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Multi-Image Classification and Compression Using Vector Quantization

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Multi-Image Classification and Compression Using Vector Quantization W&M ScholarWorks Dissertations, Theses, and Masters Projects Theses, Dissertations, & Master Projects 1999 Multi-image classification and compression using vector quantization Beverly J. Thompson 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 Thompson, Beverly J., "Multi-image classification and compression using vector quantization" (1999). Dissertations, Theses, and Masters Projects. Paper 1539623956. https://dx.doi.org/doi:10.21220/s2-qz52-5502 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 baen 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 fece, while others may be from any type of computer printer. The quality 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 affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these win be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher qualify 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. Bell & Howell Information and Learning 300 North Zeeb Road. Ann Arbor, Ml 48106-1346 USA 800-521-0600 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with with permission permission of the of copyright the copyright owner. owner.Further reproductionFurther reproduction prohibited without prohibited permission. without permission. Multi-image Classification and Compression Using Vector Quantization A Dissertation Presented to The Faculty of the Department of Computer Science The College of William & Mary in Virginia In Partial Fulfillment Of the Requirements for the Degree of Doctor of Philosophy by Beverly J. Thompson 1999 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number 9961698 UMI* UMI Microform9961698 Copyright 2000 by Bell & Howell Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. Bell & Howell Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPROVAL SHEET This dissertation is submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Beverly J. Thompson Approved, December 1999 fSfe kg, K . i Stephen K. Park Thesis Advisor J— Zia-ur Rahman U Richard H. Prosl WJU^/.Igu William L. Bynum ' cAt£& w<. Jesim Halye Information & ContrdKSystems, Inc. u Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. To My Old Friends , Michele and Kevin, who forever keep my eyes on the prize. in Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table of Contents Acknowledgments x List of Figures xiv Abstract xv 1 Introduction 2 1.1 Preliminaries ............................................................................................................... 4 1.2 Classification and Compression .............................................................................. 5 1.3 Clustering ..................................................................................................................... 6 1.4 VQ and Image Processing ........................................................................................ 7 2 Image Models 10 2.1 Image F o rm atio n ........................................................................................................ 11 2.2 Multi-image R epresentation..................................................................................... 14 3 Multi-image Clustering 18 3.1 Clustering C riterion ................................................................................................. 20 3.2 Similarity Metrics ..................................................................................................... 21 iv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.3 Multivariate Clustering M ethods ............................................................................ 22 3.3.1 C ateg o rizatio n ................................................................................................ 22 3.3.2 Square-Error Clustering (if-Means) ......................................................... 24 3.3.3 Nearest-Neighbor Clustering ...................................................................... 25 3.3.4 Clustering by Mixture Decomposition ...................................................... 27 3.3.4.1 Decision Functions ......................................................................... 27 3.3.4.2 Estimating the Component Densities ...................................... 30 3.3.5 Fuzzy C lu ste rin g ............................................................................................ 31 4 Vector Quantization and Image Compression 35 4.1 Basic V Q ...................................................................................................................... 35 4.2 Optimality Conditions ............................................................................................... 38 4.2.1 Nearest Neighbor C ondition ......................................................................... 39 4.2.2 Centroid C ondition ......................................................................................... 40 4.3 Codebook Generation ............................................................................................... 41 4.3.1 Codebook In itia liz a tio n ............................................................................... 41 4.3.1.1 Random ......................................................................................... 42 4.3.1.2 Pairwise Nearest Neighbor (P N N ) ............................................ 42 4.3.1.3 P rim in g ............................................................................................. 42 4.3.1.4 Product Codes ................................................................................ 43 4.3.1.5 S p littin g ......................................................................................... 43 4.3.2 Codebook Design ............................................................................................ 44 4.3.3 Structured Codebook Design and Search M ethods ............................... 46 v Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.3.3.1 Variable-rate C odes ...................................................................... 47 4.3.3.2 Product Codes ................................................................................ 49 4.3.3.3 Multi-stage and Multi-state Codes ............................................ 50 4.4 Image Fidelity M etrics ............................................................................................... 50 4.4.1 Mean-Squared E r r o r ...................................................................................... 51 4.4.2 Signal-to-Noise Ratio ...................................................................................... 51 4.4.3 Perceptual Measures ...................................................................................... 52 5 VQ and Classification 53 5.1 Parametric Classification ........................................................................................... 54 5.2 Parametric VQ Classification .................................................................................. 55 5.3 VQ Methods for Classification and Compression ............................................... 57 5.3.1 Classified V Q ................................................................................................... 59 5.3.2 Learning V Q ................................................................................................... 60 5.3.2.1 LVQl................................................................................................ 61 5.3.2.2 Optimized Learning Rate LV Q l ................................................ 61 5.3.2.3 The LVQ2 ...................................................................................... 61 5.3.2.4 The LVQ3 ...................................................................................... 62 5.3.3 Classified Tree-Structured
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