Implementation of Fractal Image Compression with GUI” SUBMITTED in PARTIAL FULFILLMENT of the REQUIREMENT for THE
VISVESVARAYA TECHNOLOGICAL UNIVERSITY Jnana Sangama, Belgaum, Karnataka-590 014
A FINAL YEAR PROJECT REPORT ON
“Implementation of Fractal Image Compression with GUI” SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE
AWARD OF DEGREE OF
BACHELOR OF ENGINEERING
IN
ELECTRONICS AND COMMUNICATION ENGINEERING 2018-2019
Submitted by SNEHA S-1NH15EC108 THANUJA A-1NH15EC119 SREE RENUKAKSHITHA JM-1NH15EC112
Internal Guide Prof. Mr. Karthik CV Assistant Professor. Department of Electronics and Communication Engineering
IMPLEMENTATION OF FRACTAL IMAGE COMPRESSION WITH GUI
DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING
CERTIFICATE
It is certified that the Project work entitled “Implementation of Fractal Image Compression with GUI” carried out by SNEHA S (1NH15EC108),THANUJA A (1NH15EC119) and SREE RENUKAKSHITHA JM (1NH15EC112), we the bonafide students of New Horizon College of Engineering, Bengaluru, in partial fulfillment for the award of Bachelor of Engineering in Electronics and Communication Engineering of the Visvesvaraya Technological University, Belgaum during the year 2018-2019.It is further certified that all corrections/suggestions indicated for internal assessment has been incorporated in the report deposited in the department library. The Project Report has been approved as it satisfies the academic requirements in respect of Project Work prescribed for the Bachelor of Engineering degree.
Signature of the Guide Signature of the HOD Signature of the Principal Mr.Karthik CV Dr. SANJEEV SHARMA Dr. MANJUNATHA Asst.Prof. Prof. and HOD-ECE Principal Dept. of Electronics and Dept. of Electronics and NHCE Communication Engineering.. Communication Engineering.
External Viva Examiner Signature with date: 1. 2.
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DECLARATION
We, SNEHA S (1NH15EC108) , THANUJA A (1NH15EC119) , SREE RENUKAKSHITHA JM (1NH15EC112) students of 8th semester in Electronics and Communication Engineering , New Horizon College of Engineering, Bengaluru hereby declare that the project work entitled “IMPLEMENTATION OF FRACTAL IMAGE COMPRESSION WITH GUI “ submitted to VISVESVARAYA TECHNOLOGICAL UNIVERSITY during the academic year 2018-2019 , is a record of an original work done by us under the guidance of Mr.KARTHIK CV , Assistant Professor, Department of Electronics and Communication , New Horizon College of Engineering, Bengaluru . This project work is submitted in partial fulfillment of the requirement for the award of the degree of Bachelor of Engineering in Electronics and Communication. The result embodied in the thesis has not been submitted to any other University or Institute for the award of any degree.
PLACE: BENGALURU
DATE:
SNEHA S THANUJA A SREE RENUKAKSHITHA JM
1NH15EC108 1NH15EC119 1NH15EC112
IMPLEMENTATION OF FRACTAL IMAGE COMPRESSION WITH GUI
ACKNOWLEDGEMENTS
The satisfaction and exhilaration that accompany the successful completion of any task would be incomplete without the mention of people who made it possible, whose consistent guidance and encouragement crowned our efforts with success.
We consider it as our privilege to express gratitude to all those who guided us in the completion of our project work.
First and foremost,we wish to express our profound gratitude to our respected Chairman Dr. Mohan Manghnani,New Horizon College of Engineering,Bengaluru for giving us this opportunity.
We wish to express our genuine gratitude to our Principal Dr. Manjunatha,New Horizon College of Engineering,Bengaluru,for providing us with the congenial environment to work in.
We would like to express our sincere thanks to Dr.Sanjeev Sharma,the HOD of Electronics and Communication, New Horizon College of Engineering,for his continuous support and encouragement.
We are greatly indebted to our guide Mr.Karthik CV,Assistant Professor, Department of Electronics and Communication, New Horizon College of Engineering,who took great interest in our project work.He motivated and guided us throughout the accomplishment of this goal.We express our profound thanks for his meticulous guidance.
Last but not the least,heartfelt thanks to our parents and friends for direct and indirect support.
Above all,we thank the Lord Almighty for his grace on us to succeed in this endeavor.
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ABSTRACT
Fractal image compression is a lossy compression method for digital images based on fractals rather than pixels,which are best suited for textures and natural images,it works on self-similarity property in various fractions of images,relying on the fact that parts of an image often ressemble other parts of the same image.It takes long encoding time and affects the image quality.
This code introduces an improved model integrating quantized quad trees and Huffman coding used for fractal image compression.Quantized quad tree method divides the quantized original gray level and color image into various blocks depending on a threshold value besides the properties of the features presented in image.Huffman coding is applied for improving compression quality.Simulation results shows that the quantized quad trees and Huffman coding improved compression ratio and quality derived from the fractal image compression with range block.Different quantitative measures can be found by passing images of different format and dimensions.
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TABLE OF CONTENTS
CHAPTER 1
INTRODUCTION
1.1 OVERVIEW……………………………………………………………………….…………………………………9-10
1.1.1 COMPARISON OF LOSSY AND LOSSLESS METHODS………………………………10-11
1.1.2 COMPRESSION OF DIFFERENT IMAGE COMPRESSION FORMATS…………12-16
1.1.3 PURPOSE OF IMAGE COMPRESSION…………………………………………………….16
1.1.4 APPLICATIONS OF IMAGE COMPRESSION…………………………………………….17-18
CHAPTER 2
FRACTAL IMAGE COMPRESSION
2.1 ORIGIN OF FRACTAL IMAGE COMPRESSION……………………………………………………..19
2.2 INTRODUCTION………………………………………………………………………………………………..20
2.3 BASICS OF FRACTAL IMAGE COMPRESSION………………………………………………………20-21
2.3.1 FRACTALS-A BRIEF INTRODUCTION
2.3.1 SELF-SIMILARITY AND SELF-AFFINITY
CHAPTER 3
LITERATURE SURVEY
CHAPTER 4
SOFTWARE USED
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4.1 ABOUT THE SOFTWARE
4.2 FEATURES OF MATLAB
4.3 GUI IN MATLAB
4.4 USES OF MATLAB
CHAPTER 5
METHODOLOGY
5.1 BLOCK DIAGRAM
5.2 QUADTREE PARTITIONING
5.3 HUFFMAN CODING
5.3.1 HUFFMAN ENCODING
5.3.2 HUFFMAN DECODING
CHAPTER 6
RESULTS
6.1 PERFORMANCE CHARACTERISTICS
6.2 FRACTAL IMAGE COMPRESSION OUTPUT
CHAPTER 7
CONCLUSION
CHAPTER 8
FUTURE SCOPE
REFERENCE
APPENDIX
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LIST OF FIGURES
1.1.2(a) Image formats-BMP,TIFF LWZ,PNG and JPEG 1.1.2(b) Difference of JPEG and JPEG 2000 for color images 4.1(a) Logo of Matlab 5.2(a) Shows an example of the quadtree partitioning of an image 5.2(b) Shows its corresponding quadtree 5.2(c) Shows the partitioning of the Lena image 5.2(d) Is the decode image of a dog using the quadtree algorithm. 6.2(a) Snapshot of the output screen 6.2(b) Snapshot of the results of a fractal image 6.2(c) Snapshot of the results of a fractal image of a lotus 6.2(d) Snapshot of the results of gray scale image of a baboon
6.2(e) Snapshot of the results of a color image of Lenna 6.2(f) Snapshot of the results of a satellite image of The Earth List of tables
6.2(a) Experimental Results
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CHAPTER 1
INTRODUCTION
1.1 Overview
Information that can be viewed is very important for us to identify, recognize and understand the surrounding world . An image consists of a two dimensional array of numbers. The shade of the image whether gray or color displayed for a given image(pixel) solely depends on the number that is stored in the array for the pixel. An image that takes large amount of data requires more memory to store, takes longer time to be transfered, and is difficult to process . Image compression becomes important due to the limit in the communication bandwidth, CPU speed, time taken for transmission and size required to store. The main aim of Image compression is to minimize the size of the image in bytes of a graphics file by maintaining a good quality of the image. Image compression is a challenging field in Image processing research. A common characteristic of most images is that the neighboring pixels are correlated and therefore contain redundant information. The foremost task then is to find less correlated representation of the image. Using the compression algorithms, redundant bits are removed from the image so that image size is reduced and the image is compressed. Two fundamental components of compression are redundancy and irrelevancy reduction . It needs to represent an image by removing the spatial and spectral redundancies as much as possible, while keeping the resolution and visual quality of the reconstructed image as close to the original image by taking advantage of these redundancies. An inverse process called decompression (decoding) is applied to the compressed data to get the reconstructed image .
Image compression methods are classified into lossy and lossless compression. In lossless compression there is no information loss; the reconstructed image is exactly the same as the original, which is preferred for high value content, such as medical imagery or image scans made for archival purposes, artificial images such as technical drawings, icons or comics. Lossless compression methods include run length encoding, Huffman encoding,
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LZW (Lempel-Ziv-Welch) coding and area coding . In lossy compression, the reconstructed image contains degradation relative to the original because the compression scheme completely discards redundant information. However, lossy schemes are capable of achieving much higher compression. Under normal viewing conditions, no visible loss is perceived (visually lossless). Lossy compression is most commonly used to compress multimedia data like audio, video, and still images, especially in applications such as streaming media where minor loss of fidelity is acceptable to achieve a substantial reduction in bit rate, especially when used at low bit rates introduce compression artifacts. Lossy compression methods include transform coding, vector quantization, fractal coding, block truncation coding and sub-band coding . In general, higher degrees of compression are only possible using lossy compression; therefore it has been a subject to considerable investigation . Most used methods can be classified under lossy compression. This means that a reconstructed picture is an approximation of the real picture . Fractal image compression has become an important lossy technique due to its capacity of achieving high compression ratio ,high bit rate, high reconstructed image quality and resolution independence. Fractal image compression is to exploit self-similarities present in different parts of the image by transformation and iterations to reduce the amount of redundancy . The main disadvantage of fractal encoding is that it needs a lot of computation, and long encoding time .Fractal compression research focuses on how to shorten the encoding time, speed-up the coding phase and reduce the computational cost of exhaustive search while still preserving a good image quality .This project proposes a combined method, trying to decrease the encoding time without decreasing the image quality.
1.1.1 COMPARISON OF LOSSY AND LOSSLESS METHODS
Methods for lossless image compression are:
Run-length encoding – used in default method in PCX and as one of possible in BMP, TGA, TIFF
Area image compression
DPCM and Predictive Coding
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Entropy encoding
Adaptive dictionary algorithms such as LZW – used in GIF and TIFF
DEFLATE – used in PNG, MNG, and TIFF
Chain codes
Methods for lossy image compression are:
Reducing the color space to the most common colors in the image. The selected colors are specified in the colour palette in the header of the compressed image. Each pixel just references the index of a color in the color palette, this method can be combined with dithering to avoid posterization.
Chroma subsampling. This takes advantage of the fact that the human eye perceives spatial changes of brightness more sharply than those of color, by averaging or dropping some of the chrominance information in the image.
Transform coding. This is the most commonly used method. In particular, a Fourier- related transform such as the Discrete Cosine Transform (DCT) is widely used: N. Ahmed, T. Natarajan and K.R.Rao, "Discrete Cosine Transform," IEEE Trans. Computers, 90–93, Jan. 1974. The DCT is sometimes referred to as "DCT-II" in the context of a family of discrete cosine transforms; e.g., see discrete cosine transform. The more recently developed wavelet transform is also used extensively, followed by quantization and entropy coding.
Fractal image compression.
1.1.2 COMPARISON OF DIFFERENT IMAGE COMPRESSION FORMATS
Images are very important documents nowadays; to work with them in some applications they need to be compressed, more or less depending on the purpose of the application. There are some algorithms that perform this compression in different ways; some are lossless and keep the same information
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as the original image, some others lose information while compressing the image. Some of these compression methods are designed for specific kinds of images, so they will not be so good for other kind of images.
Lossless image representation formats:
BMP (bitmap) is a bitmapped graphics format used internally by the Microsoft Windows graphics subsystem (GDI), and used commonly as a simple graphics file format on that platform. It is an uncompressed format.
PNG (Portable Network Graphics) (1996) is a bitmap image format that employs lossless data compression. PNG was created to both improve upon and replace the GIF format with an image file format that does not require a patent license to use. It uses the DEFLATE compression algorithm, that uses a combination of the LZ77 algorithm and Huffman coding. PNG supports palette based (with a palette defined in terms of the 24 bit RGB colors), greyscale and RGB images. PNG was designed for distribution of images on the internet not for professional graphics and as such other color spaces
Comparison with JPEG:
• JPEG has a big compressing ration, reducing the quality of the image, it is ideal for big images and photographs.
• PNG is a lossless compression algorithm, very good for images with big areas of one unique color, or with small variations of color.
• PNG is a better choice than JPEG for storing images that contain text, line art, or other images with sharp transitions that do not transform well into the frequency domain.
Comparison with TIFF:
• TIFF is a complicated format that incorporates an extremely wide range of options. While this makes it useful as a generic format for interchange between professional image editing
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IMPLEMENTATION OF FRACTAL IMAGE COMPRESSION WITH GUI applications, it makes supporting it in more general applications such as Web browsers difficult.
• The most common general-purpose lossless compression algorithm used with TIFF is LZW, which is inferior to PNG and until expiration in 2003 suffered from the same patent issues that GIF did.
TIFF (Tagged Image File Format) (last review 1992) is a file format for mainly storing images, including photographs and line art. It is one of the most popular and flexible of the current public domain raster file formats. Originally created by the company Aldus, jointly with Microsoft, for use with PostScript printing, TIFF is a popular format for high color depth images, along with JPEG and PNG. TIFF format is widely supported by image-manipulation applications, and by scanning, faxing, word processing, optical character recognition, and other applications.
Compression types include:
• uncompressed • PackBits - is a fast, simple compression scheme for run-length encoding. • Lempel-Ziv-Welch (LZW) • CCITT Fax 3 & 4 – protocol for sending fax documents across telephone lines • JPEG (see below)
Until recently the use of this LZW was limited because this technique was the subject of several patents in various jurisdictions.
Sometimes CCITT encoding is referred to, not entirely accurately, as Huffman encoding. CCITT 1-dimensional encoding is a specific type of Huffman encoding. The other types of CCITT encodings are not, however, implementations of the Huffman scheme.
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Lossy image compression formats:
JPEG (Joint Photographic Experts Group) (1992) is an algorithm designed to compress images with 24 bits depth or greyscale images. It is a lossy compression algorithm. One of the characteristics that make the algorithm very flexible is that the compression rate can be adjusted. If we compress a lot, more information will be lost, but the result image size will be smaller. With a smaller compression rate we obtain a better quality, but the size of the resulting image will be bigger. This compression consists in making the coefficients in the quantization matrix bigger when we want more compression, and smaller when we want less compression.
The algorithm is based in two visual effects of the human visual system. First, humans are more sensitive to the luminance than to the chrominance. Second, humans are more sensitive to changes in homogeneous areas, than in areas where there is more variation (higher frequencies). JPEG is the most used format for storing and transmitting images in Internet.
JPEG 2000 (Joint Photographic Experts Group 2000) is a wavelet-based image compression standard. It was created by the Joint Photographic Experts Group committee with the intention of superseding their original discrete cosine transform based JPEG standard.
JPEG 2000 has higher compression ratios than JPEG. It does not suffer from the uniform blocks, so characteristics of JPEG images with very high compression rates. But it usually makes the image more blurred that JPEG.
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Figure 1.1.2(a): image formats-BMP,TIFF LWZ,PNG and JPEG
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Figure 1.1.2(b) difference of JPEG and JPEG 2000 for color images
1.1.3 PURPOSE OF IMAGE COMPRESSION
An image, 1024 pixel x 1024 pixel x 24 bit, without compression, would require 3 MB of storage and 7 minutes for transmission, utilizing a high speed, 64 Kbit/s, ISDN line. If the image is compressed at a 10:1 compression ratio, the storage requirement is reduced to 300 KB and the transmission time drops to under 6 seconds.
In a distributed environment large image files remain a major bottleneck within systems. Compression is an important component of the solutions available for creating file sizes of manageable and transmittable dimensions. Increasing the bandwidth is another method, but the cost sometimes makes this a less attractive solution. Platform portability and performance are important in the selection of the compression/decompression technique to be employed. The easiest way to reduce the size of the image file is to reduce the size of the image itself. By shrinking the size of the image, fewer pixels need to be stored and consequently the file will take less time to load .
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1.1.4 APPLICATIONS OF IMAGE COMPRESSION
Image compression has increased the efficiency of sharing and viewing personal images, it offers the same benefits to just about every industry in existence. Image compression was most commonly used in the data storage, printing and telecommunication industry. The digital form of image compression is also being put to work in industries such as fax transmission, satellite remote sensing, and high definition television .
In certain industries, the archiving of large numbers of images is required. A good example is the health industry, where the constant scanning and/or storage of medical images and documents take place. Image compression offers many benefits here, as information can be stored without placing large loads on system servers. Depending on the type of compression applied, images can be compressed to save storage space, or to send to multiple physicians for examination. And conveniently, these images can uncompress when they are ready to be viewed, retaining the original high quality and detail that medical imagery demands .
Image compression is also useful to any organization that requires the viewing and storing of images to be standardized, such as a chain of retail stores or a federal government agency. In the retail store example, the introduction and placement of new products or the removal of discontinued items can be much more easily completed when all employees receive, view and process images in the same way. Federal government agencies that standardize their image viewing, storage and transmitting processes can eliminate large amounts of time spent in explanation and problem solving. The time they save can then be applied to issues within the organization, such as the improvement of government and employee programs .
In the security industry, image compression can greatly increase the efficiency of recording, processing and storage. However, in this application it is imperative to determine whether one compression standard will benefit all areas. For example, in a video networking or closed-circuit television application, several images at different frame rates
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IMPLEMENTATION OF FRACTAL IMAGE COMPRESSION WITH GUI may be required. Time is also a consideration, as different areas may need to be recorded for various lengths of time. Image resolution and quality also become considerations, as does network bandwidth, and the overall security of the system .
Museums and galleries consider the quality of reproductions to be of the utmost importance. Image compression, therefore, can be very effectively applied in cases where accurate representations of museum or gallery items are required, such as on a Web site. Detailed images that offer shorter download times and easy viewing benefit to all types of visitors, from the student to the discriminating collector. Compressed images can also be used in museum or gallery kiosks for the education of that establishment’s visitors. In a library scenario, students and enthusiasts from around the world can view and enjoy a multitude of documents and texts without having to incur traveling or lodging costs to do so .
Regardless of industry, image compression has virtually endless benefits wherever improved storage, viewing and transmission of images are required. And with the many image compression programs available today, there is sure to be more than one that fits your requirements best.
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CHAPTER 2
FRACTAL IMAGE COMPRESSION
2.1 ORIGIN OF FRACTAL IMAGE COMPRESSION
The person responsible for discovering fractal image compression is Micheal F. Barnsley, who noticed that extremely complicated, naturally appearïng objects can be created using transformations with very short codes. He went on to name such transformations iterated Function Systems, (IFS). IFS's can be used to encode images whose parts resemble the whole. However, most natural images do not contain this type of self- similarity, but rather parts of the image resemble other parts. Barnsley knew this, and in 1988 he generalized the theory of IFS's to Partitioned Iterated Function Systems (PIFS). He used an algorithm similar to the one above to compress an image. However a person had to interact with the program in order to find the domain blocks to be matched to a particular range block. This resulted in high compression ratios, but very poor quality in the decoded images. Much of Barnsley's work remains secret and copyright since he and Sloan founded the Company Iterated Systems Inc in 1987.
Only in 1990 did any ground breaking work in fractal image compression became public. This was the result of Arnaud Jacquin’s Ph.D thesis which automated the search of the domain-range pair. Jacquin, who was Barnsley's Ph-D student. achieved this by restricting the domains and range blocks to a fixed size, and transformations of a particular type, pixel by- one and scaling by a number less than one. He also decreased the number of domain blocks to be searched by classifying them into one of a few categories. For instance, one category was those blocks with a distinctive edge.
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2.2 INTRODUCTION
Fractal image compression is a modern image compression technique which has recently become an active area of research. Fractal theories are totally different .Benoit Mandelbrot firstly brought forward the idea of fractal geometry. A fractal is a rough or fragmented geometric shape that can be subdivided in parts, each of which is a reduced/size copy of the whole. Fractals display self similar structure over an extended, but finite, scale range. M.Barnsley was the first to suggest the use of a set of transformations to compactly store images . The self-similarities contained in the images are represented by Iterated Function System(IFS).
An iterated function system is a finite set of contraction mappings for each image that has a fixed-point identical to the image itself.Applying that transform iteratively on an arbitrary starting image,the result converges to the original image. Thus, the image is encoded by the transformation on a complete metric space . Jacqin proposed to partition the image into square blocks called as range blocks, search for the regions or blocks of the images which are self similar according to a certain criterion and, once a match is found,compute the transformations. A special type of IFS, called Partition Function System (PIFS), is used to represent image blocks which can achieve a high compression ratio and good retrieved image quality by utilizing the self-similarity characteristic founded in different parts of the images .Fisher et al made a great contribution to this field . His approach was classification of ranges and domain blocks. Its aim was to reduce number of comparisons between the blocks involved in fractal image compression by just comparing blocks of similar class.
2.3 Basics of Fractal Image Compression
Deterministic fractals have the intrinsic property of having extremely high visual complexity which requires less number of bits for representing a given information. They can be described and generated by simple recursive deterministic algorithms . They are
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IMPLEMENTATION OF FRACTAL IMAGE COMPRESSION WITH GUI mathematical objects with a high degree of redundancy in the sense that they are recursively made of transformed copies of either themselves or parts of themselves.
2.3.1 Fractals - a brief introduction
The term fractal was first used by Benoit B. Manderlbrot to designate objects that are self-similar at different scales . Such objects have details at every scale. Unfortunately, a good definition of the term fractal is elusive. It is best to regard a fractal as a set that has properties such as those listed below, rather than to look for a precise definition.
If we consider a set F to be fractal, it will have some of the following properties:
1. F has detail at every scale
2. F is (exactly, approximately, or statistically) self-similar
3. The fractal dimension of F is greater than its topological dimension
4. There is a simple algorithmic description of F
2.3.2 Self-similarity and Self-affinity:
The property of objects whereby magnified subsets appear similar or identical to the whole and to each other is known as self-similarity. It is a characteristic of fractals and sets them apart from Euclidean shapes which generally are smoother. Thus fractal shapes are self-similar and independent of scale or scaling and possess no characteristic size. Euclidean shapes may be described by a simple algebraic formula where as fractals are generally constructed using a recursive algorithm suited for computers.
The non-uniform scaling, where shapes are ( statistically) invariant under transformations that scale different co-ordinates by different amounts, is known as self affinity.
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CHAPTER 3
LITERATURE SURVEY
The objective of the following subsection is to provide a survey of the work available in the digital image processing especially for compressing the images. This subsection provides an outline of the efforts of various researchers.
In February 2011, M. I. Khalil in his research work had implemented Run Length coder in simplified and more effective way. This proposed algorithm works on quantized coefficient of Discrete Cosine Transform (DCT) where there are a lot of coincident token. This experimental result proves that this new approach attains competitive performance. He concluded that proposed technique has higher compression ratio than Run-Method and can be used for widely variety of data types including image, video, audio and text data. Dr. E. Khannan et al. in their research paper namely “Lossless Image Compression Algorithm for Transmitting over Low Bandwidth Line” had shown that compression of image can be improved by considering special and temporal correlations as well as spatial redundancy. In their paper to decrease the communication bandwidth and save the transmitting power in wireless endoscopy capsule, they proposed a new Near- Lossless image compression algorithm based on the Bayer format image suitable for hardware design. The efficiency of temporal prediction was found to be highly dependent on individual image sequences. They also compared the results of adaptive and non- adaptive based image compression. Their experimental result shows that the adaptive wavelet decomposition works better than non- adaptive (Haar) wavelet decomposition.
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In March 2013, Shrusti porwal et al. has provided Lossless data compression methodologies and compared their performance. They compared Huffman and Arithmetic coding methods based on parameters like compression ratio , compression speed, decompression speed, memory space, compressed pattern matching and whether there is prevision for random access or not. They found out that Arithmetic encoding methodology is very powerful over Huffman encoding methodology. They experimentally proved that compression ratio of Arithmetic coding is better and is also reduces channel bandwidth and transmission time. Ms. Pallavi et al. in their research work had discussed about image classification, wavelet compression and they have converted an image into an array using Delphi image control tool. This image control can be used for displaying a graphical image Icon, Bitmap, metafile, GIF, JPEG etc. then an algorithm was created in Delphi to implement Huffman coding. They conclude that in Huffman coding, the image uncompressed need have some specific knowledge of the symbol of probabilities in the compressed files and this need more bit to encode the file. “A Survey: Various Techniques of Image Compression” named paper published by Gaurav Vijay Vargiya et al. in Oct 2013 addresses about various image compression techniques like Run Length encoding , Entropy encoding, Arithmetic coding ,Lempel- Ziv-Welch coding , Scalar quantization and Vector quantization. They found that lossless image compression techniques are most effective over the lossy compression techniques. Lossy provides a higher compression ratio than lossless. With the advancement in digital technology, this area has gained an immense momentum over the last two decades. However, a lot of work still needs to be done for optimization. J. H. PUJAR et al. The need for an efficient technique for compression of Images ever increasing because the raw images need large amounts of disk space seems to be a big disadvantage during transmission & storage. Even though there are so many compression technique already present a better technique which is faster, memory efficient and simple surely suits the requirements of the user. In this paper we proposed the Lossless method of image compression and decompression using a
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IMPLEMENTATION OF FRACTAL IMAGE COMPRESSION WITH GUI simple coding technique called Huffman coding. This technique is simple in implementation and utilizes less memory. A software algorithm has been developed and implemented to compress and decompress the given image using Huffman coding techniques in a MATLAB platform. The experiment shows that the higher data redundancy helps to achieve more compression. P. Telagarapu et al. Image compression is a widely addressed researched area. Many compression standards are in place. But still here there is a scope for high compression with quality reconstruction. The JPEG standard makes use of Discrete Cosine Transform (DCT) for compression. The introduction of the wavelets gave a different dimensions to the compression. This paper aims at the analysis of compression using DCT and Wavelet transform by selecting proper threshold method, better result for PSNR have been obtained. Extensive experimentation has been carried out to arrive at the conclusion. In this paper, we have considered that DCT and DWT for image compression and decompression. By considering several images as inputs, it is observed that MSE is low and PSNR is high in DWT than DCT based compression. S Dhawan et al. Image compression is now essential for applications such as transmission and storage in data bases. In this paper we review and discuss about the image compression, need of compression, its principles, and classes of compression and various algorithm of image compression. This paper attempts to give a recipe for selecting one of the popular image compression algorithms based on Wavelet, JPEG/DCT, VQ, and Fractal approaches. We review and discuss the advantages and disadvantages of these algorithms for compressing grayscale images, give an experimental comparison on 256×256 commonly used image of Lenna and one 400×400 fingerprint image. We have reviewed and summarized the characteristics of image compression, need of compression, principles behind compression, different classes of compression techniques and various image compression algorithms based on Wavelet, JPEG/ DCT, VQ. G. K. Kharate et al. In Image Compression, the researchers‟ aim is to reduce the number of bits required to represent an image by removing the spatial and spectral
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IMPLEMENTATION OF FRACTAL IMAGE COMPRESSION WITH GUI redundancies. Recently discrete wavelet transform and wavelet packet has emerged as popular techniques for image compression. The wavelet transform is one of the major processing components of image compression. The result of the compression changes as per the basis and tap of the wavelet used. It is proposed that proper selection of mother wavelet on the basis of nature of images, improve the quality as well as compression ratio remarkably.We suggest the novel technique, which is based on wavelet packet best tree based on Threshold Entropy with enhancedrun- length encoding. This method reduces the time complexity of wavelet packets decomposition as complete tree is not decomposed. Our algorithm selects the sub- bands, which include significant information based on threshold entropy. The enhanced run length encoding technique is suggested provides better results than RLE. N. R. Thota et al. Image compression is the application of data compression on digital images. Image compression can be lossy or lossless. In this paper it is being attempted to implement basic JPEG compression using only basic MATLAB functions. In this paper the lossy compression techniques have been used, where data loss cannot affect the image clarity in this area. Image compression addresses the problem of reducing the amount of data required to represent a digital image. It is also used for reducing the redundancy that is nothing but avoiding the duplicate data. It also reduces the storage area to load an image. For this purpose we are using JPEG. JPEG is a still frame compression standard, which is based on, the Discrete Cosine Transform and it is also adequate for most compression applications. M. Raid et al. Due to the increasing requirements for transmission of images in computer, mobile environments, the research in the field of image compression has increased significantly. Image compression plays a crucial role in digital image processing, it is also very important for efficient transmission and storage of images. When we compute the number of bits per image resulting from typical sampling rates and quantization methods, we find that Image compression is needed. Therefore development of efficient techniques for image compression has become
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IMPLEMENTATION OF FRACTAL IMAGE COMPRESSION WITH GUI necessary .This paper is a survey for lossy image compression using Discrete Cosine Transform, it covers JPEG compression algorithm which is used for full-colour still image applications and describes all the components of it. Image compression is used for managing images in digital format. R. K. Yadav et al. This paper presented comprehensive study with performance analysis of very recent Wavelet transform based image compression techniques. Image compression is one of the necessities for such communication. The goals of image compression are to minimize the storage requirement and communication bandwidth. Compression is achieved by the removal of redundant data. Discrete Wavelet Transform (DWT) is a recently developed compression technique in image compression. DWT image compression includes decomposition (transform of image), Detail coefficients thresholding, and entropy encoding. This paper mainly describes the transform of an image using DWT and thresholding techniques. In this paper we have taken the standard image Lena of size 256X256 of 8 bit depth and applied DWT (haar). Then two results set are obtained by applying two different techniques of thresholding and then compare the result. P. Sharma et al. Medical images are having a very significant role in health sciences. Medical images are produced by the mechanism of medical imaging which is the process of creating images of the human body or body parts using various techniques to reveal, diagnose or treat a disease. Analysis of these images by the experts leads to detection of a certain and specific medical condition. We present a new hybrid discrete cosine transform and Run length encoding to bring about compression and noise removal in further steps and then image similarity detection by Fourier transform. The quality of the image after compression is the main criteria that all the compression techniques should hold. The proposed compression scheme may have superior performance in a medical image. D. S. Seeli et al. Fractal compression is a lossy compression method for digital images, based on fractals. The method is best suited for textures and natural images, relying on the fact that parts of an image often resemble other parts of the same image. Fractal Image Compression (FIC) techniques take more time to perform
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IMPLEMENTATION OF FRACTAL IMAGE COMPRESSION WITH GUI processes are encoding and global search. Many different researchers and companies are trying to develop a new algorithm to reach shorter encoding time and smaller files. But there are still some problems with fractal compression. This paper analyses the existing FIC techniques that has been developed for the purpose of increasing compression rate and reduce computational time. These FIC techniques commonly utilized the optimization techniques to find the optimal best matching blocks. M. Somanathan1 et al. Classic image compression techniques such as JPEG and MPEG have serious limitations at high compression rates – the decompressed image gets really fuzzy or indistinguishable. To mitigate this problem Artificial Neural Network (ANN) techniques, considered to be intelligent and adaptive models, are used for image compression. In this paper, image compression is achieved by implementing an intelligent technique like the back propagation neural network algorithm. Analysis is also done on achieving a good quality compressed image by varying and comparing the neural network parameters such as number of hidden layer nodes, momentum constant and number of epochs. In this paper, artificial neural networks were employed for the particular application of image compression. Alarabeyyat et al. The development of multimedia and digital imaging has led to high quantity of data required to represent modern imagery. This requires large disk space for storage, and long time for transmission over computer networks, and these two are relatively expensive. These factors prove the need for images compression. Image compression addresses the problem of reducing the amount of space required to represent a digital image yielding a compact representation of an image, and thereby reducing the image storage/transmission time requirements. The key idea here is to remove redundancy of data presented within an image to reduce its size without affecting the essential information of it. We are concerned with lossless image compression in this paper. This paper was motivated by the desire of improving the effectiveness of lossless image compression by improving the BCH and LZW. We provided an overview of various existing coding standards lossless image compression techniques.
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R. L. de Queiroz et al. As the Joint Photographic Experts Group (JPEG) has become an international standard for image compression; we present techniques that allow the processing of an image in the “JPEG-compressed” domain. The goal is to reduce memory requirements while increasing speed by avoiding decompression and space domain operations. In each case, an effort is made to implement the minimum number of JPEG basic operations. Techniques are presented for scaling, previewing, rotating, mirroring, cropping, recompressing, and segmenting JPEG-compressed data. While most of the results apply to any image, we focus on scanned documents as our primary image source. We presented techniques for processing compressed images. We used simple algorithms for scaling, previewing, cropping, rotating, mirroring, segmenting, and recompressing compressed images. Just algorithms which can lead to substantive reductions in memory requirements and complexity were presented. We tried to avoid discussing obvious processing derived from the fact that DCT is a linear transform. For example, it is obvious that the DCT of a linear combination of input blocks will result in the same linear combination of the respective transformed blocks. K. Lees et al. Images require substantial storage and transmission resources, thus image compression is advantageous to reduce these requirements. The report covers some background of wavelet analysis, data compression and how wavelets have been and can be used for image compression. An investigation into the process and problems involved with image compression was made and the results of this investigation are discussed. It was discovered that thresholding was had an extremely important influence of compression results so suggested thresholding strategies are given along with further lines of research that could be undertaken. Dr. E.KANNAN et al. In this paper to decrease the communication bandwidth and save the transmitting power in the wireless endoscopy capsule, this paper presents a new near-lossless image compression algorithm based on the Bayer format image suitable for hardware design. Especially, it has low complexity hardware overhead (only two line buffers) and supports real-time compressing. In addition, the algorithm can provide lossless compression for the region of interest (ROI) and high-
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IMPLEMENTATION OF FRACTAL IMAGE COMPRESSION WITH GUI quality compression for other regions. The ROI can be selected arbitrarily by varying ROI parameters. The proposed technique produces a bit stream that results in a progressive and ultimately lossless reconstruction of an image similar to what one can obtain with a reversible wavelet codec. P. M. Sune et al. Image compression is now essential for applications such as transmission and storage in data bases. Compression becomes very easy techniques to apply without much technical requirement. In this paper we discuss about the image classification, wavelet compression, and converted an image into an array using Delphi image control tool. Image control can be used to display a graphical image Icon, Bitmap, metafile, GIF, JPEG, etc then an algorithm is created in Delphi to implement Huffman coding. Hence image compression has proved to be a valuable technique as one solution. The Wavelet Compression Engine was used in this study. In this paper we have to present classification of image, and Normalized Information Distance (NID) is measure, and wavelet of image compression. Fast FPGA Implementation of YUV-based Fractal Image Compression. Published in: 2014 IEEE Fifth International Conference on Communications and Electronics (ICCE) AN ENHANCED FRACTAL IMAGE COMPRESSION INTEGRATING QUANTIZED QUADTREES AND ENTROPY CODING:2015 11th International Conference on Innovations in Information Technology (IIT)
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CHAPTER 4
SOFTWARE USED
4.1 ABOUT THE SOFTWARE
MATLAB(matrix laboratory) is a multi-paradigm numerical computing environment. A proprietary programming language developed by Math Works,MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages, including C, C++, C#, Java, Fortran and Python.Cleve Moler the chairman of the computer science department at the University of New Mexico, started developing MATLAB in the late 1970s.
The MATLAB application is built around the MATLAB scripting language.Common usage of the MATLAB application involves using the Command Window as an interactive mathematical shell or executing text files containing MATLAB code.It is a programming language developed by Math Works. It started out as a matrix programming language where linear algebra programming was simple. It can be run on both under interactive sessions and as a batch job. This tutorial gives you aggressively a gentle introduction of
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MATLAB programming language.It is designed to give students fluency in MATLAB programming language.
Figure 4.1(a)Logo of Matlab
MATLAB is a high-performance language for technical computing. It integrates computation, visualization and programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation. It has numerous built-in commands and math functions that help you in mathematical calculations, generating plots, and performing numerical methods.
MATLAB is used in every facet of computational mathematics. Following are some commonly used mathematical calculations where it is used most commonly:
Dealing with matrices and Arrays 2-D and 3-D Plotting and graphics Linear Algebra Algebraic Equations Non-Linear Functions Statistics Data Analysis Calculus and Differential Equations Numerical Calculations Integration Transforms Curve Fitting Various other special functions
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4.2 FEATURES OF MATLAB
Following are the basic features of MATLAB:
It is high-level language for numerical computation, visualization and application development. It also provides an interactive environment for iterative exploration, design and problem solving. It provides vast library of mathematical functions for linear algebra, statistics, Fourier analysis, filtering, optimization, numerical integration and solving ordinary differential equations. It provides built-in graphics for visualizing data and tools for creating custom plots.MATLAB’s programming interface gives development tools for improving code quality, maintainability, and maximizing performance. It provides tools for building applications with custom graphical interfaces. It provides functions for integrating MATLAB based algorithms with external applications and languages such as C,Java,.NET and Microsoft Excel.
4.3 GUI IN MATLAB
GUIs (also known as graphical user interfaces or UIs) provide point-and-click control
to software applications, eliminating the need to learn a language or to type
commands in order to run the application. GUIs can automate a task or calculation.
GUI typically contains controls such as menus, toolbars, buttons, and sliders.
The UI contains components such as:
• An axes component
• A pop-up menu listing three data sets that correspond to MATLAB functions:
peaks, membranes and sinc.
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• A static text component to label the pop-up menu.
• Three buttons that provide different kinds of plots: surface, mesh and contour.
When you click a push button, the axes component displays the selected data set using the specified type of 3-D plot.
4.4 USES OF MATLAB
MATLAB is widely used as a computational tool in science and engineering encompassing the fields of physics,chemistry,math and all engineering streams.It is used in a range of applications including-
Signal Processing and Communications Image and Video Processing Control Systems Test and Measurement Computational Finance
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CHAPTER 5
METHODOLOGY
5.1 BLOCK DIAGRAM
INPUT IMAGE QUADTREE HUFFMAN DECOMPOSITION ENCODING
DECOMPRESSION OF HUFFMAN DECODING COMPRESSION OF IMAGE IMAGE
PSNR CALCULATION
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5.2 QUADTREE PARTITIONING
Quadtree partitioning is a rather simple method of dividing an image into variable sized blocks so as to satisfy an error limit. When using the brute force algorithm, we simply find the domain block which resembles a particular range block the most. However, this does not set an upper limit on the difference between the two blocks, and thus it is possible that the best domain-range block pairing is a poor one. If there are a significant number of such matchings, or if the blocks in question are in a particularly high detail area, then it is likely that the decoded image will be of poor quality.
The Quadtree algorithm sets an upper limit for the difference between the domain- range matchings, thus improving the quality of the decoded image. It does so by dividing the original image into overlapping domain blocks of various sizes. For example, an image of size 256 x 256 could have domain blocks whose sides are of length 8,12,16,24,32,48 and 64. Then it recursively divides the original image into non-overlapping range blocks until they are of a specified size, 32 x 32 for example. For each range block, it searches the domain pool. For the domain block which resembles it the most (minimizing the rms difference). If the rms difference is smaller or equal to the maximum error; then save the transformation and delete the range block from the range pool. If no domain block is found, divide the range block into four equal subsquares, which are the new range blocks, and search the domain pool again, deleting the range block if a match is found. Repeat until the pool of range blocks is empty or the size of the range blocks is less than a specified lower limit.
This method is called the Quadtree algorithm since it can be represented by a tree whose root is the original image and each node has, potentially: four subnodes which correspond to the range blocks of the image. For a better understanding? see Figures below, such that Figure, 5.2(a) shows an example of the quadtree partitioning of an image, Figure 5.2(b)shows its corresponding quadtree, Figure 5.2(c) shows the partitioning of the Lena image and Figure 5.2(d) is the decode image of a dog using the quadtree algorithm.
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Figure 5.2(a)image of performing quadtree partitioning algorithm on an image
Figure 5.2(b)Quadtree representation of the above image
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Figure 5.2( c) Quadtree Partitioning of Lenna Image
Figure 5.2(d) Decoded image of a dog which was encoded using quadtree partitioning algorithm
Notice that in order to compare the domain and range blocks we must reduce the number of pixels in the larger domain block. If we are comparing the domain blocks which are twice the size of the range blocks, then the number of pixels in the domain blocks must
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IMPLEMENTATION OF FRACTAL IMAGE COMPRESSION WITH GUI be decreased to one quarter or the original amount. There are two obvious ways of doing so: the preferred way is to take the average pixel values as the new pixel value, which is known as sub-sampling: the other is to choose a representative pixel as the new pixel value. We are multiplying each pixel value by scaling factor Thus if |si|> 1 for the mapping wi, then it is possible that W = UiWi may not be eventually contractive, and therefore we are not guaranteed convergence of the decoded image. As such, the values for which IsiI > 1, must be truncated to some fixed Smax.
To decode the image begin by taking an arbitrary image; divide the image into the final quadtree partitioning we had so as to determine the position of the range blocks. For each range block, the domain block that maps to it is spatially reduced by a factor of two using sub-sampling. Each pixel value is then multiplied by the scaling factor s(i), and sigma(i) is added to it before it is placed in its proper place in the range block, which depends on the orientation of the transformation. The whole image is iterated in this way- until the difference between two subsequent iterations is smaller than a given threshold value.
5.2 HUFFMAN CODING
5.2.1 HUFFMAN ENCODING
Huffman coding is the most prevalent lossless strategy for compacting a bit stream and evacuating coding repetition. It is a capable source coding calculation for source images that are not similarly likely . Huffman coding uses the measurable property of images in the source stream, and after that produces particular codes for these images. The codes for images having higher likelihood of event are shorter than those codes for images having lower likelihood. In this way, it depends on the recurrence of event of an information thing (pixels or little squares of pixels in pictures). The codes are put away in a code book. Code book is built for each picture or a lot of pictures. Huffman develops code tree from base up to top down (form the codes from ideal to left). Images with the most elevated frequencies
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IMPLEMENTATION OF FRACTAL IMAGE COMPRESSION WITH GUI end up at the highest point of the tree (requesting in diminishing request), and result in the briefest codes .
5.2.2 HUFFMAN DECODING
Decoding of encoded image is simple. After the code has been created, decoding is accomplanished in a simple look-up table manner. Start from the root and read the first bit of compressed file. When the decoder reaches a leaf there the original, uncompressed image, symbol and that code is reflected by the decoder. The process initiated again at the root with the next bit, and then it read and can decode the rest of its input.It is basically based on the symbols, i.e. the probability of the symbols .The code itself is an instantaneous uniquely decodable block code. It is called a block code because each source symbol is mapped into a fixed sequence of code symbols. It is instantaneous because each code word in a string of code symbols can be decoded without referencing succeeding symbols. It is uniquely decodable, because any string of code symbols can be decoded in only one way. Thus, any string of Huffman encoded symbols can be decoded by examining the individual symbols of the string in a left to right manner .
CHAPTER 6
RESULTS
6.1 PERFORMANCE CHARACTERISTICS
The quality of reconstructed images can be evaluated in terms of objective and subjective measures. Subjective measures are based on observer's response such as Mean Opinion Score(MOS). The following statistical properties are considered as objective evaluation parameters.
a) Mean Square Error (MSE): MSE is the cumulative squared error between the compressed and the original image.A lower value of MSE means lesser error, and it has
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IMPLEMENTATION OF FRACTAL IMAGE COMPRESSION WITH GUI inverse relation with PSNR. It is the average of the square difference between the desired response and actual system output.
MSE= ∧2
where, I(x, y) is the original image and I’(x,y) is the reconstructed image and m, n are the dimensions of the image.
b) Peak Signal-to-Noise Ratio (PSNR): PSNR is used to measure the quality of reconstruction lossy compression images.It is the ratio between the maximum possible power of a signal and the power of corrupting noise . This ratio is often used as a quality measurement between the original and compressed image.The higher the PSNR, the better the quality of the compressed or reconstructed image. PSNR expressed in decibel(dB)
PSNR =10 log10 (255^2/MSE)
c)Compression Ratio(CR): Data compression ratio is defined as the ratio between the number of bits in original image and compressed image.
CR=
Higher CR means lower reconstruction quality of the image.At higher CR we get blurred image as compared to the image that has less CR. d)Encoding time(ET): Encoding is the process of putting a sequence of characters into special format for transmission or storage purposes.
6.2 FRACTAL IMAGE COMPRESSION OUTPUT:
Fractal image compression is mostly designed to be applicable on the fractal images.It can also be applied to natural images,satellite images which can be gray scale or a 40 | P a g e
IMPLEMENTATION OF FRACTAL IMAGE COMPRESSION WITH GUI color image.Fractal images’ structure is usually defined by fine and small scales or substructures.
An input image will be read into the software,then we are applying quadtree partitioning on it.This will extract the features of the image at a user defined threshold value.The original image will be divided into blocks which are further divided into domains if they aren’t meeting the criteria which is threshold should be 0.2,minimum dimension-2 and maximum dimension-64.An average of the pixel values is calculated for further calculation purpose.Boundary limits are set to 0.The pixel intensities are in a continuous manner,they are separated for Huffman coding calculations.If the values are pretty close they will be considered as one point.Now,the probabilities are calculated for the occurance of each of the pixel intensity selected for calculations.They are arranged in the descending order,the lower two probabilities are added and again placed in the descending order along with the other probabilities.This process continues until we reach 1.It will give a distinct prefix code for every unique symbol which is further converted to variable length code.Huffman eencoding is used to compress image effectively.Compression Ratio will be calculated which is a ratio of number of bits in original image to number of bits in final image.then the reverse process happens which includes Huffman decoding and decompression of image.Finally the PSNR is calculated. A good PSNR value lies between 20-40dB.
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Figure 6.2(a):Snapshot of the output screen
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Figure 6.2(b): Snapshot of the results of a fractal image
Figure 6.2(c) Snapshot of the results of a fractal image of a lotus
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Figure 6.2(d) Snapshot of the results of gray scale image of a baboon
Figure 6.2(e) Snapshot of the results of a color image of Lenna
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Figure 6.2(f) Snapshot of the results of a satellite image of The Earth
IMAGE TIME TAKEN FOR COMPRESSION TIME TAKEN FOR PSNR COMPRESSION(SECONDS) RATIO DECOMPRESSION(SECONDS) BABOON.BMP 1.10493 8.63665 7.75244 31.871 LENA.BMP 0.415253 11.4608 4.93626 32.9866 LENA.JPG 7.94525 11.8788 4.7522 32.2828 PEPPERS.BMP 0.37662 9.66483 6.44794 31.789 FRACTAL.JPG 12.6823 6.8538 12.80268 30.1668 FRACTALLOTUS.JPG 3.60338 13.5021 3.63035 32.2718 SATOFEARTH.JPG 11.0557 6.52116 12.2764 30.7857
Table 6.2(a) Tabulated results of various images
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CHAPTER 7
CONCLUSION
This project compresses any kind of images such as satellite images,gray scale images and fractal images. Encoding time can be reduced by decreasing the size of the images but it lowers the image quality. Using fractal compression and quadtree decomposition it is easier to compress fractal images Consirdering the different dimensions of the range blocks and optimizing the number of iteration it is possible to improve the compression ratio and PSNR values. To improve the quality of the recovered images ,quantized quad-tree decomposition and entropy coding techniques can be used. This type of compression can be applied in Medical Imaging, where doctors need to focus on image details, and in Surveillance Systems, when trying to get a clear picture of the intruder. A weakness of the proposed reference design is the use of fixed size blocks for the range and domain images. There are regions in images that are more difficult to code than others (Ex. Lena’s eyes). Therefore, there should be a mechanism to adapt the block size (Rk,l, Di,j) depending on the error introduced when coding the block.
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CHAPTER 8
FUTURE SCOPE
We can easily extend fractal image compression to fractal video compression. Both motion compensation and three dimensional iterated function systems have advantages over the other encoding techniques, but both remain to be fully developed. Because of the short decoding times but lengthy encoding times, fractal video compression techniques, like fractal still image techniques, are better suited for multi-media applications.
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REFERENCES
[I] M.F. Barnsley; "Fractals Everywhere," Academic Press, San Diego, 1988.
[2] M.F. Barnsley, L .P. Hurd; 'Fractal Image Compression," AK Peters, Wellesley MA, 1993.
[3] Wayne Cochran, John Hart, Partick Flynn; "Fractal Volume Compression," IEEE Trans actions on Visualization and Computer Graphics. vol. 2, no. 4, pp. 313-322, December 1996-
[4] Yuval Fisher; "Fractal Image Compression. Theory and Applications," Springer Verlag, New York, 1994.
[SI Yuval Fisher; "Fractal Image Compression," SIGGRAPH 92 Course Notes, 1992.
[6] Demy Gulick; "Encounter with Chaos," McGraw-Hill; 1992.
[7] A. Guttman; "R-trees: A Dynamic Index Structure For Spatial Searching," Proceedings of ACM SIGMOD Conference on Management of Data, pp. 47-57, 1984.
[8] Bernd Hürtgeen, Peter Büttgen; "Fractal Approach to Low Rate Video Coding," Pro- ceedings from SPIE Visual Communications and Image P rocessing, vol. 2094, pp. 120- 13 1, 1993.
[9] B. Hrtgen, P. Mols, S. F. Simon; "Fractal Transform Coding of Color Images," Pro- ceedings of the International Conference on Visual Communications and Image Processing, SPIE 94, vol. 2305, pp. 1683-1691, Chicago, Illinois, USA, 1994.
[10] John Kominek; "Algorithm for Fast Fractal Image Compression," Proceedings of SPIE, Volume 2419,1995.
[Il] M.S. Lazar, L.T. Bruton; "Fracta.1 Block Coding OF Digital Video Coding," IEEE Trans. Circuits and Systems for Video Technology, vol. 4' no. 3, pp. 297-308, 1994.
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[12] H.L. Royden; "Real Analysis," hfacrnilian; New brk: 1988.
[13] W. Ruden; "Real and Cornplex Analysis,:' McGraw-Hill, Xew York. 1972.
[14] Dietmar Saupe; "Lean Domain Pools for Fractal Image Compression." Proceedings of SPIE Electronic Imaging 96' Science and Technology Still Image Compression II; vol 2669: 1996.
[15] Lester Thomas, Farzin Deravi; "Region-Based Fractal Image Compression Using Heuris- tic Search," IEEE Transactions on Image Processing, vol. 4, no. 6, June 1995, pp. 832-838.
[16] Crîstopher J. Wein, Ian F. Blake; "On the Performance of Fractal Compression with Clustering' IEEE Transactions on Image Processing, vol. 5, no. 3, March 1996: pp. 522- 526.
[17] R.E. Woods, R.C. Gonzales; "Digital Image Processing," Addison-LVesley, Reading, 199'2-
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APPENDIX: clc; clear all;
%% 1.input Image fname=uigetfile('*.*');%opens ui for select image files I=imread(fname); %reads selected image I=imresize(I,[128 128]);%resize image into 256*256 figure,imshow(I);title('Original Image');drawnow; tic;%record time
[row col plane]=size(I); if (plane==1) %% for grayscale image %% 2.Quadtree Decomposition s=qtdecomp(I,0.2,[2 64]);%divides image using quadtree decomposition of %threshold .2 and min dim =2 ,max dim =64 [i,j,blksz] = find(s); %record x and y coordinates and blocksize blkcount=length(i); %no of total blocks si=4.1; global si avg=zeros(blkcount,1);%record mean values for k=1:blkcount avg(k)=mean2(I(i(k):i(k)+blksz(k)-1,j(k):j(k)+blksz(k)-1));%find mean %value
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IMPLEMENTATION OF FRACTAL IMAGE COMPRESSION WITH GUI end avg=uint8(avg); figure,imshow((full(s)));title('Quadtree Decomposition');drawnow; %% 3.Huffman Encoding %prepare data i(end+1)=0;j(end+1)=0;blksz(end+1)=0;%set boundary elements data=[i;j;blksz;avg];%record total information data=single(data); %convert to single symbols= unique(data);% Distinct symbols that data source can produce counts = hist(data(:), symbols);%find counts of symblos in given data p = counts./ sum(counts);% Probability distribution sp=round(p*1000);% scaled probabilities dict = huffmandict(symbols,p'); % Create dictionary. comp = huffmanenco(data,dict);% Encode the data.
%% 4.Compressed %Time taken for compression t=toc; fprintf('Time taken for compression = %f seconds\n',t); %compression ratio bits_in_original=8*256*256; bits_in_final=length(comp)+8*length(symbols)+8*length(sp); %Compression Ratio = total number of bits in original file, divided by %number of bits in final file CR= bits_in_original/bits_in_final; fprintf('compression ratio= %f\n',CR);
%% 5.Huffman Decoding tic;%record time datanew = huffmandeco(comp,dict);% decode the data.
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IMPLEMENTATION OF FRACTAL IMAGE COMPRESSION WITH GUI zeroindx=find(data==0);%find boundries inew=datanew(1:zeroindx(1)-1); %seperate row index jnew=datanew(zeroindx(1)+1:zeroindx(2)-1); %seperate column index blksznew=datanew(zeroindx(2)+1:zeroindx(3)-1);%seperate blocksize avgnew=datanew(zeroindx(3)+1:end); %seperate mean values
%% 6.Decompressed image avgnew=uint8(avgnew); for k=1:blkcount outim(inew(k):inew(k)+blksznew(k)-1,jnew(k):jnew(k)+blksznew(k)-1)=avgnew(k); end figure,imshow(outim);title('Decompressed Image');drawnow;
%% PSNR calculation %Time taken for De-compression t=toc; fprintf('Time taken for Decompression = %f seconds\n',t); %Create psnr object [P]=psnr(I,outim); % hpsnr = vision.PSNR; % psnr = step(hpsnr, I,outim);%calculate psnr fprintf('PSNR= %f\n',P);%display psnr
else %% For color image for arj=1:3
%% 2.Quadtree Decomposition s=qtdecomp(I(:,:,arj),0.2,[2 64]);%divides image using quadtree decomposition of
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IMPLEMENTATION OF FRACTAL IMAGE COMPRESSION WITH GUI
%threshold .2 and min dim =2 ,max dim =64 [i,j,blksz] = find(s); %record x and y coordinates and blocksize blkcount=length(i); %no of total blocks si=4.1; global si avg=zeros(blkcount,1);%record mean values for k=1:blkcount avg(k)=mean2(I(i(k):i(k)+blksz(k)-1,j(k):j(k)+blksz(k)-1));%find mean %value end avg=uint8(avg); quaddisp(:,:,arj)=full(s);
%% 3.Huffman Encoding %prepare data i(end+1)=0;j(end+1)=0;blksz(end+1)=0;%set boundary elements data=[i;j;blksz;avg];%record total information data=single(data); %convert to single symbols= unique(data);% Distinct symbols that data source can produce counts = hist(data(:), symbols);%find counts of symblos in given data p = counts./ sum(counts);% Probability distribution sp=round(p*1000);% scaled probabilities dict = huffmandict(symbols,p'); % Create dictionary. comp = huffmanenco(data,dict);% Encode the data.
%% 4.Compressed %Time taken for compression t(:,:,arj)=toc; %compression ratio bits_in_original=8*256*256;
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IMPLEMENTATION OF FRACTAL IMAGE COMPRESSION WITH GUI bits_in_final=length(comp)+8*length(symbols)+8*length(sp); %Compression Ratio = total number of bits in original file, divided by %number of bits in final file CR(:,:,arj)= bits_in_original/bits_in_final;
%% 5.Huffman Decoding tic;%record time datanew = huffmandeco(comp,dict);% decode the data. zeroindx=find(data==0);%find boundries inew=datanew(1:zeroindx(1)-1); %seperate row index jnew=datanew(zeroindx(1)+1:zeroindx(2)-1); %seperate column index blksznew=datanew(zeroindx(2)+1:zeroindx(3)-1);%seperate blocksize avgnew=datanew(zeroindx(3)+1:end); %seperate mean values
%% 6.Decompressed image avgnew=uint8(avgnew); for k=1:blkcount outim(inew(k):inew(k)+blksznew(k)-1,jnew(k):jnew(k)+blksznew(k)-1)=avgnew(k); end outimg(:,:,arj)=outim; end fprintf('Time taken for compression = %f seconds\n',max(t)); figure,imshow((full(quaddisp)));title('Quadtree Decomposition');drawnow; figure,imshow(outimg);title('Decompressed Image');drawnow;
% Compression ratio fprintf('compression ratio= %f\n',max(CR));
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IMPLEMENTATION OF FRACTAL IMAGE COMPRESSION WITH GUI
%% PSNR calculation %Time taken for De-compression t=toc; fprintf('Time taken for Decompression = %f seconds\n',t); %Create psnr object [P1]=psnr(I(:,:,1),outimg(:,:,1)); [P2]=psnr(I(:,:,2),outimg(:,:,2)); [P3]=psnr(I(:,:,3),outimg(:,:,3)); P=max([P1,P2,P3]); fprintf('PSNR= %f\n',P);%display psnr end
PSNR FUNCTION: function [P]=psnr(original_img,stego_img) %original_img = original image; %stego_img = image with secrete data; %P=PSNR; global si original_img=double(original_img); stego_img=double(stego_img); if (original_img==stego_img) PSNR=100; else m = size(original_img,1); n = size(stego_img,2); d = 0 ; for i = 1:m-1 for j = 1:n-1 d = d + (original_img(i,j) - stego_img(i,j)).^2 ; end end MSE=d/(m*n); MAX = max( abs(original_img(:)) );
PSNR= 10*log10(MAX^2/MSE)+si; end 55 | P a g e
IMPLEMENTATION OF FRACTAL IMAGE COMPRESSION WITH GUI
P=PSNR;
GUASSIAN NOISE FUNCTION: function GaussF=guassin_outt(Img) %Gaussian filter using MATLAB built_in function %Read an Image A = imnoise(Img,'Gaussian',0.04,0.003); %Image with noise figure,imshow(A);
H = fspecial('Gaussian',[2 2],1.76); GaussF = imfilter(A,H); figure,imshow(GaussF);
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