. The images are rescaled to an 8-bit format to facilitate the comparison between the different forest types. This can also help in illustrating how the computed fractal dimension varies with change in resolution and season. Fractal dimension for each subset are calculated globally and locally using the methods mentioned. The results are graphically plotted for different variables and further analyzed.
Detailed methodology: The elaborate steps involved within the methods are described by a conceptual flow chart given below in Figure 3-5.
21 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
LISS 3 ASTER LISS 4
PREPROCESSING OF DATA Includes import of raw images and geometric correction and re-projection
Subset Rescale to ASTER DEM NDVI generation 8-bit
Convert to .lan format
Convert to GROUND TRUTH .bsq format DATA
Calculate Fractal dimension by Isarithm, TPSAM and Variogram methods
Plot results Analysis and graphically Final results
Figure 3-5: Detailed methodology flow chart
Step 1. Procuring and importing of data Remote sensing data from different sensors were collected. Aster data were ordered from www.glovis.usgs.gov . The data are in Hierarchical data format (HDF-EOS). It is imported as IMG format through ERDAS Imagine™ import data module. IRS data which comprise of LISS III and LISS IV data were either available at Indian Institute of Remote Sensing (IIRS) or ordered through NDC of NRSA. The raw data from NDC are in generic binary form.
Step 2. Pre-processing of data Pre-processing of the data involves cloud or haze removal, image geometric correction and re- projection of the data. For this study cloud free images were required, so that no masking of ground features occurs due to clouds. The ASTER and LISS images used here are either cloud free or existing clouds did not cover any part of the study area.
Geometric correction: • Image to map registration- Survey of India topo-sheets were used as reference data for image to map geometric correction. Permanent features like road crossings, bridges, railway lines, reservoir and dams which were easy to locate both on map and ASTER image of March 2004 were used as Ground control points (GCP) for geometric correction. Theoretically three GCPs are required for this but other 16 GCPs well distributed over the study area were taken for final geo-correction (Jenson, 1996). The Root Mean Square error on geo-correction was 0.676
22 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
Pixels. The transformation projection selected for the geometric correction was Universal Transverse Mercator (UTM) and Datum as WGS84. • Image to image registration - The geo-referenced Aster 2004 image was used to co-register the other images used in the study. The root mean square error (RMSE) on final image to image co-registration was kept as low as possible. During this process special care was taken in selecting well distributed GCPs as any mis-registration at this stage could give erroneous result. Through visual inspection of geo-linked pixels on both the images the geo-registration was ascertained to be within sub pixel level. The correctness of geo-registration was further cross verified by swiping and flickering in ERDAS Imagine™ 8.7.
Step 3. Computation of NDVI NDVI has been computed using the red and infrared bands. For the aster images bands 3a and 2 represent the infrared and red wavelength of the electro-magnetic spectrum, while for the LISS 3 and LISS 4 images they are band 3 and 2 respectively. NDVI is calculated in ENVI and the files are saved as ERDAS Imagine format. Mathematically the equation for NDVI can be defined as: NDVI = (NIR − R) /(NIR + R) , which for aster images becomes NDVI = (band3a − band2) /(band3a + band2) , and for LISS images NDVI = (band3 − band2) /(band3 + band2) .
Step 4. Rescaling of NDVI The NDVI images are rescaled to an 8-bit format in ERDAS Imagine™ 8.7 by means of the module Interpreter in order to facilitate the comparison between the different forest types. This can also help in illustrating how the computed fractal dimension varies with change in resolution and season.
Step 5. Subset generation Subsets were mostly generated taking the field data points (Figure 3-3) as reference. This helped in taking pure samples of the concerned vegetation. Square subsets were generated using AOI tools in ERDAS Imagine™ Data Preparation module. A number of concentric squares of size (750m) 2 , (500m) 2 ,(250m) 2 were used as AOIs for global approach and (1km) 2 for local approach. These are used where the forest patches have large extent and homogeneity. Subsets were generated from images of ASTER and LISS for different vegetation types as well as the NDVI image. Similar subsets were generated from the DEM, for both the regions, using the same AOIs. The average elevation were then calculated from the DEM and used as a reference for altitude of the patches whose FD is to be calculated for further use in the study.
23 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
SAL PLANTATION MIXED BROAD LEAF MOUNTAIN VEG. Figure 3-6: Some selected subsets of vegetations
Step 6. Conversion to LAN format All the subsets have to be converted to LAN format before being fed to ICAMS. ICAMS can only recognize images with LAN format, so the images are converted to LAN through Export option in ERDAS Imagine™ 8.7.
Step 7. Conversion to BSQ Format LAN images have to be converted to BSQ Generic Binary format to do the data processing and calculations in ICAMS. So the subsets were first imported in ICAMS in BSQ format.
Step 8. Calculation of fractal dimension Local (window based) and Global (entire image) FD by all the three methods are calculated in ICAMS through characterization tab (discussed in chapter 4). For Isarithm method, the software default ‘Isoline interval’ and ‘Number of steps’ are taken and for the Method option both rows and columns were chosen. This is done for all subset sizes and bands. All default options provided in the TPSAM window are taken for calculation, whereas parameters for the Variogram method are chosen after a careful examination of inputs and results. After a series of experiments the parameters that to be used were decided. Sampling method- Stratified random, Sample interval- 5, Group- 10, Break 1- 1, break 2- 5 were taken for further analysis. Other values for parameters either did not give any result at all or if it did, it was unacceptably erroneous.
24 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
Step 9. Plotting of results graphically The results of the fractal models were fractal dimensions in the form of numerical values. These values were plotted in graphs to analysis so that they can be meaningfully interpreted. Graphs were plotted with the different variables used in the study and analyzed to achieve the objectives of the study and to subsequently answer the research questions. The output images of local fractal approach had FD values for every pixel. This pixel data were extracted from the image and the frequency of every FD occurring in the image were noted. The percentage of pixels for every FD present in the image was plotted against the values of FD. This gave curves for the different vegetation in the study area. These curves were further analyzed.
Step 10: Statistical analysis To analyse the graphical results both visual and statistical approaches were taken. Standard deviation and R2 were taken as the statistical indicators. Graphs between FD - spectral bands, resolution, season and altitude were plotted and statistical inferences were made depending on the relation they gave indicated by R2 and standard deviation. Finally the inferences are integrated and presented.
3.4. Software used ICAMS: The Image Characterization and Modeling System (ICAMS) is used in the study to calculate the fractal dimension of the remotely sensed images. Apart from calculating the fractal dimension, this integrated software package provides specialized spatial analytical functions for visualizing and interpreting remote sensing data, which includes Variogram, spatial autocorrelation, wavelet and texture analysis. It also has modules for calculating NDVI, land-water boundary and synthesis of artificial images. ICAMS has the ability to compute fractal dimension and spatial autocorrelation indices either in a global (whole image or subset) or local approach using a moving window filter (Emerson et al., 2005) Image file format conversions, image geometric correction, classification, calculating NDVI and other image processing were done in ERDAS Imagine™ version 8.6 (Leica Geosystems, 2002) and ENVI version 4.3 (RSI Inc, 2006).
25 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
4. Results & Discussions
This chapter presents the results of the study analysed, to fulfil the research objective and answer the research questions.
This study is mainly concerned with vegetation types in the study area. The spectral characteristics of vegetation play an important part in the experiments conducted. It is known that the spectral reflectance of vegetation canopy varies because of pigmentation, physiological structure and water content. In the visible wavelength, pigmentation dominates the spectral response of the plant wherein chlorophyll is especially important. Absorption by chlorophyll gives low reflectance in red and blue bands while a peak reflectance at about 0.5 µm is seen because of the green colour of the leaf. Apart from this, the morphological characters of the vegetation, i.e. shape, size, height and density also play an important role. The structure of the canopy and the light scattering between the leaves causes the spectral response of the canopy of the different vegetation types to vary. The seasonal state of maturity of a plant also influences its spectral reflectance by altering its proportion, or by controlling the presence or absence of some of its parts. Flowering usually occurs over a short period during the growth cycle of the vegetation. Evergreen trees shed their leaves regularly but the simultaneous leafing out never renders them leafless while on the other hand deciduous trees shed their leaves during peak winter which drastically change the appearance from summer. Because of these factors the spectral signature of a plant species may vary during a season and its life cycle.
This study uses both the local and global approaches to calculate the fractal dimension of the vegetations. Local and global are generic terms in remote sensing, but in fractal calculations, these refer to two methods where the resultant FD is calculated by two different approaches. In global approach, resultant FD is estimated by the slope of the regression line for the whole image or a major subset, while in local approach, a kernel of a chosen size is moved over the input image and a type of convolution operation is done resulting in an image consisting of FD values for each pixel.
Not all vegetations in the study area have large extent or textural homogeneity, and as such the problem of taking equal area subsets were a difficult task not only for the global approach but also for the local methods. The minimum subset size of 250m by 250m for global calculations could not be used for local calculations because of window size constraints of the software used. A window size of 1km by 1km was fixed for local approach after careful consideration of the factors involved in proper demarcation of the vegetation areas as discussed in section 3.3. For local approach, five subsets each of Sal and planted forests were taken while three subsets each for mixed broad leaf and mountain forests were taken.
26 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
LOCAL MAJOR GLOBAL APPROACH APPROACH TYPES OF CLASS Number of subsets TREES Number of (Size of subsets = Subset Size subsets 1km by 1km) 250m by 250m
SAL 500m by 500m Sal, Teak 5 10 750m by 750m
Teak, Shisham, 250m by 250m PLANTATION Poplar 5 13 500m by 500m
MIXED Sal, Khair, 250m by 250m BROAD LEAF Shisham 3 10 500m by 500m
MOUNTAIN
VEGETATIO Oak , Pine 250m by 250m 3 10 N Table 4-1: Details of subsets used for local and global fractal approaches
4.1. Selection of optimal spectral band(s) for differentiating different vegetation types Past researches have shown that the fractal dimension calculated from different computational methods give different results for the same datasets. The differences between different methods vary so considerably that comparison between computed FD values obtained are meaningless (Sun et al., 2006). But in this study we are interested, not in the difference in FD values from different methods, but in the trends that they show when used on different spectral bands for different types of vegetations. Different vegetations have different response in different bands and so they can have contrasting FD values, which may or may not show a similar trend with other vegetations making them distinct to help in their discrimination.
Selection of an optimal spectral band or bands which can help in differentiating the different types of vegetation found in the study area was the foremost objective of the study. This selection would not only help in discriminating the vegetation but will also reduce the effort and time required in handling and processing of large datasets used in remote sensing. Both local and global approaches were taken for this purpose. A visual interpretation of the results of the local approach is done to analyse the different spectral band characteristics while a statistical inference is done in attempt to analyse the bands in the global methods. Area subsets of all image data were used, covering all the vegetation types in the area (details given before) for local fractal dimension estimation using local Isarithm, local TPSAM and local Variogram methods. Fractal dimension is plotted against percentage of pixels in a given class. This is done for the green, red, infra-red and NDVI band images for all the vegetation type for two seasons. The degree of separability between the different vegetation types using the above methods is indicated by the amount of overlap between the curves. The detailed analysis of the Aster and LISS images obtained by both Local and Global fractal approach are discussed and given below. The output images of local fractal approach have FD for each
27 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
pixel, which were grouped based on the frequency of occurrence. The percentage of pixels of each FD of the image is plotted against the total range of FD of the image. This is done for all the vegetation subsets and combined in one graph to analyse their degree of separability in terms of FD.
Local Isarithm method: The graphical plot of the March images show that the four vegetation type have somewhat distinct curve in the IR and NDVI images but overlap in the other two spectral bands viz. green and red. Same results were observed in the October images and although the curves of MV and plantation overlap in the IR and NDVI images, they are not totally eclipsed and differentiation is seen to be possible. The degree of separability in all the LISS 3 images is observed to be low. The result from these images is somehow mixed. Some of the vegetations are easily distinguishable but others have major or full overlaps. In the red band images of both the seasons, Sal and MV have distinct peaks while plantation and MBL have major overlaps rendering them to be unrecognizable. MV shows prominent peaks in all the images baring NDVI image of November while Sal also shows distinct peaks in almost all the images. In all it is seen that IR and green bands show good discriminating character (Appendix -5).
Local TPSA method: In the March images, MV could be easily separated from all the other types of vegetation as seen by the distinctly separated curves (Appendix 5). In the green and red bands, the other vegetation types are hardly distinguishable. The IR image shows a good distinction between the vegetation types, with prominent peaks indicating vegetation types with varying fractal dimensions. It is also seen that the curve of Sal shows two peaks, which may be due to difference in growing phases and hence having a different textural feature. The MV has wide ranged curves, which may be attributed to the fact that at the centre of the forest, the FD is low while at the fringe where two species meet, a high FD is yielded. An interesting result was obtained in this method for the LISS-III images. Unlike the previous ones, a good degree of separation is observed in green, red and NDVI image outputs where distinct peaks were observed for each vegetation type. Sal and plantation showed some major overlaps in these images but the maximum value were seen to be different, thus clearly differentiating them into two groups. The IR images gave the noisiest plots; curves having almost total overlaps are seen in the images of both the seasons
Local variogram method: In all the four resultant images, the differentiation of the vegetation could hardly be done except for Sal which has prominent peak in all plots. MBL forest showed some distinct multimodal curves in IR images (figure 4-1). In the LISS 3 images, the degree of separability in almost all the output fractal images was low. All vegetation has distinct peaks in the January IR image while the November image has a unique multimodal curve for MV and MBL (figure 4-2).
28 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
24.00 INFRA RED SA L 21.00 INFRA RED PLANTN 18.00 INFRA RED MV 15.00 INFRA RED MBL 12.00
% pxls 9.00 6.00 3.00 0.00 2.50 2.55 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00 3.05 3.10 FD
Figure 4-1: Plot of Local Variogram method, ASTER October
18.00 INFRA RED SA L 16.00 INFRA RED PLANTN 14.00 INFRA RED MV 12.00 INFRA RED MBL 10.00 8.00 % pxls 6.00 4.00 2.00 0.00 2.50 2.55 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00 3.05 3.10 FD Figure 4-2: Plot of Local Variogram method, LISS III November
MARCH ASTER SUITABLE BANDS VEGETATION SAL PLANTATION MIXED BROAD LEAF MOUNTAIN VEG METHODS ISA TPSA VAR ISA TPSA VAR ISA TPSA VAR ISA TPSA VAR SUBSET SIZE BAND NDVI NDVI NDVI IR NDVI IR NDVI IR GREEN NDVI IR NDVI 250 MEAN FD 2.9388 2.9798 2.9087 2.6931 2.4734 2.8521 2.8343 2.5908 2.8062 2.7112 2.6099 2.8293 SD 0.0970 0.1789 0.0693 0.3374 0.0886 0.0494 0.0784 0.1208 0.1255 0.1312 0.0854 0.0765 CV 3.3016 6.0025 2.3813 12.6414 3.5868 1.7309 2.7646 4.6608 4.4724 4.8313 3.2737 2.7031 R SQ 0.9662 0.9192 0.9595 0.9528 0.9670 0.9042 0.9711 0.9217 0.9300 0.9292 0.9922 0.9632
500 BAND NDVI NDVI NDVI NDVI GREEN IR NDVI NDVI IR MEAN FD 2.9401 2.9588 2.9648 2.6803 2.3271 2.8148 2.7132 2.2827 2.8545 SD 0.0351 0.1094 0.0194 0.1208 0.1418 0.0475 0.1168 0.1450 0.0226 CV 1.1953 3.6959 0.6552 4.4771 5.7969 1.6956 4.3054 6.3511 0.7932 R SQ 0.9270 0.9109 0.9649 0.9264 0.9773 0.9738 0.9800 0.9595 0.9047
750 BAND NDVI NDVI IR MEAN FD 2.9139 2.9479 2.9359 SD 0.0686 0.0672 0.0107 CV 2.3549 2.2781 0.3639 R SQ 0.9856 0.9294 0.9375
Table 4-2: Suitable bands and corresponding R2 values of Global approach
29 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
Global Approach: Mean FD, Standard deviation (SD), CV and R2 were taken into account in the Global fractal approach. It is seen that the SD decreases with the increase in FD in almost all the cases, but this cannot be used for differentiating different bands which has to be selected in the study. SD does not measure the spatial arrangement of the bright and the dark pixels but it gives the relationship to the mean brightness value. SD, a non-spatial measure of variation bears no relationship with FD which is a spatial measure of variation. So SD alone cannot be used. But on the other hand the use of SD cannot be ruled out. In the previous studies it was reported that a moderate inverse relationship exist between FD and SD. This can be used as a part of metadata for the image to form a broad impression of the image even without viewing it. For example, when an image has a high SD and a relatively low FD, the surface would exhibit a spatially homogeneous pattern. On the other hand a low SD with high FD would represent a fragmented and spatially varying surface. (Kulkarni, 2004). For our purpose, an investigation was made to find out the bands with the maximum R2. The spectral bands having the maximum R2 were chosen from each vegetation type and are shown in table 4-2.
2.9500
2.9000 SAL_VAR 2.8500 PLANTN_VAR
FD MBL_VAR 2.8000 MV_VAR 2.7500
2.7000 GREEN RED IR NDVI SPECTRAL BANDS
Figure 4-3: Change of FD with spectral bands
Results from the local fractal graphs show that different vegetation gives different distinct curves, which in most of the outputs above presents a key in distinguishing them. It is also seen that for different sensors the hierarchy at which the curves of different vegetation occur on the graph are almost identical, baring a few instances of overlap. This may be due to the fact that these vegetations have different degree of homogeneity and thus possess different fractal dimensions. At the same time the textural homogeneity changes when they are observed at different resolutions, giving different fractal dimensions and position on the graph’s scale for different sensors. For example, the curves of plantations for Aster images is seen to be placed lower than all other vegetations while that of Mountain vegetations on the higher side. This can be explained by the fact that the plantations or the planted forests have human involvement in their growth, i.e. forest of the same parcel are planted at the same time and at definite pattern which makes them more or less homogenous, resulting in lower fractal dimension. At the same time the curves for mountain vegetation seems to have the highest FD and range, which can be due to the presence of more than one species in this class, viz. dominantly oak and pine. The fractal dimension at the fringes or the contact point of these forests will yield large FD and gradually become lower at the centre. Moreover these forests are old naturally growing forests, like most of the sal and mixed broad leaf forest taken in this study and thus are heterogeneous both in terms of maturity and pattern, giving larger FD than the planted ones. This fact also contributes to the presence of more than one peak in their plots. This is true for plantations also, as a single parcel
30 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
containing the desired vegetation was not available. The inclusion of other parcel possibly containing another type of vegetation may lead to multiple peaks in this class too. Results from this experiment indicates that FD can be used to differentiate different vegetation types found in the study area but optimal band selection by only visual interpretation of the results is not enough. It is difficult to pick out a band which truly differentiates the vegetation type. One vegetation type can often be easily differentiated in a particular band but there is hardly any band capable of clearly separating them. Though it is seen that IR band is prominent among all in differentiating followed by NDVI, to come to a conclusion, a comparison of the results of the global approach was also taken into account. Table 4-2 shows the collection of the bands which had the highest R2 along with the SD and CV. It is seen from table 4-2 that NDVI and IR bands have the maximum number of occurrences of highest R2 (which is in confirmation with the inference of local approach) and thus it is concluded from the result of the experiment that these two bands are optimum for discriminating the vegetation types found in the region.
Table 4-2 also shows that the results of local fractal approach are significantly different only at the level of second and third decimal places. So the results should be interpreted carefully before coming to a conclusion. These results, along with the previous, show that the combination of both local and global approaches are feasible, in discriminating the vegetation types in the area, but they require utmost care in interpretation so as not to lead to wrong conclusions. At the same time, one band can not be used to differentiate the various vegetation types as the response of two vegetations for the same bands can be identical and render the process of differentiating them tedious. On the contrary a combination of two bands can make the task easier and useful in the study.
4.2. Change of FD with spatial resolution: To examine the variation of fractal dimension of remote sensing images with the change of spatial resolution, datasets of different resolution from three different sensors were taken and analysed. Fractal dimension was calculated for the three available bands and NDVI of all the datasets. The resultant mean FD calculated from three methods were plotted against the spatial resolution, individually for each band and vegetation type. R2 was calculated from the trend lines obtained from the regression equation. A close examination of the results shows that the three methods have greatly varying results having no correlation among them. An individual assessment of the vegetation is briefly described below.
Sal: The study area consists of large extents of Sal forests and thus it was possible to generate three subset sizes of 750 by 750, 500 by 500 and 250 by 250 m, containing homogenous patches. Calculations were done on these three subsets sizes for 10 sample locations, distributed throughout the study area. Isarithm and TPSA methods behaved strangely with the change in spatial resolution. Both the methods showed a fall and then a rise in fractal dimension from 5.8m to 15m and then to 23.5m for green and red bands for all subset sizes. Variogram method on the other hand showed a decrease of FD from finer to coarser resolution in all the bands and subset sizes baring the NDVI image.
31 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
SAL 250 SENSOR (SPATIAL RESOLUTION) SEASON 1 LISS 3 (23.5m) ASTER (15m) LISS 4 (5.8m) BANDS METHODS MIN MAX MEAN MIN MAX MEAN MIN MAX MEAN GREEN ISA 2.0000 3.4037 2.8683 2.0000 3.0402 2.3785 2.8072 3.0737 2.9273 TPSAM 2.4030 3.3713 2.9646 2.2350 3.3727 2.6760 2.5864 2.7484 2.6622 VAR 2.2895 2.8366 2.6048 2.6433 2.9575 2.8219 2.8330 2.8956 2.8574
RED ISA 2.0000 3.1477 2.4867 2.0000 3.0847 2.4001 2.7080 3.1181 2.9100 TPSAM 2.4034 4.1334 3.1090 2.3037 3.3148 2.6815 2.6103 2.7736 2.6978 VAR 2.1377 2.8039 2.5702 2.7123 2.9653 2.8486 2.8468 2.8915 2.8668
IR ISA 2.7900 3.1108 2.9897 2.6698 3.2953 2.8519 2.7243 2.9258 2.8098 TPSAM 2.5291 3.5359 3.0225 2.2541 3.1126 2.6419 2.5586 2.7335 2.6654 VAR 2.4414 3.0524 2.6650 2.7655 2.9073 2.8282 2.8185 2.8916 2.8543
NDVI ISA 2.7125 3.2932 2.9369 2.7926 3.0818 2.9388 2.7786 2.8805 2.8337 TPSAM 2.3548 3.5534 3.0033 2.7865 3.3183 2.9798 2.5465 2.7078 2.6412 VAR 2.3258 2.8896 2.6358 2.7984 3.0259 2.9087 2.7080 2.8862 2.8365 Table 4-3: Change of FD with spatial resolution; ex: sal (season 1, 250m by 250m subset)
SAL SUBSET SIZE METHOD BANDS S 250 500 750 GREE N ISA 0.0096 0.3148 0.0095 TPSAM 0.7841 0.7208 0.4353 VAR 0.8529 0.9832 0.8406
RED ISA 0.6018 0.1121 0.0022 TPSAM 0.7202 0.7326 0.5615 VAR 0.7957 0.8058 0.7373
IR ISA 0.9139 0.9982 0.6521 TPSAM 0.7009 0.7382 0.6847 VAR 0.8509 0.9998 0.7848
NDVI ISA 0.7359 0.8696 0.2768 TPSAM 0.7984 0.9936 0.1322 VAR 0.5034 0.0362 0.2536 Table 4-4: R-square values for sal forests
32 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
3.6000 ISA TPSAM 3.4000 VAR MEAN 3.2000 MEAN MEAN 3.0000
2.8000
2.6000 Fractal Dimension (FD) 2.4000
2.2000
(1)5.8m (2)15m (3)23.5m Spatial Resolution
Figure 4-4: Variation of range of FD with spatial resolution Sal (NDVI example)
Figure 4-4 shows the change in the range of FD with the change of spatial resolution. The top and the bottom bars in each representation indicates the maximum and minimum FD values for each method
Plantation: South of Haldwani with Gola and Bakra rivers as its eastern and western boundaries respectively, there is a vast extent of planted forests having moderate to small parcel sizes. Due to the small sizes of parcels, only subsets of 250 by 250 and 500 by 500 m could be generated containing more or less homogeneous patches. 13 such subsets were used to calculate fractal dimensions. Out of the methods, highest variability in terms of abrupt change in fractal dimensions was observed in case of TPSAM. Variogram methods as was in the case of Sal shows a decrease of FD from finer to coarser resolution in the 250m subset while a small fall and a rise in the coarsest resolution is observed in 500m subset. Isarithm method along with TPSAM shows variable results.
PLANTATION 250 SENSOR (SPATIAL RESOLUTION) SEASON 1 LISS 3 (23.5m) ASTER (15m) LISS 4 (5.8m) BANDS METHODS MIN MAX MEAN MIN MAX MEAN MIN MAX MEAN GREEN ISA 2.0000 2.9933 2.6222 2.0000 2.9969 2.5421 2.7228 3.0065 2.8671 TPSAM 2.2150 3.3896 2.3761 2.4096 2.8207 2.5191 2.2415 2.6272 2.3675 VAR 2.4516 2.9297 2.7481 2.7350 2.8951 2.8322 2.8364 2.9266 2.8935
RED ISA 2.0000 3.6610 2.7214 2.0000 3.6644 2.5231 2.5804 2.9783 2.7468 TPSAM 2.2269 3.2411 2.3835 2.4202 2.7402 2.5413 2.2655 2.6601 2.3997 VAR 2.1560 2.8895 2.7017 2.7759 2.9247 2.8632 2.8517 2.9249 2.8959
IR ISA 2.3056 3.0506 2.6875 2.0000 3.0764 2.6931 2.5355 2.8924 2.7277 TPSAM 2.2666 3.1645 2.4104 2.3858 2.6894 2.5199 2.2171 2.6587 2.3778 VAR 2.7114 2.9302 2.8191 2.7705 2.9077 2.8521 2.8211 2.9224 2.8781
NDVI ISA 2.4640 2.9769 2.6919 2.5380 3.1124 2.8190 2.4678 2.8817 2.7499 TPSAM 2.1999 3.2908 2.3499 2.3633 2.5764 2.4734 2.2611 2.6788 2.4023 VAR 2.5142 2.8867 2.7610 2.6698 2.9359 2.8379 2.8074 2.9248 2.8782 Table 4-5: Change of FD with spatial resolution; ex: plantation (season 1, 250m by 250m subset)
33 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
PLANTATION SUBSET SIZE BANDS METHODS 250 500 GREE N ISA 0.5231 0.9405 TPSAM 0.0026 0.6327 VAR 0.9919 0.0557
RED ISA 0.0108 0.6834 TPSAM 0.0088 0.5064 VAR 0.8720 0.2693
IR ISA 0.8513 0.5019 TPSAM 0.0478 0.5839 VAR 0.9953 0.1878
NDVI ISA 0.2075 0.9055 TPSAM 0.1784 0.1102 VAR 0.9684 0.0294 Table 4-6: R-square values for plantations
ISA 3.2000 TPSAM VAR 3.0000 MEAN MEAN MEAN 2.8000
2.6000
2.4000 Fractal Dimension (FD) Dimension Fractal
2.2000
(1)5.8m (2)15m (3)23.5m Spatial Resolution
Figure 4-5: Variation of range of FD with spatial resolution Plantations (NDVI example)
Mixed broad leaf: Mixed broad leaved forests, north of Haldwani and extending both east and west along the foothills of the Himalayas are taken for the study. The topography of the area becomes increasingly undulating as we go north and therefore demarcation of homogeneous forest patches for generating subsets was a difficult task. 10 patches of subset size 500m and 250m each was used for FD calculations. Variogram method showed a trend in line with the trend seen in other two vegetations assessed before, showing a fall in FD with an increase in spatial resolution. The two other methods gave inconsistent results both in 250 and 500m subsets. Isarithm method showed a fall–rise pattern in the green and red bands while an opposite was seen in the next two bands. TPSAM although showed a fall–rise pattern in all the bands of 250m subset but an opposite trend of rise–fall was seen in the 500m subsets.
34 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
MXD BRD LEAF 250 SENSOR (SPATIAL RESOLUTION) SEASON 1 LISS 3 (23.5m) ASTER (15m) LISS 4 (5.8m) BANDS METHODS MIN MAX MEAN MIN MAX MEAN MIN MAX MEAN GREEN ISA 2.4651 3.0547 2.7388 2.0000 2.8534 2.2567 2.5986 3.0781 2.7928 TPSAM 2.2278 3.6201 2.5465 2.3021 2.7073 2.5615 2.2646 2.6756 2.4116 VAR 2.5828 2.9073 2.7708 2.5282 2.9394 2.8062 2.8484 2.9011 2.8798
RED ISA 2.0000 3.3888 2.6206 2.0000 3.2546 2.6128 2.5847 3.0005 2.4529 TPSAM 2.2640 3.4926 2.5386 2.3705 2.9271 2.6253 2.3133 2.7008 2.8531 VAR 2.2991 2.9192 2.6422 2.4549 2.9378 2.8400 2.6920 2.9080 2.6741
IR ISA 2.4619 2.8191 2.6228 2.5870 3.0933 2.8139 2.4522 2.8477 2.6741 TPSAM 2.2338 3.2295 2.5340 2.3705 2.7594 2.5908 2.2977 2.6679 2.4526 VAR 2.6839 2.9350 2.8057 2.7339 2.9114 2.8533 2.8394 2.9016 2.8785
NDVI ISA 2.5114 3.0650 2.6842 2.7213 2.9260 2.8343 2.4060 2.8558 2.6597 TPSAM 2.1667 3.2404 2.4530 2.1198 2.8543 2.5134 2.2576 2.6620 2.4106 VAR 2.4713 2.8897 2.7890 2.7187 2.8785 2.8361 2.8475 2.9017 2.8736 Table 4-7: Change of FD with spatial resolution; ex: mixed broad leaf (season 1, 250m by 250m subset)
MIXED BROAD LEAVES SUBSET SIZE METHOD BANDS S 250 500 GREE N ISA 0.0084 0.0010 TPSAM 0.6676 0.3884 VAR 0.9605 0.8773
RED ISA 0.7018 0.1617 TPSAM 0.2470 0.5016 VAR 0.7963 0.8680
IR ISA 0.0671 0.0314 TPSAM 0.3433 0.4690 VAR 0.7963 0.7077
NDVI ISA 0.0167 0.0160 TPSAM 0.1688 0.1306 VAR 0.9957 0.6377 Table 4-8: R- square values for mixed broad leaf forests
35 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
3.2500 ISA TPSAM 3.0000 VAR MEAN MEAN MEAN 2.7500
2.5000
Fractal Dimension (FD) 2.2500
2.0000
(1)5.8m (2)15m (3)23.5m Spatial Resolution
Figure 4-6: Variation of range of FD with spatial resolution MBL (NDVI example)
Mountain vegetation: Beyond the foothill regions, the Lesser Himalayas starts. The mountainous region around Nainital and Bhowali were taken for investigation because of the dense forest found in these areas. The increasing complexity of the terrain with the increase in altitude hinders the site- selection for generation subsets of desired sizes. In this case only 10 subset size of 250 by 250m could be made for FD calculations. Baring the NDVI band, variogram method showed a decreasing trend from a higher spatial resolution to lower spatial resolution with a peak R2 value of 0.9865 in the red band. TPSAM showed identical trends in all the bands, but its R2 was too low to be considered.
MOUNTAIN VEG 250 SENSOR (SPATIAL RESOLUTION) SEASON 1 LISS 3 (23.5m) ASTER (15m) LISS 4 (5.8m) BANDS METHODS MIN MAX MEAN MIN MAX MEAN MIN MAX MEAN GREEN ISA 2.2435 3.2965 2.6973 2.0000 3.0397 2.6096 2.6474 2.7847 2.7238 TPSAM 2.2734 3.1855 2.5146 2.5045 2.7373 2.5985 2.2609 2.4999 2.3952 VAR 2.6609 2.9151 2.7736 2.7804 2.9184 2.8488 2.8660 2.9185 2.8881
RED ISA 2.2351 2.7470 2.4963 2.3798 3.2229 2.6696 2.6942 2.7230 2.7128 TPSAM 2.2670 3.1278 2.5665 2.5525 2.8483 2.6384 2.3104 2.5580 2.4392 VAR 2.7101 2.9007 2.7892 2.7240 2.9456 2.8353 2.8887 2.9222 2.9048
IR ISA 2.3138 2.7646 2.5807 2.5036 2.9212 2.7257 2.3608 2.8573 2.5998 TPSAM 2.3707 3.0397 2.5975 2.4825 2.7643 2.6099 2.3167 2.5506 2.4369 VAR 2.6293 3.0794 2.8170 2.8581 2.9565 2.8969 2.8191 2.9252 2.8850
NDVI ISA 2.3971 2.7444 2.5757 2.5296 3.0044 2.7112 2.4849 2.6754 2.5797 TPSAM 2.3263 3.5337 2.5205 2.3691 2.8955 2.5355 2.2278 2.3848 2.2991 VAR 2.6075 2.8642 2.7948 2.6878 2.9081 2.8293 2.3848 2.8909 2.7346 Table 4-9: Change of FD with spatial resolution; eg: mountain vegetation (season 1, 250m by 250m subset)
36 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
MOUNTAIN VEG. SUBSET SIZE METHOD BANDS S 250 GREE N ISA 0.0490 TPSAM 0.3416 VAR 0.9682
RED ISA 0.8925 TPSAM 0.3981 VAR 0.9865
IR ISA 0.0147 TPSAM 0.6925 VAR 0.6230
NDVI ISA 0.0007 TPSAM 0.6995 VAR 0.3945 Table 4-10: R- square values for mountain vegetations
3.6000 ISA TPSAM 3.4000 VAR MEAN 3.2000 MEAN MEAN 3.0000
2.8000
2.6000 Fractal Dimension (FD) 2.4000
2.2000
(1)5.8m (2)15m (3)23.5m Spatial Resolution
Figure 4-7: Variation of range of FD with spatial resolution, MV (NDVI example)
Results from this section show that fractal dimension change with the change in the spatial resolution of the image, which is in violation of the self-similarity property underlying the fractal model i.e. the pattern of the spatial phenomenon (forests in this case) remains unchanged throughout all resolutions. This can be taken positively because when viewed at a coarser scale (LISS3 in this study), a bigger area or a few number of pixels would be observed in a particular subset making it more homogeneous and less complex with smoother texture. As the scale or resolution increases, more information is gained and the complexity of the image increases. This can be explained by the example of a forest. At coarse resolution only forest patches are visible, which seems more or less homogeneous. Zooming into a finer resolution, one can distinguish between groups of trees and even discriminate single trees if one shifts to more finer resolution. In this case there would be a greater variation in the image and thus high textural heterogeneity. So it can be said that the information of a particular geographic phenomenon changes with resolution. On the contrary, it can be said that fractal dimension decreases
37 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
with the decrease in spatial resolution as decrease in heterogeneity would affect the fractal dimension of an image and lead to the decrease in the dimension. But it should be kept in mind that it is only applicable to images where only a particular phenomenon is analysed, as is in this study. It is been observed by (Emerson et al., 1999) that the fractal dimension of different land–cover types increases, decreases or remains more or less same with the change in spatial resolution. They found that complexity of agricultural land grew more complex, forest patches grew smoother and urban areas remained the same with the increase in pixel size from 10m to 80m. In this study only one class of vegetation was taken at a time and the area of the subset being fixed. So it is more likely for fractal dimension to decrease with the decrease in spatial resolution. Performing analysis in this direction, it is seen that only variogram method shows a decreasing trend with the decrease in spatial resolution, mostly in the 250 by 250m subsets. This indicates that variogram method is the most suitable fractal model to differentiate the different vegetation type found in this study area, in the above mentioned subset size. This conclusion was drawn after analysing the trend of the values given by different bands and NDVI images; moreover Variogram method has the least variation of maximum and minimum FD as seen in the plots. It is evident from the tables, variogram methods scores above all in R2 values in almost all the vegetation types. It can also be seen that other methods give high R2 values in few scattered incidents but they were not taken into account as they show different trends from those discussed above. Outcome of the experiment indicate that variogram method shows little variation in the spatial resolution of 23.5m and hence it can be concluded that the combination of variogram method along with the above spatial resolution is the best when studying vegetation in this area.
4.3. Change of FD with seasons Vegetation reacts to seasonal variation more than all other natural phenomenon. Therefore studying the change in vegetation characteristics due to seasonal variation is an important aspect in any study related to forestry. The present area falls in a region where change due to seasons is very prominent. As one goes from the plains to the mountains the temperature decreases and remains cold almost throughout the year. Temperature plays an important role in the type of vegetations that are found in an area. Trees which are found on the mountains are mostly evergreen with long leaf longevity (Singh and Singh, 1992). A substantial part of the study area falls in the western Himalayan region where different forest region can be found. Different forest or vegetation types which are demarcated for analysis fall under different climatic region and hence show different response to seasonal changes. To examine whether the change of seasons has any effect on the fractal dimension of the vegetation, data of two seasons of Aster and LISS III sensors were analysed for all the vegetations in the 250 by 250m area subsets.
Sal: Sal trees dominated by Shorea robusta are found in the Sub-montane or Sub-tropical Region. It is semi-evergreen in habit with a short leafless period of upto a fortnight, usually at the beginning of summer season.
The plots of seasonal Aster images for all images and NDVI show that there is an increase in fractal dimension for the NDVI images from March to October for all the methods having higher fractal dimension values than all other bands. IR bands show a decrease in value from March to October. The remaining two bands show inconsistent behaviour in all the methods. The fractal images for the LISS III data show a reverse trend to that of Aster images. Here it is seen that the green and IR bands show
38 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
an increase in FD values for all the methods while, except for variogram method, NDVI showed a decrease in FD value. Red band gives erratic results.
3.1000 GREEN IR 3.0000 NDVI RED 2.9000 MEAN MEAN 2.8000 MEAN MEAN 2.7000
2.6000 Fractal dimension (FD) 2.5000
2.4000
(1) SEASON 1 (2) SEASON 2 SEASONS
Figure 4-8: Variation of FD with the change in season in Sal (Results of Variogram method as seen with aster image of 250m by 250m subset)
SAL 250 Change of FD with seasons SENSOR LISS 3 (23.5m) ASTER (15m) BANDS METHODS SEASON 1 SEASON 2 SEASON 1 SEASON 2 GREEN ISA 2.8683 2.9111 2.3785 2.5443 TPSAM 2.9646 3.0375 2.6760 2.6678 VAR 2.6048 2.6576 2.8219 2.7827
RED ISA 2.4867 2.9265 2.4001 2.4529 TPSAM 3.1090 3.1066 2.6815 2.7213 VAR 2.5702 2.5947 2.8486 2.8055
IR ISA 2.9897 3.0489 2.8519 2.7661 TPSAM 3.0225 3.0404 2.6419 2.6305 VAR 2.6650 2.7142 2.8282 2.7989
NDVI ISA 2.9369 2.8594 2.9388 2.9758 TPSAM 3.0033 2.8726 2.9798 3.1335 VAR 2.6358 2.8626 2.9087 2.9396 Table 4-11: Change of FD with Seasons with different methods; Sal (250m by 250m subsets)
Plantations: Planted forest or plantations are mainly grown in the plains under the supervision of the Forest department. Small to moderate sized parcels of pure as well as mixed varieties of species are grown. Teak, shisham, poplar and sal are grown in these plantations. These area, with mixed species having different characters are bound to have different response to the change in season, at different
39 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
resolutions. IR bands in the Aster images for all the methods shows an increase in fractal dimension values except for TPSAM where it has a decrease of a magnitude in the range of 0.001, which is too low to be considered. NDVI shows a minimal increase in the values for all the methods. The same trend is seen in the LISS III images, while the IR and NDVI gave identical results for all the methods, red and green bands were the most inconsistent. Since the area subsets were fixed for all the methods and resolution, the change in trend in NDVI and IR images should not vary considerably with the change in pixel size or resolution. The only change can be in the values of FD as is evident from the plots shown below.
2.9500 GREEN IR 2.9000 NDVI RED MEAN 2.8500 MEAN MEAN 2.8000 MEAN
2.7500 Fractal Dimension (FD) 2.7000
2.6500
(1) SEASON 1 (2) SEASON 2 SEASONS
Figure 4-9: Variation of FD with the change in season in plantation (Results of Variogram method as seen with aster image of 250m by 250m subset)
PLANTN 250 Change of FD with seasons SENSOR LISS 3 (23.5m) ASTER (15m) BANDS METHODS SEASON 1 SEASON 2 SEASON 1 SEASON 2 GREEN ISA 2.6222 2.7670 2.5421 2.4045 TPSAM 2.3761 2.3970 2.5191 2.5455 VAR 2.7481 2.7977 2.8322 2.8348
RED ISA 2.7214 2.5847 2.5231 2.1259 TPSAM 2.3835 2.4169 2.5413 2.5404 VAR 2.7017 2.8112 2.8632 2.8165
IR ISA 2.6875 2.7026 2.6931 2.8245 TPSAM 2.4104 2.4274 2.5199 2.5157 VAR 2.8191 2.8249 2.8521 2.8614
NDVI ISA 2.6919 2.7489 2.8190 2.8628 TPSAM 2.3499 2.3619 2.4734 2.4728 VAR 2.7610 2.7900 2.8379 2.8367 Table 4-12: Change of FD with Seasons with different methods; plantations (250m by 250m subsets)
40 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
Mixed broad leaf: As discussed in the previous section, these forests are found in the lower Himalayan foothills, found north of Haldwani. These forests are fairly dense and a number of dominant evergreen and deciduous species like sal, khair, shisham and sometimes even chir–pine occur. Heavy growths of climber are also seen in these forests. Different method show different results and response in the Aster images, Variogram method shows an increase in FD value from March to October images of NDVI and IR bands. While isarithm method shows an increase in the values of FD for NDVI and a decrease of FD for IR values, TPSAM shows results opposite to that of isarithm method.
3.0000 GREEN IR 2.9000 NDVI RED MEAN 2.8000 MEAN MEAN 2.7000 MEAN
2.6000 Fractal Dimension (FD) 2.5000
2.4000
(1) SEASON 1 (2) SEASON 2 SEASONS
Figure 4-10: Variation of FD with the change in season in MBL (Results of Variogram method as seen with aster image of 250m by 250m subset)
MBL 250 Change of FD with seasons SENSOR LISS 3 (23.5m) ASTER (15m) BANDS METHODS SEASON 1 SEASON 2 SEASON 1 SEASON 2 GREEN ISA 2.7388 2.7556 2.2567 2.3441 TPSAM 2.5465 2.5555 2.5615 2.5609 VAR 2.7708 2.7783 2.8062 2.8310
RED ISA 2.6206 2.6767 2.6128 2.2300 TPSAM 2.5386 2.6252 2.6253 2.6028 VAR 2.6422 2.7756 2.8400 2.8592
IR ISA 2.6228 2.7392 2.8139 2.7101 TPSAM 2.5340 2.5516 2.5908 2.5877 VAR 2.8057 2.8445 2.8533 2.8810
NDVI ISA 2.6842 2.7248 2.8343 2.9047 TPSAM 2.4530 2.4856 2.5134 2.4902 VAR 2.7890 2.8337 2.8361 2.8722 Table 4-13: Change of FD with Seasons with different methods; mixed broad leaf (250m by 250m subsets)
41 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
Mountain vegetation: Mountain vegetation in this study is referred to those vegetations which fall in the transition of Sub-montane and Montane regions. The height of this vegetation is little below 1500 metres to above 2000 metres. The lower part is dominated mainly by pine trees while the upper portion by oak trees. The floor of these forests is covered by a good growth of perennial and annual grasses. A review of all the methods shows that NDVI images show an increase in FD values with change in season from March to October, along with a decrease in the IR band for Aster images. The opposite trend is seen in the LISS III images where NDVI decreases and IR shows an increase.
3.0000 GREEN IR NDVI RED 2.9000 MEAN MEAN MEAN MEAN 2.8000 Fractal Dimension (FD) 2.7000
(1) SEASON 1 (2) SEASON 2 SEASONS
Figure 4-11: Variation of FD with the change in season in MV (Results of Variogram method as seen with aster image of 250m by 250m subset)
MV 250 Change of FD with seasons SENSOR LISS 3 (23.5m) ASTER (15m) BANDS METHODS SEASON 1 SEASON 2 SEASON 1 SEASON 2 GREEN ISA 2.6973 2.8321 2.6096 2.6079 TPSAM 2.5146 2.5414 2.5985 2.5691 VAR 2.7736 2.7744 2.8488 2.8448
RED ISA 2.4963 2.8654 2.6696 2.5081 TPSAM 2.5665 2.6185 2.6384 2.5994 VAR 2.7892 2.7973 2.8353 2.8467
IR ISA 2.5807 2.6672 2.7257 2.6843 TPSAM 2.5975 2.6427 2.6099 2.5792 VAR 2.8170 2.8387 2.8969 2.8680
NDVI ISA 2.5757 2.6275 2.7112 2.7274 TPSAM 2.5205 2.5134 2.5355 2.5331 VAR 2.7948 2.7529 2.8293 2.8569 Table 4-14: Change of FD with Seasons with different methods; MV (250m by 250m subsets)
42 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
From the above analysis it is seen that in almost all the methods, there is a positive increase in FD values for NDVI images. Most of the vegetation types found in the area are evergreen and semi- evergreen with few deciduous varieties. So there is no season where trees are bare or with minimal leaves for a long period. If there is leaf flushing, then it takes place before summer for a short period. October and November are the months where plants have maximum canopy cover to utilize the sunlight just after the Monsoons. One is expected to find heterogeneity in both IR and NDVI values because of undergrowth, climbers and other secondary vegetations in different stages of growth. On the contrary, months of January and March have extremely cold climate in the upper regions of the study area and presence of any undergrowth can be ruled out. The result obtained from fractal analysis is in tune with this and hence it can be concluded that fractal dimension changes with the change in season depending upon the phenology of the concerned vegetation. The results depends mostly on the factor explained but the method adopted and experiment induced factors cannot be ruled out. If a certain forest contains trees with varying age then fractal dimension calculated for different seasons will show more heterogeneity than those with pure strands with similar ages. Similarly a mixed forest with two or more dominant species will have higher fractal dimension in contrast to those with one prominent species. The results of fractal analysis can give insight on the health of the vegetation and seasonal information between two images. Information about the phenological characteristics of the vegetation type is necessary to come to a conclusion about the image seasons.
4.4. Change of FD with altitude: To study the effect of altitude on fractal dimension, the area subsets of all the vegetations except the plantation are taken. The reason for not selecting plantations is that the elevation difference of the subsets is not conspicuous and hence makes little or no meaning in this analysis. Other vegetation especially, mountain vegetation show a good change in elevation value. For comparing elevation with fractal dimension, average elevation values of the subsets were derived from ASTER Digital Elevation Model of 30m resolution. Mean elevation of each subset was taken. Mean altitude of each patch (as shown in figures 4-9 to 4-11) of the individual vegetation are plotted against fractal dimension and analysed. NDVI and IR bands were analysed for this purpose as these are the bands found to be most optimum for the purpose of our study.
The subsets of sal vegetation in the study area range from a height of 273m to a maximum of 922m at the foothills, MBL have an elevation range from 621m to 1257m and 1338m to 2190m for high altitude MV. A closer look at the plots reveals that though all of the bands or methods show a complicated result but they do somehow are able to give a trend. As seen from the figure 4-9 below, the November plot is higher than the January plot, with a big dip around 474m, because of phenology reasons discussed before. The overall trend in both the plots seems to increase with the increase in altitude with a slump in the last patch. This may be due to the reason that beyond a particular elevation, Sal becomes less dense and scarce. The same trend was seen for the other two vegetation types, showing a subtle increase in FD with the increase in elevation. The variation within each plot showing occasional peaks and dips may not be only due to the effect of vegetation and elevation. The effect of the underlying factors like the rugged topography giving rise to spatial irregularities of the geomorphological features play an important role in determining the FD of the particular phenomenon studied. It is also understood that the textural homogeneity of vegetation will change as one goes from one climatic regime to another.
43 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
The results were not able to give a definite answer or relation between altitude and fractal dimension, but they should not be underscored as a subtle relation was observed. The elevations as taken for this experiment were discreet values for each of the subsets and were not continuous; hence the exact relation of FD with the increase or decrease of altitude could not be ascertained fully. The results from this experiment are in acceptance with previous studies as given in (Xia and Clarke, 1997) which states that the trend of FD varied with landform characteristics of different geographic area. Some showed a trend of increasing FD with elevation while others showed an opposite trend. Yet others displayed more complicated patterns. Similar complicated patterns are also seen in this case. The important factors that can affect the relation of FD with altitude may be the characteristics of landform which include the major rock types, geological structure, climate at varying altitude and the stage of landform evaluation. This holds true as the study area falls in a region which is tectonically active consisting of young fold mountains, which lead to a topography which is irregular and changes abruptly with change in altitude. So it can be concluded that when the relationship between altitude and fractal dimension is analysed, the characteristics of the underlying topography, geological factors and climate should be taken into consideration as this is beyond the scope of this study.
3.0000 2.9000 2.8000 2.7000
FD 2.6000 2.5000 NDVI_LISS3_JAN 2.4000 NDVI_LISS3_NO 2.3000
) ) m m 2m) 2m) 73 47m) 0 74m) 01 86m) 3 2 3 4 5 5 ( ( ( ( 1 2 (294m) 3 4 (4 5 ( 6 7 (510m) 8 9 (6 10 (922m) PATCHES WITH ALTITUDE (m) Figure 4-12: Effect of change of FD with Altitude, Sal LISS III
3.0000
2.9000
2.8000
2.7000
FD 2.6000
2.5000 NDV I_JA N 2.4000 NDV I_NOV 2.3000
) ) ) m 1m) 6 8m) 2 9 82 872m 958m (6 ( ( (8 ( (965m) 1257m) 1 2 (707m) 3 4 (828m) 5 6 7 (929m) 8 9 ( 10 PATCHES WITH ALTITUDE (m) Figure 4-13: Effect of Change of FD with Altitude, MBL LISS III
44 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
3.0000
2.9000
2.8000
2.7000
FD 2.6000
2.5000 NDV I_JA N 2.4000 NDV I_NOV 2.3000
) ) ) m) m m m) m 6 (2190m) 1 (1338m)2 (1388m)3 (139 4 (1494 5 (1661 6 (1747m)7 (1856m) 8 (1897 9 (1961 10 PATCHES WITH ALTITUDE (m) Figure 4-14: Effect of Change of FD with Altitude, MV LISS III
4.5. Comparison: The results obtained from all the investigation from Haldwani were compared with that of Dehradun area. Since only one dominant type of vegetation, sal, is abundant in this area, other vegetation type could not be verified. Same procedure like that of Haldwani is followed in this area. The comparison is aimed to see whether the results obtained in the study area are locally applicable or can be applied to other region also. In this section all the results obtained in the experiments above are compared with the results obtained by the same procedure for the Dehradun data
4.5.1. Optimal band selection As all the vegetation types are not found in Dehradun, only Sal is chosen for comparison. The graphs of local approach and the tabular R2 values of global approach are compared side by side as given below in Figure 4-15, 4-16 and Table 4-15. Since we have chosen NDVI and IR bands as the possible bands that would help in investigating and differentiating different vegetation types, the same bands from Dehradun are selected for validation.
IR_DDN_LISS3 8.00 IR_HALD_LISS3 7.00 6.00 5.00 4.00
% PXLS 3.00 2.00 1.00 0.00 2.50 2.60 2.70 2.80 2.90 3.00 3.10 FD
Figure 4-15: Comparison of IR plots for local fractal approach, Haldwani and Dehradun.
45 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
9.00 NDVI_DDN_LISS3 8.00 NDVI_HALD_LISS3 7.00 6.00 5.00 4.00 % PXLS 3.00 2.00 1.00 0.00 2.50 2.60 2.70 2.80 2.90 3.00 3.10
FD Figure 4-16: Comparison of NDVI plots for local fractal approach, Haldwani and Dehradun.
As evident from the above graphs local FD curve of Dehradun and Haldwani are more or less similar and thus they indicate that this vegetation from two different places can be recognised effectively through local fractal approach. Due to the inability to compare other vegetations, the results could not be verified for them. The results confirm that NDVI and IR bands are suitable for differentiating vegetation types. The table below shows the R2 values obtained by Global fractal approach of Sal from the two areas. It is observed here yet again that NDVI and IR bands dominate. It can be confidently summarised that these two bands are the most suitable for differentiating vegetation types. It is also to be noted that though these two bands are comparatively, the most optimal bands, the importance of other bands for discrimination cannot be ruled out.
SENSOR ASTER SEASON 1 ASTER SEASON 2 SUBSET AREA METHOD ISA TPSA VAR ISA TPSA VAR 250m HALD BANDS NDVI NDVI NDVI NDVI IR IR R-Square 0.9662 0.9192 0.9595 0.9785 0.9318 0.9414
DDN BANDS NDVI NDVI IR GREEN NDVI IR R-Square 0.9287 0.9591 0.8972 0.8894 0.9753 0.9562
500m HALD BANDS NDVI NDVI NDVI NDVI NDVI GREEN R-Square 0.9270 0.9109 0.9649 0.9566 0.9333 0.9734
DDN BANDS IR NDVI NDVI NDVI NDVI NDVI R-Square 0.9433 0.9805 0.9127 0.9769 0.9900 0.8706
750m HALD BANDS NDVI NDVI IR NDVI NDVI IR R-Square 0.9856 0.9294 0.9375 0.9745 0.9529 0.8573
DDN BANDS IR NDVI IR GREEN IR NDVI R-Square 0.9057 0.9158 0.9469 0.9824 0.9505 0.9777 Table 4-15: Optimum bands of Dehradun (DDN) and Haldwani (HALD); (Aster)
46 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
4.5.2. Fractal dimension and spatial resolution: In the previous section, it was discussed that fractal dimension should decrease with the increase in coarseness of the spatial resolution of the data. So in this study the fractal dimension is expected to decrease from LISS IV to Aster and finally to LISS III. Results in the previous section showed that variogram method gave the most appropriate results with R2 reaching a maxima of 0.8529 in the green band of the area subset 250 by 250 m. In the previous sections, it was discussed that the above area subset size is optimal for studying vegetation types in the study area. To cross check the results and assumption the same methodology was adapted for the Dehradun datasets and compared. The results of the comparison is shown in the graphs and tabulated below. It is seen that apart from 250m subset all other subsets show trends which are not in accordance with the reasoning cited above. This also confirms that for this study area the 250m subset is optimum and can be used in further studies.
3.2000 ISA TPSAM 3.0000 VAR MEAN MEAN MEAN 2.8000
2.6000
Fractal Dimension (FD) Dimension Fractal 2.4000
2.2000
(1)5.8m (2)15m (3)23.5m Spatial Resolution
Figure 4-17 : Plot of variation of FD with spatial resolution, DDN
SUBSET SIZE SAL 250 500 750 BANDS METHODS DDN HALD DDN HALD DDN HALD GREEN ISA 0.0096 0.0001 0.3148 0.2776 0.0095 0.0000 TPSAM 0.7841 0.9274 0.7208 0.8175 0.4353 0.9086 VAR 0.8529 0.9895 0.9832 0.1734 0.8406 0.1203
RED ISA 0.6018 0.0584 0.1121 0.2757 0.0022 0.0140 TPSAM 0.7202 0.7740 0.7326 0.8174 0.5615 0.9455 VAR 0.7957 0.9531 0.8058 0.0003 0.7373 0.0377
IR ISA 0.9139 0.5738 0.9982 0.6745 0.6521 0.2667 TPSAM 0.7009 0.8963 0.7382 0.8393 0.6847 0.9919 VAR 0.8509 0.9780 0.9998 0.0014 0.7848 0.0523
NDVI ISA 0.7359 0.7405 0.8696 0.9978 0.2768 0.7616 TPSAM 0.7984 0.6921 0.9936 0.9529 0.1322 0.9757 VAR 0.5034 0.9830 0.0362 0.2815 0.2536 0.0571 Table 4-16: Global R- square values of Dehradun (DDN) and Haldwani (HALD); (Aster)
47 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
4.5.3. Fractal dimension and change in season: Fractal dimension is seen to change with the change in season for the vegetation in Haldwani. Every band was seen to show a variation, in tune with other bands or had its unique trend. This change was attributed to the phenological character of the vegetation which tends to have different influence on the spectral bands as well as the subset size. However comparing the results to that of Dehradun it was seen that though some bands showed trends similar to that of Haldwani, they were not always identical. This can be explained on the fact that though broadly they are called sal forests, the species that is found in these areas may differ or may have different percentage of each species rendering them different from one another. This is true because the sal forests found in the Dun valley have Adina cordifolia and Shorea robusta, as the two main species, but in the hills of Ramnagar–Haldwani area have Adina cordifolia as the dominant sal species with Shorea robusta as the sixth important (Negi, 2000).
3.0000 GREEN IR 2.8000 NDVI RED MEAN MEAN 2.6000 MEAN MEAN
2.4000
Fractal Dimension (FD) Dimension Fractal 2.2000
2.0000
(1) SEASON 1 (2) SEASON 2 SEASONS
Figure 4-18: Plot of change of FD with the variation of spectral bands and season, DDN
SAL 250 Change of FD with seasons SENSOR LISS 3 (23.5m) ASTER (15m) BANDS METHODS SEASON 1 SEASON 2 SEASON 1 SEASON 2 GREEN ISA 2.8144 2.8158 2.4146 2.6191 TPSAM 2.7438 2.7746 2.6111 2.6158 VAR 2.5558 2.5429 2.6402 2.7243
RED ISA 2.8990 2.8118 2.5383 2.7103 TPSAM 2.8326 2.8224 2.6114 2.6726 VAR 2.5523 2.4452 2.7003 2.7133
IR ISA 2.9429 2.8642 2.6506 2.6812 TPSAM 2.7448 2.8609 2.6061 2.5610 VAR 2.6166 2.6046 2.6687 2.7028
NDVI ISA 2.7553 2.7859 2.7556 2.8592 TPSAM 2.7468 2.8226 2.7624 3.0043 VAR 2.7667 2.5432 2.7479 2.8375 Table 4-17: Change of FD with Season; Dehradun Sal ( 250m by 250m subset)
48 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
The above table 4-17 shows the change in the value FD with the change in season that was observed in the Dehradun area. Table 4-11 shows the similar relation in the Haldwani area.
4.5.4. Fractal dimension and altitude The relationship of FD with altitude gave a hint of a slight relationship but could not be validated or crosschecked with Dehradun as the change in elevation of Sal forest found here did not have a marked elevation gradient and so comparison was meaningless.
This study produced some defining results which can be further used to investigate vegetation types found in the area. Variogram method used in the spatial resolution of 23.5m can help in differentiating the vegetation types found if used in NDVI and IR images.
49 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
5. Conclusions and recommendations
This chapter gives the details of the conclusions arrived after a thorough examination of the utility of the three fractal models in discriminating different vegetation types found in the area of interest. It attempts to evaluate the different relationships that were proposed for the study and their effectiveness. The chapter is comes to an end with the limitation of the research and followed by recommendation for further study in this topic
5.1. Conclusions The main objective of the study was to compare various fractal models for analysing the vegetation types found in the study area at different resolutions, with the change in season and altitude. Many variables may have their influence on the calculation of FD, like – type of vegetation, spatial and spectral resolution of satellite sensor, season, altitude and different computational methods. Fractal dimension calculated from different methods were checked for the relation they may hold these variables. It is beyond the scope of this study as well as Fractal geometry to differentiate vegetation types only on the basis of FD. As such FD value is not an index like NDVI, it gives an indication of the textural heterogeneity/homogeneity, and it cannot differentiate species type as such.
The variation in the values of FD with the vegetation type can be attributed to the different morphological and phenological characters of the different vegetation types and corresponding differences in spectral response. FD showed a slight increase with the increase in altitude, but it is evident that it depends on the character of the vegetation, the climatic regime and altitude. The response of fractal dimension with the change in altitude showed some subtle trend, but could not be properly delineated as it is not only the change in elevation which causes the change in fractal dimension but the underlying topography, because of the local geological conditions, also plays an important role. Along with this, experimental limitations also had their influence. This finding about the effect of topography can be a basis for concluding that for understanding the relationships between FD and the concerned variables, a thorough knowledge of the regional geology is needed. Relation of fractal dimension with other variables used in the study does show some trend albeit with some limitations but can be used in investigations pertaining to studies related to them. The results presented here shows promise, further research is required to utilise them for studying image complexity. Texture, as seen here, is observed to be scale dependent and so the size of the moving window, in the local approach, along with the spatial resolution of the remote sensing data plays an important role in determining the features that are highlighted in the methods used.
The following research questions were answered to meet the objectives of the present study:
Which fractal model is best suited to differentiate the vegetation types in the area? An approach in this study was taken on the assumption that remote sensing images are not strictly fractals and that their dimension would change from one spatial resolution to another. It is assumed that fractal dimension would decrease with the increase in coarseness of spatial resolution as briefed in section 4.2. It was observed that the Variogram method gives the most appropriate results, scoring well both in statistical results as well as visual interpretation of the graphs derived using local approach. The variogram method gives the maximum R2 values in almost all the experiments concerned. It is
50 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
reported that variogram method is more reliable than isarithm method and can be effectively used for both regular and irregular data (Sun et al., 2006). Taking this into consideration variogram method for calculating FD can be said to be the better method that can be used in the conditions of the study area.
How does fractal dimension change with spatial resolution and spectral bands for different vegetations with the change in season and altitude? Spectral characteristics of vegetation change with season, due to their phenology, and with different species because of their morphological character. The change in spectral reflectance has a direct impact on the fractal dimension and it depends on the response of the concerned vegetation to a particular spectral band. Variogram method shows a definite trend of decreasing FD with the coarseness of spatial resolution, but for other methods it was somewhat unpredictable. The variation of FD with spectral resolution is evident as the results show a difference in peak growth season to that of lean seasons. In the peak season the period of growth is directly related to the health of the vegetation and hence shows a rise in NDVI and IR values. Altitude change as discussed earlier has an effect on FD but it requires more information and care in understanding the relationship between them.
Can we differentiate various types of vegetation found in the study area with the help of fractal dimensions obtained? Fractal dimension as calculated from the local approach have shown its usefulness in differentiating the different vegetation types found in the area. This can be achieved by observing the degree of separability of the curves of different vegetations. The degree of separability is indicated by the amount of overlap between the curves. The results from global approach should also be taken into consideration as discussed in Section 4.1. In this case a thorough investigation is required for the distinction of the optimal band that has the highest degree of separability. The results from the research done, show that the combination of both local and global approaches, is more effective in discriminating the vegetation types in the area than a single approach taken at a time. This requires utmost care in interpretation so that one does not come to wrong conclusion.
5.2. Limitations of the study The study dealt with different fractal models and their response to the different types of vegetation found in the area. The area was suitable for the study because of its diversity in vegetation and change of altitude in a very short span of distance. But the main limitation of the study was in selecting subset of suitable size. Uniform subset size was not possible for all the vegetations used because either they have area less than that of the subsets or were in the complex topography of the mountains where forests are mainly on the hill-slopes and their area in plan view in the image were less than the actual area of the subsets. The two approaches, local and global, taken for the study has limitation in the criteria of the subset size. Careful consideration of all the factors is required for selecting the subset size. Ground truth collection was done during the study but samples had to be taken mostly near the forest edge as the forests were very dense and inaccessible. Some of the points taken were very high and going beyond that altitude was not possible. For this reason some of the vegetation that are found high up could not be included in this study. In the comparison part, only Sal forest characters were used, as the other vegetation types are not found in required amount in Dehradun area. Data from other area where enough amount of vegetation exists were not available and it would not have been cost effective to procure them from different sources. Also, other spatial statistics, such as local variance,
51 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
Moran’s I, could not be used be used due to lack of time and scope. The uncertainties related with the methods used, were not taken into consideration.
5.3. Future recommendations
• Future studies in an area where the vegetation are more homogeneous, well distributed and with better aerial extent should be carried out for better understanding. • To better understand the relation between fractal dimension and change in altitude, the study should be done in an area where there is a gradual and continuous rise in height. • Other spectral bands present in the thermal range could also be considered in the future to check their effectiveness. • Use of spatial statistics along with fractal dimension can be used in future studies to characterise the spatial complexity of the images and data mining. • Future research in this area should consider the underlying factors related to topography, geology, human disturbance and other local factors which have an effect on the calculation of fractal dimension of images. .
52 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
6. References
2005-06. Uttaranchal Forest Statistics. Forest Department, Uttaranchal. Bisoi, A.K., and j. Mishra. 2001. On Calculation of Fractal Dimension of Images. Pattern Recognition Letters 22:631-637. Cihlar, H. 2000. Land cover mapping of large areas from satellites: status and research priorities. International Journal of Remote Sensing 21:1093-1114. Emerson, C.W., N. Lam, and D.A. Quattrochi. 1999. Multi-Scale Fractal Analysis of Image Textureand Pattern. Photogrammetric Engineering & Remote Sensing 65:51-61. Emerson, C.W., N. Lam, and D.A. Quattrochi. 2005. A comparison of local variance, fractal dimension, and Moran's I as aids to multispectral image classification. International Journal of Remote Sensing 26:1575-1588. Goodchild, M.F. 1980. Fractals and the Accuracy of Geographical Measures. Journal of the International Association For Mathematical Geology 12:85-98. Jaggi, S., D.A. Quattrochi, and N. Lam. 1993. Implementation and operation of three fractal measurement algorithms for analysis of remote-sensing data. Computer and Geosciences 19:745-767. Jenson, J.R. 1996. Introductory Digital Image processing Prentice Hall Inc. G. G. Wilkinson, et al. (ed.) 1994. Fractals in Geosciences and Remote Sensing, Proceedings of A Joint JRC/EARSeL Expert Meeting Ispra, Itally. European Commission, Luxembourg. Jong, S.D., and P.A. Burrough. 1995. A Fractal Approach to the Classification of Mediterranean Vegetation Types in Remotely Sensed Images. Photogrammetric Engineering & Remote Sensing 61:1041-1053. Klonowski, W. 2000. Signal and Image Analysis Using Chaos Theory and Fractal Geometry. Lab. of Biosignal Analysis Fundamentals, Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences, Warsaw. Kolibal, J., and J. Monde. 1998. Fractal image error analysis. Computer and Geosciences 24:785-795. Kulkarni, A. 2004. Evaluation of the impacts of hurricane Hugo on the land cover of Francis Marion National Forest, South Carolina using remote sensing, Louisiana State University. Kumar, G. 2005. Geology of Uttar Pradesh and Uttaranchal Geological Society of India, Bangalore. Lam, D.N., H.-l. Qiu, D.A. Quattrochi, and C.W. Emerson. 2002. An Evaluation of Fractal Methods for Characterizing Image Complexity. Cartography and Geogreaphic Information Science 29:25-35. Lam, N. 1990. Description and Measurement of Landsat TM Images Using Fractals. Photogrammetric Engineering & Remote Sensing 56:187-195. Leica Geosystems. 2002. ERDAS Imagine Version 8.6, Atlanta, Georgia, USA. Lovejoy, S., D. Schertzer, Y. Tessier, and H. Gaonac'h. 2001. Multifractals and resolution-independent remote sensing algorithms: the example of ocean colour. International Journal of Remote Sensing 22:1191-1234. Mandelbrot, B.B. 1982. The Fractal Geometry of Nature W.H.Freeman & Company, New York. Negi, S.S. 2000. Himalayan Forests and Forestry. Second ed. Indus Publishing Company, New Delhi. Parrinello, T., and R.A. Vaughan. 2002. Multifractal analysis and feature extraction in satellite imagery. International Journal of Remote Sensing 23:1799-1825. Qiu, H.-l., N. Lam, D.A. Quattrochi, and J.A. Gamon. 1999. Fractal Characterization of Hyperspectral Imagery. Photogrammetric Engineering & Remote Sensing 65:63-71. Quattrochi, D.A., N.S.-N. Lam, H.-l. Qiu, and W. Zhao. 1997. Scale in Remote Sensing and GIS. Read, J.M., and N. Lam. 2002. Spatial methods for characterising land cover and detecting land-cover changes for the tropics. International Journal of Remote Sensing 23:2457-2474. Roach, D., and K.B. Fung. 1994. Fractal-Based Textural Descriptors for Remotely Sensed Forestry Data. Canadian Journal of Remote Sensing 20:59-70. RSI Inc. 2006. ENVI Version 4.3, Boulder, USA. Singh, J.S., and S.P. Singh. 1992. Forests of Himalaya Gyanodaya Prakashan, Nainital.
53 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
Sun, W., G. Xu, P. Gong, and S. Liang. 2006. Fractal analysis of remotely sensed images: A review of methods and applications. International Journal of Remote Sensing 27:4963-4990. Tate, N.J. 1998. Estimating the Fractal Dimension of Synthetic Topographic Surfaces. Computer and Geosciences 24:325-334. Weng, Q. 2003. Fractal Analysis of Satellite-Detected Urban Heat Island Effect. Photogrammetric Engineering & Remote Sensing 69:555-566. Xia, Z.-G., and K.C. Clarke. 1997. Scaling in Remote Sensing and GIS. Zhou, G., and N. Lam. 2005. A comparision of fractal dimension estimators based on multiple surface generation algorithms. Computer and Geosciences 31:1260-1269.
54 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
Appendix – 1
ICAMS interface and fractal image
Interface for local fractal approach
Interface for global fractal approach
Fractal image generation through local approach
55 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
Input BSQ image
Output fractal image
56 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
Appendix – 2
Plots of change of FD with Spatial resolution and Spectral bands: ( Aster images, calculated in 250mby 250m subsets)
3.6000 ISA TPSAM 3.4000 VAR MEAN 3.2000 MEAN MEAN 3.0000
2.8000
2.6000 Fractal Dimension (FD) Dimension Fractal 2.4000
2.2000
(1)5.8m (2)15m (3)23.5m Spatial Resolution
(a) Sal
3.2000 ISA TPSAM 3.0000 VAR MEAN MEAN 2.8000 MEAN
2.6000
2.4000 Fractal Dimension (FD) Dimension Fractal 2.2000
2.0000
(1)5.8m (2)15m (3)23.5m Spatial Resolution
(b) Plantation
57 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
3.4000 ISA TPSAM 3.2000 VAR MEAN MEAN 3.0000 MEAN
2.8000
2.6000 Fractal Dimension (FD) Fractal Dimension 2.4000
2.2000
(1)5.8m (2)15m (3)23.5m Spatial Resolution
(c) Mixed Broad Leaf
3.1000 ISA 3.0000 TPSAM VAR 2.9000 MEAN MEAN 2.8000 MEAN
2.7000
2.6000
2.5000 Fractal Dimension (FD)
2.4000
2.3000
(1)5.8m (2)15m (3)23.5m Spatial Resolution
(d) Mountain vegetation
58 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
Appendix – 3
Plots of variation of FD with the change in altitude: (a) Sal patches 3.2000
3.0000
2.8000
2.6000 FD
2.4000
2.2000 IR_LISS3_JA N IR_LISS3_NOV 2.0000
) ) ) ) m m 7m) 2m 6m) 2m 22 34 40 58 9 (294m) ( ( (474 (501m) (510m) ( (63 ( 1 (273m) 2 3 4 5 6 7 8 9 10 PATCHES WITH ALTITUDE(m)
3.1000
3.0000
2.9000
2.8000 FD
2.7000 NDVI_ASTER_MAR NDVI_ASTER_OCT 2.6000
2.5000 ) ) ) ) ) ) ) m m m m) 2 73m 402m ( (510m 1 (2 2 (294 3 (347m 4 5 (474 6 (501m) 7 8 (586 9 (632m) 10 (92 PATCHES WITH ALTITUDE (m) 3.0000
2.9000
2.8000 FD 2.7000
IR_ASTER_MAR 2.6000 IR_ASTER_OCT
2.5000 273 294 347 402 474 501 510 586 632 922 PATCHES WITH ALTITUDE(m)
59 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
(b) Mixed broad leaf patches
3.0000
2.9000
2.8000 FD 2.7000
2.6000 IR_LISS3_JAN IR_LISS3_NOV 2.5000
) ) ) ) ) ) ) m m m m m 9m 28 2 826m 8 9 257m) (621 ( ( (872 ( (958 (965 1 1 2 (707m) 3 4 5 6 (898m) 7 8 9 10 ( PATCHES WITH ALTITUDE(m) 3.0000
2.9000
2.8000 FD
2.7000 NDV I_A STER_MA R NDV I_A STER_OCT 2.6000
) ) ) ) ) m m 7 9 7m 0 2 621m) 828m 898m) 965m ( (7 ( ( (9 ( 125 1 2 3 (826m) 4 5 (872m) 6 7 8 (958m) 9 ( 10 PATCHES WITH ALTITUDE(m) 3.0000
2.9000
2.8000 FD
2.7000 IR_MA R IR_OCT
2.6000
) ) ) ) ) ) ) ) ) ) m m m m 7 6m 2 9 5 7m 70 2 87 898m 2 96 (621m ( (8 ( ( (9 (958m ( 1 2 3 4 (828m 5 6 7 8 9 (125 10 PATCHES WITH ALTITUDE(m)
60 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
(c) Mountain vegetation patches
3.2000 3.1000 3.0000 2.9000 2.8000 FD 2.7000
2.6000 IR_JA N 2.5000 IR_NOV 2.4000
) ) m) m m 8m) 6 4m) 7 6m) 1 3 88m) 9 9 4 5 97m) 6 3 3 3 7 8 8 9 1 1 1 1 1 ( ( (14 ( ( ( 1 2 (1 3 4 5 (1661m) 6 7 8 (1 9 10 (2190m) PATCHES WITH ALTITUDE(m)
3.0000
2.9000
2.8000 FD
2.7000 NDVI_MAR NDV I_OCT 2.6000
) 6m) 1m) 5 6 8 1 (1338m 1 2 (1388m) 3 (1396m) 4 (1494m) 5 (1661m) 6 (1747m) 7 ( 8 (1897m) 9 (19 10 (2190m) PATCHES WITH ALTITUDE(m)
3.0000 2.9500 2.9000 2.8500
FD 2.8000 2.7500 IR_MA R 2.7000 IR_OCT 2.6500
m) m) m) m) 6m) 88 9 61 47 61 3 6 7 9 1 (1 (1 (1 1 (1338m) 2 3 (13 4 (1494m) 5 6 ( 7 (1856m) 8 (1897m) 9 10 (2190m) PATCHES WITH ALTITUDE(m)
61 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
Appendix – 4
Plots of change of FD with spectral bands for different vegetation types ( a) Isarithm method results for Aster, LISS III and LISS IV respectively
3.0000
2.8000
2.6000 sal_isa FD 2.4000 plantn_isa mbl_isa 2.2000 mv_isa
2.0000 GREEN RED IR NDVI SPECTRAL BANDS
3.2000
3.0000
2.8000
2.6000 FD SAL_ISA 2.4000 PLA NTN_ISA 2.2000 MBL_ISA MV _ISA 2.0000 GREEN RED IR NDVI SPECTRAL BANDS
3.0000
2.9000
2.8000
2.7000 FD SAL_ISA 2.6000 PLA NTN_ISA
2.5000 MBL_ISA MV _ISA 2.4000 GREEN RED IR NDVI SPECTRAL BANDS
62 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
(b) TPSA method results for Aster, LISS III and LISS IV respectively
3.2000 SAL_TPSAM PLA NTN_TPSA M 3.0000 MBL_TPSA M 2.8000 MV _TPSA M
2.6000 FD
2.4000
2.2000
2.0000 GREEN RED IR NDVI SPECTRAL BANDS
3.2000
3.0000
2.8000 SAL_TPSAM 2.6000 PLA NTN_TPSA M FD MBL_TPSA M 2.4000 MV _TPSA M
2.2000
2.0000 GREEN RED IR NDVI SPECTRAL BANDS
2.8000 2.7000 2.6000 2.5000 2.4000 FD 2.3000 SAL_TPSAM 2.2000 PLA NTN_TPSA M MBL_TPSA M 2.1000 MV _TPSA M 2.0000 GREEN RED IR NDVI SPECTRAL BANDS
63 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
(c) Variogram method results for Aster, LISS III and LISS IV respectively
3.0000 SAL_VAR 2.9500 PLANTN_VAR MBL_VAR 2.9000 MV_VAR
2.8500 FD
2.8000
2.7500
2.7000 GREEN RED IR NDVI SPECTRAL BANDS
2.9000
2.8000
2.7000 FD 2.6000 SAL_VAR PLANTN_VAR 2.5000 MBL_V A R MV _V A R 2.4000 GREEN RED IR NDVI SPECTRAL BANDS
2.9500
2.9000
2.8500
FD SAL_VAR 2.8000 PLANTN_VAR MBL_V A R 2.7500 MV _V A R
2.7000 GREEN RED IR NDVI SPECTRAL BANDS
64 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
Appendix – 5
Plots of Local fractal approach for optimal band selection Isarithm method
14.00 8.00 (a) 12.00 (b) INFRA RED SA L 7.00 10.00 INFRA RED PLANTN 6.00 NDV I SA L INFRA RED MV NDVI PLANTN 5.00 8.00 INFRA RED MBL NDV I MV 4.00 NDV I MBLi
% pxls 6.00 % pxls 3.00 4.00 2.00 2.00 1.00 0.00 0.00
0 40 55 70 85 00 15 10 .25 55 70 .85 00 15 45 60 1.80 1.95 2.10 2.25 2. 2. 2. 2. 3. 3. 3.30 3.45 3.60 3.75 1.80 1.95 2. 2 2.40 2. 2. 2 3. 3. 3.3 3. 3. 3.75 FD FD
7.00 (a) 6.00 8.00 7.00 IR SA L 5.00 (b) NDV I SA L IR PLA NTN 6.00 NDV I PLA NTN 4.00 IR MV 5.00 NDV I MV IR MBL
% pxls 3.00 4.00 NDV I MBL % pxls 2.00 3.00 2.00 1.00 1.00 0.00 0.00 0 5 0 0 5 0 0 5 0 5 0 5 .8 .25 .4 .0 .1 .6 .7 0 5 0 5 0 5 0 5 0 5 0 5 0 5 1 1.9 2.1 2 2 2.5 2.7 2.85 3 3 3.3 3.4 3 3 8 2 4 5 7 1 3 7 1. 1.9 2.1 2. 2. 2. 2. 2.8 3.0 3. 3. 3.4 3.6 3. FD FD
Aster: (a) March, (b) October
8.00 7.00 7.00 INFRA RED SA L 6.00 6.00 (a) INFRA RED PLA NTN (b) NDV I SA L 5.00 5.00 INFRA RED MV NDV I PLA NTN 4.00 NDV I MV 4.00 INFRA RED MBL NDV I MBL % pxls
3.00 % pxls 3.00 2.00 2.00
1.00 1.00
0.00 0.00 5 0 0 5 5 .1 .4 5 1.80 1.9 2 2.25 2.4 2.55 2.70 2.85 3.00 3.15 3.30 3 3.60 3.7 .10 .25 .85 .00 1.80 1.95 2 2 2.40 2.55 2.70 2 3 3.15 3.30 3.45 3.60 3.7 FD FD
12.00 7.00 (a) 10.00 6.00 (b) INFRA RED SA L 8.00 5.00 NDV I SA L INFRA RED PLANTN NDV I PLA NTN INFRA RED MV 4.00 6.00 NDV I MV INFRA RED MBL
%pxls NDV I MBL % pxls 3.00 4.00 2.00
2.00 1.00
0.00 0.00 0 5 0 5 0 5 0 5 0 0 5 0 5 5 .1 .2 .8 .0 .75 .95 .10 .25 .40 .8 .00 .15 .30 .60 .7 1.8 1.9 2 2 2.4 2.5 2.7 2 3 3.15 3.3 3.4 3.6 3 1.80 1 2 2 2 2.55 2.70 2 3 3 3 3.45 3 3 FD FD
LISS III: (a) January (b) November
65 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
TPSAM
18.00 20.00 18.00 16.00 INFRA RED SA L 16.00 (b) 14.00 INFRA RED PLA NTN (a) 14.00 NDV I SA L 12.00 INFRA RED MV 12.00 NDVI PLANTN 10.00 INFRA RED MBL NDV I MV
pxls 10.00
8.00 % pxls NDV I MBL % 8.00 6.00 6.00 4.00 4.00 2.00 2.00 0.00 0.00
10 60 10 00 1.90 2.00 2. 2.20 2.30 2.40 2.50 2. 2.70 2.80 2.90 3.00 3.10 3.20 3.30 3.40 1.90 2.00 2. 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90 3. 3.10 3.20 3.30 3.40 FD FD
14.00 20.00 NDVI SA L 18.00 12.00 (b) NDVI PLA NTN 16.00 (a) INFRA RED SA L NDVI MV 10.00 14.00 INFRA RED PLA NTN NDVI MBL 12.00 8.00 INFRA RED MV INFRA RED MBL 10.00 % pxls % pxls 6.00 8.00 4.00 6.00 4.00 2.00 2.00 0.00 0.00
0 0 .20 .80 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90 3.00 2.00 2.1 2 2.30 2.40 2.50 2.60 2.7 2 2.90 3.00 FD FD
Aster
12.00 INFRA RED SA L (b) 14.00 INFRA RED PLA NTN NDV I SA L 10.00 12.00 (a) INFRA RED MV NDV I PLA NTN 8.00 10.00 NDV I MV INFRA RED MBL NDV I MBL 6.00 8.00
% pxls 6.00 4.00 % pxls 4.00 2.00 2.00 0.00 0.00
5 0 5 0 0 5 5 0 0 5 5 05 25 30 35 50 60 0 .1 .20 2 .3 .45 5 .6 6 .70 7 .00 .80 2. 2.05 2 2.15 2 2. 2.30 2 2.40 2 2. 2.55 2 2. 2 2. 2.80 2 2. 2.10 2.1 2.20 2. 2. 2. 2.4 2.45 2. 2.55 2. 2.6 2.70 2.75 2 FD FD
14.00 NDV I SA L 9.00 12.00 NDVI PLANTN (b) INFRA RED SA L 8.00 NDV I MV INFRA RED PLANTN 10.00 (a) 7.00 NDV I MBL 6.00 INFRA RED MV 8.00 5.00 INFRA RED MBL
% pxls 6.00 4.00 % pxls 3.00 4.00 2.00 2.00 1.00 0.00 0.00
05 15 25 30 35 40 50 55 60 65 70 75 80 85 90 95 00 10 15 30 35 55 75 .80 00 . . . . . 2.00 2.05 2. 2. 2.20 2.25 2. 2. 2.40 2.45 2.50 2. 2.60 2.65 2.70 2. 2 2.85 2.90 2.95 3. 2.00 2. 2.10 2 2.20 2 2. 2 2. 2.45 2. 2. 2 2. 2 2. 2. 2. 2. 2. 3. FD FD LISS III
66 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
Variogram method
18.00 (a) 16.00 INFRA RED SA L 14.00 (b) INFRA RED PLA NTN NDV I SA L 14.00 12.00 NDVI PLANTN 12.00 INFRA RED MV 10.00 NDV I MV 10.00 INFRA RED MBL 8.00 NDV I MBL 8.00 % pxls 6.00 6.00 % pxls 4.00 4.00 2.00 2.00 0.00 0.00
0 5 5 0 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 .5 .5 .60 .7 .8 .85 .0 .0 .10 .5 .5 .6 .6 .7 .7 .8 .8 .9 .9 .0 .0 .1 2 2 2 2.65 2.70 2 2 2 2.90 2.95 3 3 3 2 2 2 2 2 2 2 2 2 2 3 3 3 FD FD
14.00 14.00 (b) INFRA RED SA L (a) 12.00 NDV I SA L INFRA RED PLANTN 12.00 NDV I PLA NTN 10.00 INFRA RED MV 10.00 NDV I MV 8.00 INFRA RED MBL 8.00 NDV I MBL
6.00 %pxls 6.00 % pxls 4.00 4.00 2.00 2.00 0.00 0.00
.10 2.50 2.55 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00 3.05 3 2.50 2.55 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00 3.05 3.10 FD FD
Aster
18.00 NDV I SA L 20.00 16.00 NDV I SA L NDVI PLANTN 18.00 (a) 14.00 NDVI PLANTN (b) NDV I MV 16.00 12.00 14.00 NDV I MV NDV I MBL 10.00 12.00 NDV I MBL 8.00 10.00 % pxls 6.00 % pxls 8.00 6.00 4.00 4.00 2.00 2.00 0.00 0.00
0 5 0 5 0 5 0 5 0 5 0 5 0 5 5 6 6 7 7 8 8 9 9 0 0 1 0 ...... 55 .60 .65 .70 .80 .85 .90 .95 .0 .05 2 2 2 2 2 2 2 2 2 2 3 3 3 2.50 2 2 2 2 2.75 2 2 2 2 3 3 3.10 FD FD
LISS III
67 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
Appendix – 6
FD values calculated with different methods TABLE 1: HALDWANI
ASTER MARCH; SEASON 1 HALDWANI : CHANGE OF FRACTAL DIMENSION WITH METHODS SPECTRAL BANDS GREEN RED IR NDVI VEG SUBSET SIZE ISA TPSAM VAR ISA TPSAM VAR ISA TPSAM VAR ISA TPSAM VAR SAL 250 * 250 2.3785 2.6760 2.8219 2.4001 2.6815 2.8486 2.8519 2.6419 2.8282 2.9388 2.9798 2.9087 500 * 500 2.5063 2.5250 2.8768 2.4196 2.5647 2.8860 2.8231 2.5348 2.8858 2.9401 2.9588 2.9648 750 * 750 2.7964 2.5421 2.9174 2.5422 2.6041 2.9338 2.7733 2.5747 2.9359 2.9139 2.9479 2.9727
PLANTATION 250 * 250 2.5421 2.5191 2.8322 2.5231 2.5413 2.8632 2.6931 2.5199 2.8521 2.8190 2.4734 2.8379 500 * 500 2.6286 2.3271 2.8536 2.5429 2.3509 2.8549 2.5719 2.3211 2.8148 2.6803 2.2665 2.8325 750 * 750
MXD B LEAVES 250 * 250 2.2567 2.5615 2.8062 2.6128 2.6253 2.8400 2.8139 2.5908 2.8533 2.8343 2.5134 2.8361 500 * 500 2.6044 2.4020 2.8597 2.7444 2.4763 2.8566 2.6952 2.4428 2.8545 2.7132 2.2827 2.8310 750 * 750
MOUNTAIN VEG 250 * 250 2.6096 2.5985 2.848822 2.6696 2.6384 2.835254 2.7257 2.6099 2.896858 2.7112 2.5355 2.829328 500 * 500 750 * 750
68 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
TABLE 2:
ASTER OCTOBER; SEASON 2 HALDWANI : CHANGE OF FRACTAL DIMENSION WITH METHODS SPECTRAL BANDS GREEN RED IR NDVI VEG SUBSET SIZE ISA TPSAM VAR ISA TPSAM VAR ISA TPSAM VAR ISA TPSAM VAR SAL 250 * 250 2.5443 2.6678 2.7827 2.4529 2.7213 2.8055 2.7661 2.6305 2.7989 2.9758 3.1335 2.9396 500 * 500 2.3884 2.5084 2.8481 2.5689 2.5521 2.8450 2.8018 2.5239 2.8649 2.9460 2.9565 2.9487 750 * 750 2.5021 2.5128 2.9123 2.7294 2.5560 2.8799 2.7618 2.5640 2.9128 2.9141 2.9315 2.9615
PLANTATION 250 * 250 2.4045 2.5455 2.8348 2.1259 2.5404 2.8165 2.8245 2.5157 2.8614 2.8628 2.4728 2.8367 500 * 500 2.3806 2.3342 2.8415 2.1085 2.3510 2.8430 2.6970 2.2982 2.8211 2.7643 2.2467 2.8303 750 * 750
MXD B LEAVES 250 * 250 2.3441 2.5609 2.8310 2.2300 2.6028 2.8592 2.7101 2.5877 2.8810 2.9047 2.4902 2.8722 500 * 500 2.4700 2.3868 2.8579 2.6633 2.4454 2.8647 2.7066 2.4240 2.8619 2.7890 2.2669 2.8389 750 * 750
MOUNTAIN VEG 250 * 250 2.6079 2.5691 2.844797 2.5081 2.5994 2.846711 2.6843 2.5792 2.868002 2.7274 2.5331 2.856942 500 * 500 750 * 750
69 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
TABLE 3:
LISS 3 JANUARY; SEASON 1 HALDWANI : CHANGE OF FRACTAL DIMENSION WITH METHODS SPECTRAL BANDS GREEN RED IR NDVI VEG SUBSET SIZE ISA TPSAM VAR ISA TPSAM VAR ISA TPSAM VAR ISA TPSAM VAR SAL 250 * 250 2.8683 2.9646 2.6048 2.4867 3.1090 2.5702 2.9897 3.0225 2.6650 2.9369 3.0033 2.6358 500 * 500 3.0860 3.3058 2.8599 2.9024 3.2669 2.8173 2.9440 3.1728 2.8772 2.9950 3.2871 2.8736 750 * 750 2.9006 2.7482 2.9153 2.8567 2.7511 2.9028 2.8451 2.7518 2.9167 2.8598 2.7135 2.8998
PLANTATION 250 * 250 2.6222 2.3761 2.7481 2.7214 2.3835 2.7017 2.6875 2.4104 2.8191 2.6919 2.3499 2.7610 500 * 500 2.5541 2.4777 2.8593 2.5613 2.5112 2.8781 2.6157 2.5638 2.8790 2.5591 2.4718 2.8621 750 * 750
MXD B LEAVES 250 * 250 2.7388 2.5465 2.7708 2.6206 2.5386 2.6422 2.6228 2.5340 2.8057 2.6842 2.4530 2.7890 500 * 500 2.8351 2.6867 2.8488 2.9367 2.7390 2.8463 2.7677 2.7399 2.8574 2.8010 2.6383 2.8409 750 * 750
MOUNTAIN VEG 250 * 250 2.6973 2.5146 2.773616 2.4963 2.5665 2.789181 2.5807 2.5975 2.817042 2.5757 2.5205 2.794811 500 * 500 750 * 750
70 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
TABLE 4:
LISS 3 NOVEMBER; SEASON 2 HALDWANI : CHANGE OF FRACTAL DIMENSION WITH METHODS SPECTRAL BANDS GREEN RED IR NDVI VEG SUBSET SIZE ISA TPSAM VAR ISA TPSAM VAR ISA TPSAM VAR ISA TPSAM VAR SAL 250 * 250 2.9111 3.0375 2.6576 2.9265 3.1066 2.5947 3.0489 3.0404 2.7142 2.8594 2.8726 2.8626 500 * 500 3.0652 3.3309 2.8661 3.0246 3.3270 2.8936 3.0408 3.3142 2.9013 3.0021 3.1689 2.9464 750 * 750 2.9061 2.7684 2.9046 2.8918 2.7910 2.9172 2.8655 2.7943 2.9142 2.8781 2.8902 2.9496
PLANTATION 250 * 250 2.7670 2.3970 2.7977 2.5847 2.4169 2.8112 2.7026 2.4274 2.8249 2.7489 2.3619 2.7900 500 * 500 2.5828 2.5300 2.8511 2.4454 2.5626 2.8815 2.6085 2.6389 2.8583 2.5274 2.4892 2.8560 750 * 750
MXD B LEAVES 250 * 250 2.7556 2.5555 2.7783 2.6767 2.6252 2.7756 2.7392 2.5516 2.8445 2.7248 2.4856 2.8337 500 * 500 2.8710 2.6842 2.8708 2.7873 2.7495 2.8555 2.7492 2.7293 2.8692 2.7860 2.6386 2.8506 750 * 750
MOUNTAIN VEG 250 * 250 2.8321 2.5414 2.774371 2.8654 2.6185 2.797337 2.6672 2.6427 2.838669 2.6275 2.5134 2.752922 500 * 500 750 * 750
71 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
TABLE 5:
LISS4 APRIL; SEASON 1 HALDWANI : CHANGE OF FRACTAL DIMENSION WITH METHODS SPECTRAL BANDS GREEN RED IR NDVI VEG SUBSET SIZE ISA TPSAM VAR ISA TPSAM VAR ISA TPSAM VAR ISA TPSAM VAR SAL 250 * 250 2.9273 2.6622 2.8574 2.9100 2.6978 2.8668 2.8098 2.6654 2.8543 2.8337 2.6412 2.8365 500 * 500 2.7599 2.5543 2.8874 2.7381 2.5806 2.8915 2.6830 2.5446 2.8940 2.6613 2.5250 2.8919 750 * 750 2.9131 2.6096 2.9317 2.8743 2.6350 2.9332 2.7817 2.5890 2.9368 2.7998 2.5771 2.9365
PLANTATION 250 * 250 2.8671 2.3675 2.8935 2.7468 2.3997 2.8959 2.7277 2.3778 2.8781 2.7499 2.4023 2.8782 500 * 500 2.8179 2.3479 2.8612 2.7665 2.3929 2.8661 2.7366 2.3667 2.8511 2.7145 2.4025 2.8567 750 * 750
MXD B LEAVES 250 * 250 2.7928 2.4116 2.8798 2.7429 2.4529 2.8531 2.6741 2.4526 2.8785 2.6597 2.4106 2.8736 500 * 500 2.8437 2.5073 2.9104 2.8589 2.5463 2.9099 2.7845 2.5309 2.9087 2.7889 2.5083 2.9052 750 * 750
MOUNTAIN VEG 250 * 250 2.7238 2.3952 2.888107 2.7128 2.4392 2.904758 2.5998 2.4369 2.885046 2.5797 2.2991 2.734557 500 * 500 750 * 750
72 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
TABLE 6-10: DEHRADUN
ASTER FEB; SEASON 1 DEHRADUN : CHANGE OF FRACTAL DIMENSION WITH METHODS SPECTRAL BANDS GREEN RED IR NDVI VEG SUBSET SIZE ISA TPSAM VAR ISA TPSAM VAR ISA TPSAM VAR ISA TPSAM VAR SAL 250 * 250 2.4146 2.6111 2.6402 2.5383 2.6114 2.7003 2.6506 2.6061 2.6687 2.7556 2.7624 2.7479 500 * 500 2.5802 2.5380 2.7122 2.5587 2.5618 2.7285 2.6364 2.5493 2.7302 2.7652 2.6411 2.7521 750 * 750 2.6153 2.5563 2.7401 2.6015 2.5895 2.7421 2.6148 2.5756 2.7469 2.6971 2.6804 2.7928
ASTER OCTOBER; SEASON 2 DEHRADUN : CHANGE OF FRACTAL DIMENSION WITH METHODS SPECTRAL BANDS GREEN RED IR NDVI VEG SUBSET SIZE ISA TPSAM VAR ISA TPSAM VAR ISA TPSAM VAR ISA TPSAM VAR SAL 250 * 250 2.6191 2.6158 2.7243 2.7103 2.6726 2.7133 2.6812 2.5610 2.7028 2.8592 3.0043 2.8375 500 * 500 2.2755 2.4524 2.7493 2.4959 2.4944 2.7425 2.7055 2.4566 2.7659 2.8539 2.8521 2.8449 750 * 750 2.2755 2.4492 2.8182 2.4959 2.4907 2.7823 2.7055 2.4952 2.8114 2.8539 2.8357 2.8613
LISS 3 MAR; SEASON 1 DEHRADUN : CHANGE OF FRACTAL DIMENSION WITH METHODS SPECTRAL BANDS GREEN RED IR NDVI VEG SUBSET SIZE ISA TPSAM VAR ISA TPSAM VAR ISA TPSAM VAR ISA TPSAM VAR SAL 250 * 250 2.8144 2.7438 2.5558 2.8990 2.8326 2.5523 2.9429 2.7448 2.6166 2.7553 2.7468 2.7667 500 * 500 2.9602 3.2769 2.7586 2.9035 3.2570 2.7942 2.9437 3.2454 2.8040 2.9146 3.1102 2.8512 750 * 750 2.8268 2.6832 2.8001 2.7893 2.7013 2.8148 2.7589 2.6854 2.8159 2.7733 2.7925 2.8528
73 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
LISS 3 NOVEMBER; SEASON 2 DEHRADUN : CHANGE OF FRACTAL DIMENSION WITH METHODS SPECTRAL BANDS GREEN RED IR NDVI VEG SUBSET SIZE ISA TPSAM VAR ISA TPSAM VAR ISA TPSAM VAR ISA TPSAM VAR SAL 250 * 250 2.8158 2.7746 2.5429 2.8118 2.8224 2.4452 2.8642 2.8609 2.6046 2.7859 2.8226 2.5432 500 * 500 2.9928 3.2312 2.7497 2.7889 3.1893 2.7096 2.8437 3.0743 2.7748 2.8831 3.2164 2.7696 750 * 750 2.7534 2.6527 2.8099 2.7481 2.6494 2.8032 2.7566 2.6605 2.8141 2.7628 2.6255 2.7981
LISS4 APRIL; SEASON 1 DEHRADUN : CHANGE OF FRACTAL DIMENSION WITH METHODS SPECTRAL BANDS GREEN RED IR NDVI VEG SUBSET SIZE ISA TPSAM VAR ISA TPSAM VAR ISA TPSAM VAR ISA TPSAM VAR SAL 250 * 250 2.8197 2.5651 2.7612 2.8084 2.6041 2.7662 2.7083 2.5702 2.7574 2.7312 2.5459 2.7361 500 * 500 2.7599 2.4642 2.7920 2.7224 2.4925 2.7957 2.6647 2.4534 2.8009 2.6383 2.4329 2.7986 750 * 750 2.8277 2.5194 2.8326 2.7652 2.5434 2.8336 2.6845 2.4955 2.8375 2.6959 2.4840 2.8378
74 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
Appendix – 7
Field photographs Sal forests
Point 2 of figure 3-4
Point 6 of figure 3-4
75 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
Plantations
Point 14 of figure 3-4
Point 17 of figure 3-4
Mixed broad leaf vegetation
76 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
Point 18 of figure 3-4
Point 4 of figure 3-4
77 COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON
Mountain vegetations
Point 21 of figure 3-4
Point 23 of figure 3-4
78