View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by British Columbia's network of post-secondary digital repositories A New Highly Efficient Algorithm For Lossless Binary Image Compression Lele Zhou B.Sc., The University Of Northern British Columbia, 2004 Thesis Submitted In Partial Fulfillment Of The Requirements For The Degree Of Master Of Science in Mathematical, Computer, and Physical Science (Computer Science) The University Of Northern British Columbia December 2006 © Lele Zhou, 2006 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 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The author retains copyright L'auteur conserve la propriete du droit d'auteur ownership and moral rights in et des droits moraux qui protege cette these. this thesis. Neither the thesis Ni la these ni des extraits substantiels de nor substantial extracts from it celle-ci ne doivent etre imprimes ou autrement may be printed or otherwise reproduits sans son autorisation. reproduced without the author's permission. In compliance with the Canadian Conformement a la loi canadienne Privacy Act some supporting sur la protection de la vie privee, forms may have been removed quelques formulaires secondaires from this thesis. ont ete enleves de cette these. While these forms may be includedBien que ces formulaires in the document page count, aient inclus dans la pagination, their removal does not represent il n'y aura aucun contenu manquant. any loss of content from the thesis. i * i Canada Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Abstract Lossless binary image compression is desirable for the enormous amount of images that are stored and transmitted in a wide range of applications. In this thesis, we present a new efficient algorithm for lossless binary image compression. This algorithm consists of two modules: Direct Redundancy Exploitation and Improved Arithmetic Coding. It is referred to as the Two Module Based Algorithm (TMBA). The Direct Redundancy Exploitation module exploits the two-dimensional redundancy of an image by removing identical consecutive rows and columns of pixels. Binary reference vectors are generated to indicate the exact locations where removals take place so that the removed rows and columns of pixels can be recovered in the decoding process. In the Improved Arithmetic Coding module, the Markov Model order 2 is applied to the reference vectors. A new Static Binary Tree Model is introduced to efficiently model the Reduced Blocks which are produced by the Direct Redundancy Exploitation module. The modelling processes provide the probability distributions which are then used for arithmetic coding. The Two Module Based Algorithm has demonstrated excellent compression performance. The simulation results showed that the proposed algorithm well outperformed the G3 and G4 coding schemes. In addition, the proposed algorithm has also yielded an increase of compression performance in comparison to the JBIG1 and JBIG2 standards. The Two Module Based Algorithm is an efficient method for lossless binary image com­ pression. It offers an alternative approach other than the industrial standards. More impor­ tantly, it has the comparable or better compression performance than the current industrial standards. ii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. To my wife Jing and my son Matthew iii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. “Imagination is more important than knowledge...” — Albert Einstein (1879 - 1955) iv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission Contents Abstract ii Dedication iii Quotation iv Contents v List of Tables vii List of Figures viii List of Programs x Acknowledgments xi 1 Introduction 1 1.1 Thesis Contributions.................................................................................................. 1 1.2 Thesis Outline ........................................................................................................... 2 2 Background 3 2.1 Definitions.................................................................................................................... 4 2.2 Image Compression.................................................................................................... 5 2.3 E n tro p y....................................................................................................................... 6 2.3.1 Zero Order E n tr o p y..................................................................................... 6 2.3.2 First Order E n tro p y ..................................................................................... 7 2.4 Huffman C o d in g ....................................................................................................... 9 2.5 Run Length Coding ................................................................................................. 12 2.5.1 Principle of Run Length Coding ............................................................... 12 v Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.5.2 Probability Based Run Length C oding ......................................................... 13 2.6 Arithmetic C o d in g.................................................................................................... 15 2.6.1 Finite Context M o d ellin g........................................................................... 16 2.6.2 Adaptive Modelling ..................................................................................... 17 2.6.3 The JBIG Standards ..................................................................................... 19 3 The Proposed Algorithm 21 3.1 Direct Redundancy Exploitation (D R E ) .............................................................. 22 3.1.1 Margin Elimination ..................................................................................... 22 3.1.2 Macro Redundancy E x p lo itatio n............................................................... 23 3.1.3 Micro Redundancy Exploitation .............................................................. 25 3.1.4 Summary and Results of the DRE Module ................................................ 29 3.2 Improved Arithmetic Coding (IAC)....................................................................... 32 3.2.1 Context M odelling........................................................................................ 32 3.2.2 Arithmetic C oder........................................................................................... 38 3.2.3 Summary and Results of the IAC M o d u le ............................................... 44 3.3 Simulation R e s u lts....................................................................................................... 44 4 Conclusion 48 A Test Images 50 Bibliography 53 vi Reproduced with permission of the copyright owner. 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List of Tables 2.1 the Initial Alphabet of Nine Symbols.................................................................... 10 2.2 the Codeword for Each S y m b o l.............................................................................. 11 2.3 the Codeword for Each R u n.................................................................................... 13 2.4 Run Length Probability Distribution for Iteapot .................................................. 14 2.5 the Compression Results of order 0 and order 1 onItrain .................................. 17 2.6 the Number of Bits Required to Code the Probability Distributions ............... 18 3.1 DRE Compression Results on 40 Tested Images.................................................. 31 3.2 Compression Results Using Different Orders of M odels......................................... 34 3.3 the Updated Values of Each Iteration of the Encoding Process ......................... 42 3.4 the Decoding Process of Each Sym bol.....................................................................43 3.5 The Average Compression Rate on 40 Tested Images............................................44 3.6 IAC Compression Results on 40 Tested Im ages..................................................... 45 3.7 Compression Results in Bits on 40 Tested Images ........................................... 46 3.8 Compression