DOCSLIB.ORG

Hexagonal Image Processing in the Context of Machine Learning: Conception of a Biologically Inspired Hexagonal Deep Learning Framework

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Hexagonal Image Processing in the Context of Machine Learning: Conception of a Biologically Inspired Hexagonal Deep Learning Framework Hexagonal Image Processing in the Context of Machine Learning: Conception of a Biologically Inspired Hexagonal Deep Learning Framework Tobias Schlosser , Michael Friedrich , and Danny Kowerko Junior Professorship of Media Computing, Chemnitz University of Technology, 09107 Chemnitz, Germany, {firstname.lastname}@cs.tu-chemnitz.de Abstract—Inspired by the human visual perception system, While the structure and functionality of artificial neural hexagonal image processing in the context of machine learning networks is inspired by biological processes, they are also deals with the development of image processing systems that limited by their underlying structure due to the current state combine the advantages of evolutionary motivated structures based on biological models. While conventional state-of-the-art of the art of recording and output devices. Therefore, mostly image processing systems of recording and output devices almost square structures are used, which also significantly restrict exclusively utilize square arranged methods, their hexagonal subsequent image processing systems, as the set of allowed counterparts offer a number of key advantages that can benefit operations is reduced depending on the arrangement of the both researchers and users. This contribution serves as a general underlying structure [4]. application-oriented approach the synthesis of the therefore designed hexagonal image processing framework, called Hexnet, In comparison to the current state of the art in machine the processing steps of hexagonal image transformation, and learning, the human visual perception system suggests an alter- dependent methods. The results of our created test environment native, evolutionarily-based structure, which manifests itself in show that the realized framework surpasses current approaches the human eye. The retina of the human eye displays according of hexagonal image processing systems, while hexagonal artificial to Curcio et al. [5] a particularly strong hexagonal arrangement neural networks can benefit from the implemented hexagonal architecture. As hexagonal lattice format based deep neural of sensory cells, whereas following Middleton and Sivaswamy networks, also called H-DNN, can be compared to their square [6] the processing of incoming signals is handled much more counterparts by transforming classical square lattice based data efficiently. Through the layers of the retina the reduction of sets into their hexagonal representation, they can also result in a the received information to the nerve fibers takes place, which reduction of trainable parameters as well as result in increased are connected to the brain via afferents over the optic nerve. training and test rates. Hubel and Wiesel Index Terms—Computer Vision, Pattern and Image Recogni- [7] demonstrated that the image in the visual tion, Deep Learning, Convolutional Neural Networks, Hexagonal cortex is projected retinotopic, whereas adjacent structures of Image Processing, Hexagonal Lattice, Hexagonal Sampling the retina are preserved and processed through the following areas of the brain. I. INTRODUCTION AND MOTIVATION The use of hexagonal structures emerges therefore as an evolutionarily motivated approach. Compared to its square Following the developments of recent years, machine learn- counterpart, the hexagonal lattice format (Fig.1) features a ing methods in the form of artificial neural networks are be- number of decisive advantages. These include the homogeneity arXiv:1911.11251v7 [cs.LG] 18 Mar 2021 coming increasingly important. Convolutional neural networks of the hexagonal lattice format, whereby the equidistance and (CNN) for object recognition and classification in this context uniqueness of neighborhood as well as an increased radial are one of the approaches that are in the focus of current symmetry are given. Together with an by 13:4 % increased research in the domain of deep learning. In order to meet transformation efficiency as shown by Petersen and Middleton the ever-increasing demands of more complex problems, novel [8] and Mersereau [9], hexagonal representations enable the application areas, and larger data sets, following Krizhevsky et storage of larger amounts of data on the same number of al. [1], more and more novel models and procedures are being sampling points, which following Golay [10] result in reduced developed, as their complexity and diversity following Szegedy computation times, less quantization errors, and an increased et al. [2] steadily increases. However, novel architectures efficiency in programming. for artificial neural networks, including convolutional and pooling layers, are being developed that exceed the conven- A. Related work tional cartesian-based architectures. These include, but are not Current hexagonal image processing research includes ap- limited to, spherical or non-Euclidean manifolds, as current plications in the fields of observation, experiment, and simula- research by Bronstein et al. [3] demonstrates. tion in ecology by Birch et al. [11], the design of geodesic grid 978-1-7281-4550-1/19/$31.00 © 2019 IEEE, 10.1109/ICMLA.2019.00300 y y z 0 1 2 3 2 (0, 0) (1, 0) (2, 0) (0, 1) (1, 1) 3 4 5 4 0 1 1 x p 1 1 x (0, 1) (1, 1) (2, 1) (-1, 0) (0, 0) (1, 0) 2 6 7 8 5 6 (0, 2) (1, 2) (2, 2) (-1, -1) (0, -1) (a) Linewise address- (b) Spiral addressing ing [27], [28] (a) Square lattice format (b) Hexagonal lattice format 23 22 Figure 1: Square and hexagonal lattice format in comparison. (1, 4) (2, 4) 24 20 21 13 12 (0, 3) (1, 3) (2, 3) (3, 3) (4, 3) 33 32 25 26 14 10 11 systems by Sahr et al. [12], sensor-based image processing and (-2, 2) (-1, 2) (0, 2) (1, 2) (2, 2) (3, 2) (4, 2) 34 30 31 3 2 15 16 remote sensing [13], [14], [15], medical imaging [16], [17], (-3, 1) (-2, 1) (-1, 1) (0, 1) (1, 1) (2, 1) (3, 1) 35 36 4 0 1 63 62 [18], and image synthesis [19]. (-3, 0) (-2, 0) (-1, 0) (0, 0) (1, 0) (2, 0) (3, 0) Furthermore, first experimental results for supply demand 43 42 5 6 64 60 61 (-3, -1) (-2, -1) (-1, -1) (0, -1) (1, -1) (2, -1) (3, -1) forecasting by Ke et al. (2018) [20] and the analysis of atmo- 44 40 41 53 52 65 66 spheric telescope data for event detection and classification (-4, -2) (-3, -2) (-2, -2) (-1, -2) (0, -2) (1, -2) (2, -2) 45 46 54 50 51 by Erdmann et al. (2018) [21] and Shilon et al. (2019) [22] (-4, -3) (-3, -3) (-2, -3) (-1, -3) (0, -3) give an overview over currently emerging application areas for 55 56 hexagonal image processing in the context of machine learn- (-2, -4) (-1, -4) ing. These application areas show promising opportunities as (c) Combination of (a) and (b) current research often deploys an initial processing step to Figure 2: Construction of hexagonal addressing schemes. transform the given hexagonal lattice format based image data into a square representation [23], [24]. As the amount of research which combines principles from As this contribution aims to benefit both researchers and hexagonal image processing and machine learning is quite lim- users alike by providing the necessary tools to ease the ited, this contribution also aims to overcome the downsides of application and development of hexagonal models, we will currently developed hexagonal machine learning approaches. also provide the tools to evaluate said models with focus These include not only the development of hexagonal convo- on their performance and transformation quality as compared lutional layers following Hoogeboom et al. (2018) [25] and to classical square and hexagonal lattice format based ap- Steppa and Holch (2019) [26], but also the implementation proaches. The related developed architectures, procedures, of the underlying addressing scheme as well as the necessary and test results, including future developments and further processing steps for transformation and visualization. application-specific contributions, are made publicly available to the research community via open science and are found on B. Contribution of this work the project page of Hexnet and its repository1. In order to combine the advantages of the research fields of hexagonal image processing and machine learning in the II. FUNDAMENTALS AND METHODS form of deep neural networks, this contribution serves as To allow the addressing, transformation, and visualization a general application-oriented approach the conception of a of images in their hexagonal representation, the necessary first hexagonal deep learning framework. While serving the processing steps as well as their underlying addressing scheme recognition and classification of objects in larger data sets have to be determined. The following sections introduce our where the original image resolution often needs to be reduced proposed hexagonal addressing scheme as identified for its as an initial processing step, the necessary information content applicability in comparison to currently deployed square and should also be maximized. With focus on the implementation hexagonal lattice format based architectures. In conjunction of the underlying structure, the designed framework, called with the proposed architecture, we will then introduce the Hexnet, includes the necessary processing steps as well as its principles of hexagonal image processing in the context of underlying hexagonal addressing scheme. deep learning. However, as hexagonal image data has to be captured using a hexagonal sensor, and the corresponding hardware is A. The hexagonal addressing scheme either rare or limited in its applicability, alternatives include While the one-dimensional spiral architecture addressing the transformation or synthesis of hexagonal image data. scheme (SAA) introduced by Burt [27] and Gibson and Lucas Therefore, the question arises, in which way and to what [28] established itself as the preferred addressing scheme degree currently deployed square lattice format based data sets for hexagonal lattice format based image processing systems can be leveraged in the context of hexagonal deep learning approaches. 1https://github.com/TSchlosser13/Hexnet Input (75 × 86) FM2 (6 @ 8 × 9) FCLs + Output FM3 (6 @ 3 × 3) FM1 (6 @ 25 × 28) .
Load more

Recommended publications
  • Hexagonal Structure for Intelligent Vision
    © 2005 IEEE. Reprinted, with permission, from Xiangjian He, Hexagonal Structure for Intelligent Vision . Information and Communication Technologies, 2005. ICICT 2005. First International Conference on, August 2005. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Technology, Sydney's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs- [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it HEXAGONAL STRUCTURE FOR INTELLIGENT VISION Xiangjian He and Wenjing Jia Computer Vision Research Group Faculty of Information Technology University of Technology, Sydney Australia Abstract: greater angular resolution, and a reduced need of storage Using hexagonal grids to represent digital images has and computation in image processing operations. been studied for more than 40 years. Increased processing In spite of its numerous advantages, hexagonal grid has so capabilities of graphic devices and recent improvements in far not yet been widely used in computer vision and CCD technology have made hexagonal sampling graphics field. The main problem that limits the use of attractive for practical applications and brought new hexagonal image structure is believed due to lack of interests on this topic. The hexagonal structure is hardware for capturing and displaying hexagonal-based considered to be preferable to the rectangular structure images.
    [Show full text]
  • Multidimensional Sampling Dr
    Multidimensional Sampling Dr. Vishal Monga Motivation for the General Case for Sampling We need the more general case to treat three important applications. 1. Human Vision System: the human vision system is a nonlinear, spatially- varying, non-uniformly sampled system. Rods and cones on the retina, which spatially sample are not arranged in rows and columns. a. Hexagonal Sampling: when modeled as a linear shift-invariant system, the human visual system is circularly bandlimited (lowpass in radial frequency). The optimal uniform sampling grid is hexagonal. Optimal means that we need the fewest discrete-time samples to sample the continuous-space analog signal without aliasing. b. Foveated grid: This is based on the fovea in the retina. When you focus on an object, you sample the object at a high resolution, and the resolution falls off away from the point-of-focus. Shown below is a simple example of a foveated grid. The grid is a 4 x 4 uniform sampling with each of the middle four grids subdivided into 4 x 4 grids themselves. The point of focus is at the middle of the grid. We can convert this grid to a uniform grid in several ways. For example, we could start with a rectangular grid and keep the resolution at the point-of-focus. Then, away from the point-of-focus, we can average the pixel values in increasingly larger blocks of samples. This approach allows the use a foveated grid while maintaining compatibility with systems that require rectangular sampling (e.g. image and video compression standards). 2. Television 650 samples /row 362.5 rows /interlace 2 interlaces /frame 30 frames /sec No two samples taken at the same instant of time Can signals be sampled this way without losing information? How can we handle a.
    [Show full text]
  • ARRAY SET ADDRESSING: ENABLING EFFICIENT HEXAGONALLY SAMPLED IMAGE PROCESSING by NICHOLAS I. RUMMELT a DISSERTATION PRESENTED TO
    ARRAY SET ADDRESSING: ENABLING EFFICIENT HEXAGONALLY SAMPLED IMAGE PROCESSING By NICHOLAS I. RUMMELT A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2010 1 °c 2010 Nicholas I. Rummelt 2 To my beautiful wife and our three wonderful children 3 ACKNOWLEDGMENTS Thanks go out to my family for their support, understanding, and encouragement. I especially want to thank my advisor and committee chair, Joseph N. Wilson, for his keen insight, encouragement, and excellent guidance. I would also like to thank the other members of my committee: Paul Gader, Arunava Banerjee, Jeffery Ho, and Warren Dixon. I would like to thank the Air Force Research Laboratory (AFRL) for generously providing the opportunity, time, and funding. There are many people at AFRL that played some role in my success in this endeavor to whom I owe a debt of gratitude. I would like to specifically thank T.J. Klausutis, Ric Wehling, James Moore, Buddy Goldsmith, Clark Furlong, David Gray, Paul McCarley, Jimmy Touma, Tony Thompson, Marta Fackler, Mike Miller, Rob Murphy, John Pletcher, and Bob Sierakowski. 4 TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................. 4 LIST OF TABLES ...................................... 7 LIST OF FIGURES ..................................... 8 ABSTRACT ......................................... 10 CHAPTER 1 INTRODUCTION AND BACKGROUND ...................... 11 1.1 Introduction ................................... 11 1.2 Background ................................... 11 1.3 Recent Related Research ........................... 15 1.4 Recent Related Academic Research ..................... 16 1.5 Hexagonal Image Formation and Display Considerations ......... 17 1.5.1 Converting from Rectangularly Sampled Images .......... 17 1.5.2 Hexagonal Imagers ..........................
    [Show full text]
  • Hexagonal QMF Banks and Wavelets
    Hexagonal QMF Banks and Wavelets A chapter within Time-Frequency and Wavelet Transforms in Biomedical Engineering, M. Akay (Editor), New York, NY: IEEE Press, 1997. Sergio Schuler and Andrew Laine Computer and Information Science and Engineering Department UniversityofFlorida Gainesville, FL 32611 2 Hexagonal QMF Banks and Wavelets Sergio Schuler and Andrew Laine Department of Computer and Information Science and Engineering University of Florida Gainesville, FL 32611 Introduction In this chapter weshalllay bare the theory and implementation details of hexagonal sampling systems and hexagonal quadrature mirror lters (HQMF). Hexagonal sampling systems are of particular interest b ecause they exhibit the tightest packing of all regular two-dimensional sampling systems and for a circularly band-limited waveform, hexagonal sampling requires 13.4 p ercentfewer samples than rectangular sampling [1]. In addition, hexagonal sampling systems also lead to nonseparable quadrature mirror lters in which all basis functions are lo calized in space, spatial frequency and orientation [2]. This chapter is organized in two sections. Section I describ es the theoretical asp ects of hexagonal sampling systems while Section I I covers imp ortant implementation details. I. Hexagonal sampling system This section presents the theoretical foundation of hexagonal sampling systems and hexagonal quadrature mirror lters. Most of this material has app eared elsewhere in [1], [3], [4], [5], [2], [6] but is describ ed here under a uni ed notation for completeness. In addition, it will provide continuity and a foundation for the original material that follows in Section I I. The rest of the section is organized as follows. Section I-A covers the general formulation of a hexagonal sampling system.
    [Show full text]
  • DCT Coding of Nonrectangularly Sampled Images Emre Giinduzhan, A
    IEEE SIGNAL PROCESSING LETTERS, VOL. 1, NO. 9, SEPTEMBER 1994 131 DCT Coding of Nonrectangularly Sampled Images Emre Giinduzhan, A. Enis Cetin, and A Murat Tekalp ... Abstmct-Discrete cosine transform (DCT) coding is widely used for compression of re.ctangularly sampled images. In this .... ................ letter, we address efficient DCT coding of "rectangularly sam- ... ....... pled images. To eKect, we discuss efecient method for .......... this an -....__ -._. the computation of the DCT on nomctanpb sampling grids .. ..........~--__ using the Smith-normal &"position. Sim- results are provided. .... .......... I. INTRODUCTION ...I.. ...... ... N DIGITAL representation of multidimensional (M-D) .... Isignals, various sampling structures can be used that are usually in the form of a lattice or a union of coset of a N=[; :]=[2-1]r-110312 '1 lattice [ 11. Rectangular sampling grids (orthogonal lattices) are the most commonly used lattice smcture. It is well Fig. 1. Coordinate transformation in a hexagonal lattice. known that the sampling efficiency of e depends on the region of support of the spectrum malog signal [2]r [3]. In still images, a 2-D nonreckuguhr sampling grid is first transformed onto a new coordinate system, where it is may require. a smaller number of sampks'per unit area than rectangularly periodic. Rectangular M-D DCT of the trans- a rectangular grid. In video, interlaced sampling grids (3-D formed sequence is computed in the new coordinates, and the nonrectangular @ids) are widely used for reduced flickering result is transformed back to the original coordinates. A short without increasing the transmission bandwidth. review of the notation and the Smith-normal decomposition Most algorithm currently used for processing and compres- is given in Section 11.
    [Show full text]
  • A New Family of Rotation-Covariant Wavelets on the Hexagonal Lattice
    A new family of rotation-covariant wavelets on the hexagonal lattice Laurent Condata, Brigitte Forster-Heinleina and Dimitri Van De Villeb aGSF - National Research Center for Environment and Health, 85764 Neuherberg, Germany bBiomedical Imaging Group (BIG), EPFL, CH-1015 Lausanne, Switzerland ABSTRACT We present multiresolution spaces of complex rotation-covariant functions, deployed on the 2-D hexagonal lattice. The designed wavelets, which are complex-valued, provide an important phase information for image analysis, which is missing in the discrete wavelet transform with real wavelets. Moreover, the hexagonal lattice allows to build wavelets having a more isotropic magnitude than on the Cartesian lattice. The associated filters, fully characterized in the Fourier domain, yield an efficient FFT-based implementation. Keywords: Complex wavelets, 2-D lattices, hexagonal sampling, multiresolution, scaling functions, rotation- covariance 1. INTRODUCTION Multiresolution analysis and the discrete wavelet transform (DWT) have proved to form a powerful framework in a wide range of signal processing applications. When applied to 2-D signals and images defined on the traditional Cartesian lattice, the most frequently used DWT are separable; their basis functions and filters are simply tensor products of the 1-D ones, which makes the implementation simple. The downside, however, is that these decompositions tend to privilege the vertical and horizontal directions. They also create a “diagonal” cross-term that does not have a straightforward directional interpretation. So, the need exists for transforms able to correct this deficiency of the separable transforms and to capture the regularity of 1-D singularities having arbitrary orientations, like edges in the images. Non-separable wavelets, by contrast, offer more freedom and can be better tuned to provide more isotropy.
    [Show full text]
  • Application of Randomized Sampling Schemes to Curvelet-Based Sparsity
    Application of randomized sampling schemes to curvelet-based sparsity-promoting seismic data recovery Reza Shahidi1 ([email protected]), Gang Tang12 ([email protected]), Jianwei Ma3 ([email protected]) and Felix J. Herrmann1 ([email protected]) 1Seismic Laboratory for Imaging and Modeling, Department of Earth and Ocean Sciences, The University of British Columbia, 6339 Stores Road, Vancouver, BC, Canada, V6T 1Z4 2Research Institute of Petroleum Exploration and Development, PetroChina, Beijing, China 3Institute of Applied Mathematics, Harbin Institute of Technology, Harbin, China 1 ABSTRACT Reconstruction of seismic data is routinely used to improve the quality and resolu- tion of seismic data from incomplete acquired seismic recordings. Curvelet-based Recovery by Sparsity-promoting Inversion, adapted from the recently-developed theory of compressive sensing, is one such kind of reconstruction, especially good for recovery of undersampled seismic data. Like traditional Fourier-based methods, it performs best when used in conjunction with randomized subsampling, which converts aliases from the usual regular periodic subsampling into easy-to-eliminate noise. By virtue of its ability to control gap size, along with the random and irregular nature of its sampling pattern, jittered (sub)sampling is one proven method that has been used successfully for the determination of geophone positions along a seismic line. In this paper, we extend jittered sampling to two-dimensional acquisition design, a more difficult problem, with both underlying Cartesian, and hexagonal grids. We also study what we term separable and non-separable two-dimensional jittered samplings. We find hexagonal jittered sam- pling performs better than Cartesian jittered sampling, while fully non-separable jittered sampling performs better than separable jittered sampling.
    [Show full text]
  • Sampling and Quantization for Optimal Reconstruction by Shay Maymon Submitted to the Department of Electrical Engineering and Computer Science
    Sampling and Quantization for Optimal Reconstruction by Shay Maymon Submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements for the degree of MASSACHUSETTS INSTITUTE OF TECHNOLOGY Doctor of Philosophy in Electrical Engineering JUN 17 2011 at the LIBRARIES MASSACHUSETTS INSTITUTE OF TECHNOLOGY ARCHiVES June 2011 @ Massachusetts Institute of Technology 2011. All rights reserved. Author ..... .......... De 'artment of'EYectrical Engineerin /d Computer Science May 17,2011 Certified by.. Alan V. Oppenheim Ford Professor of Engineering Thesis Supervisor Accepted by............ Profeksor Lelif". Kolodziejski Chairman, Department Committee on Graduate Theses 2 Sampling and Quantization for Optimal Reconstruction by Shay Maymon Submitted to the Department of Electrical Engineering and Computer Science on May 17, 2011, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Electrical Engineering Abstract This thesis develops several approaches for signal sampling and reconstruction given differ- ent assumptions about the signal, the type of errors that occur, and the information available about the signal. The thesis first considers the effects of quantization in the environment of interleaved, oversampled multi-channel measurements with the potential of different quan- tization step size in each channel and varied timing offsets between channels. Considering sampling together with quantization in the digital representation of the continuous-time signal is shown to be advantageous. With uniform quantization and equal quantizer step size in each channel, the effective overall signal-to-noise ratio in the reconstructed output is shown to be maximized when the timing offsets between channels are identical, result- ing in uniform sampling when the channels are interleaved.
    [Show full text]
  • Simoncelli89-Reprint
    Non-Separable Extensions of Quadrature Mirror Filters to Multiple Dimensions Quadrature Mirror Filter (QMF) banks have been used in a variety perfect reconstruction filter banks based on a polyphase of one-dimensional signal processing applications, and have been matrix decomposition in the frequency domain [7]. Vetterli applied separably in two dimensions. As with most one-dimen- sional filters, separable extension to multiple dimensions pro- was the first to propose the use of QMFs for image decom- duces a transform in which the orientation selectivity of some of position [8]. He showed examples of both separable and the high-pass filters is poor. We describe generalized non-separa- non-separable non-oriented QMF decompositions in two ble extensions of QMF banks to two and three dimensions, in dimensions. Vaidyanathan established criteria for perfect which the orientation specificity of the high-pass filters is greatly improved. In particular, we discuss extensions to two dimensions reconstruction QMF banks for two-dimensional applica- with hexagonal symmetry, and three dimensional spatio-temporal tions [9]. Viscito and Allebach developed perfect recon- extensions with rhombic-dodecahedral symmetry. Although these struction multi-dimensional filter banks with arbitrarydeci- filters are conceived and designed on non-standard sampling lat- mation patterns [IO]. Woods and O’Neil used separable tices, they may be applied to rectangularly sampled images. As in QMFs for image data compression [Ill. Several other one dimension, these transformations may be hierarchically cas- caded to form a multi-scale “pyramid” representation. We design authors have used QMF pyramid transforms for data a set of example filters and apply them to the problems of image compression [12]-[14].
    [Show full text]
  • Subband Vector Quantization of Images Using Hexagonal Filter Banks 1
    Subband Vector Quantization of Images Using Hexagonal Filter Banks 1 Osama S. Haddadin, V. John Mathews, and Thomas G. Stockham, Jr. Department of Electrical Engineering University of Utah Salt Lake City, Utah 84112 Abstract Results of psychophysical experiments on human vision conducted in the last three decades indicate that the eye performs a multichannel decomposition of the incident images. This paper presents a subband vector quantization algorithm that employs hexagonal filter banks. The hexagonal filter bank provides an image de­ composition similar to what the eye is believed to do. Consequently, the image coder is able to make use of the properties of the human visual system and produce compressed images of high quality at low bit rates. We present a systematic ap­ proach for optimal allocation of available bits among the subbands and also for the selection of the size of the vectors in each of the subbands. 1. Introduction Vector quantization (VQ) is a very powerful approach to data compression and has been successfully applied to a variety of signals [7J [17J [20J. In VQ a sequence of continuous or high rate discrete k-dimensional vectors is mapped into a sequence suitable for transmission over a digital channel or storage. The simplest form of vector quantizer operates as follows. First, a codebook of k-dimensional vectors is created using a training set representative of the waveforms. Once the codebook is designed and the representative vectors are stored, the process of encoding the incoming waveform can begin. k consecutive samples of the waveform are grouped together to form a k-dimensional vector at the input of the vector quantizer.
    [Show full text]
  • Chapter 4 Subband Transforms
    MIT Media Laboratory Vision and Modeling Technical Report Appears in Subband Coding edited by John Woods Kluwer Academic Press Chapter Subband Transforms y z Eero PSimoncelli and Edward H Adelson Vision Science Group The Media Lab oratoryand y DepartmentofElectrical Engineering and Computer Science z Departmentof Brain and CognitiveScience Massachusetts Institute of Technology Cambridge Massachusetts Linear transforms are the basis for manytechniques used in image pro cessing image analysis and image co ding Subband transforms are a sub class of linear transforms whichoer useful prop erties for these applications In this chapter wediscuss a varietyofsubband decomp ositions and illustrate their use in image co ding Traditionallycoders based on linear transforms are divided into twocategories transform co ders and subband co ders This distinction is due in part to the nature of the computational metho ds used for the twotyp es of representation Transform co ding techniques are usually based on orthogonal linear trans forms The classic example of suchatransform is the discrete Fourier trans form DFT whichdecomp oses a signal into sinusoidal frequency comp o nents Twoother examples are the discrete cosine transform DCT and the KarhunenLo evetransform KLT Conceptually these transforms are com puted bytaking the inner pro duct of the nitelength signal with a set of basis functions This pro duces a set of co ecients which are then passed on to the This work was supp orted bycontracts with the IBM Corp oration agreementdated and DARPA Rome
    [Show full text]
  • End-To-End Analysis of Hexagonal Vs Rectangular Sampling in Digital Imaging Systems
    W&M ScholarWorks Dissertations, Theses, and Masters Projects Theses, Dissertations, & Master Projects 1993 End-to-end analysis of hexagonal vs rectangular sampling in digital imaging systems John Clifton Burton II College of William & Mary - Arts & Sciences Follow this and additional works at: https://scholarworks.wm.edu/etd Part of the Computer Sciences Commons Recommended Citation Burton, John Clifton II, "End-to-end analysis of hexagonal vs rectangular sampling in digital imaging systems" (1993). Dissertations, Theses, and Masters Projects. Paper 1539623834. https://dx.doi.org/doi:10.21220/s2-19ge-rt36 This Dissertation is brought to you for free and open access by the Theses, Dissertations, & Master Projects at W&M ScholarWorks. It has been accepted for inclusion in Dissertations, Theses, and Masters Projects by an authorized administrator of W&M ScholarWorks. For more information, please contact [email protected]. INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The q u a li t y of this reproduction Is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely afreet reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion.
    [Show full text]