Fractal-Based Image and Video Coding

This chapter reviews the theoretical foundations and implementation issues of fractal-based image coding methods. The concepts of fractals, iterated function systems, and local iterated function systems are discussed and different implementations of compression of both still images and image sequences are reviewed.

[1]  Dietmar Saupe,et al.  Chaos and fractals - new frontiers of science , 1992 .

[2]  Monson H. Hayes,et al.  Video coding based on iterated function systems , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[3]  Michael C. Stein Fractal Image Models And Object Detection , 1987, Other Conferences.

[4]  Edward R. Vrscay,et al.  Iterated Function Systems and the Inverse Problem of Fractal Construction Using Moments , 1989, Computers and Mathematics.

[5]  Michael F. Barnsley,et al.  Fractals everywhere , 1988 .

[6]  M. Barnsley,et al.  Solution of an inverse problem for fractals and other sets. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[7]  Giorgio Mantica,et al.  Chaotic Optimization and the Construction of Fractals: Solution of an Inverse Problem , 1989, Complex Syst..

[8]  Kenneth J. Hintz,et al.  Fractional Brownian motion models for synthetic aperture radar imagery scene segmentation , 1993, Proc. IEEE.

[9]  Giorgio Mantica,et al.  Inverse problems in fractal construction: moment method solution , 1990 .

[10]  Reginald L. Lagendijk,et al.  Fractal coding in an object-based system , 1994, Proceedings of 1st International Conference on Image Processing.

[11]  Hong Yan,et al.  Hybrid image compression method based on fractal geometry , 1991 .

[12]  Bernd Hürtgen,et al.  Fractal approach to low-rate video coding , 1993, Other Conferences.

[13]  F. Arduini,et al.  ON COMPUTING MULTIFRACTALITY FOR TEXTURE DISCRIMINATION , 1992 .

[14]  M. Barnsley Fractal modelling of real world images , 1988 .

[15]  Dietmar Saupe,et al.  Breaking the Time Complexity of Fractal Image Compression , 1994 .

[16]  T. Peli Multiscale fractal theory and object characterization , 1990 .

[17]  M. Kabrisky,et al.  Synthetic aperture radar segmentation using wavelets and fractals , 1991, IEEE 1991 International Conference on Systems Engineering.

[18]  Leonard T. Bruton,et al.  Fractal block coding of digital video , 1994, IEEE Trans. Circuits Syst. Video Technol..

[19]  J.M.T. Thompson,et al.  Chaotic dynamics and fractals , 1987 .

[20]  Tor A. Ramstad,et al.  Attractor image compression with a fast non-iterative decoding algorithm , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[21]  M. Barnsley,et al.  A new class of markov processes for image encoding , 1988, Advances in Applied Probability.

[22]  Alex Pentland Fractal Surface Models For Communication About Terrain , 1987, Other Conferences.

[23]  David W. Lin,et al.  Fractal image coding as generalized predictive coding , 1994, Proceedings of 1st International Conference on Image Processing.

[24]  L.P. Hurd,et al.  Fractal video compression , 1992, Digest of Papers COMPCON Spring 1992.

[25]  Chienchung Chang,et al.  Fractal based approach to shape description, reconstruction and classification , 1989, Twenty-Third Asilomar Conference on Signals, Systems and Computers, 1989..

[26]  Arnaud E. Jacquin,et al.  Image coding based on a fractal theory of iterated contractive image transformations , 1992, IEEE Trans. Image Process..

[27]  Alex Pentland,et al.  Fractal-Based Description of Natural Scenes , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[28]  Simonetta Abenda,et al.  Inverse problem for fractal sets on the real line via the moment method , 1989 .

[29]  Kai Uwe Barthel,et al.  A new image coding technique unifying fractal and transform coding , 1994, Proceedings of 1st International Conference on Image Processing.

[30]  Edward R. Vrscay,et al.  “Missing moment” and perturbative methods for polynomial iterated function systems , 1991 .

[31]  Franklin Mendivil,et al.  Genetic Algorithms for the 1-D Fractal Inverse Problem , 1991, ICGA.

[32]  Stephen Demko,et al.  Stable recovery of fractal measures by polynomial sampling , 1991 .

[33]  Monson H. Hayes,et al.  Adaptive IFS image coding with proximity maps , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[34]  Joseph Naor,et al.  Multiple Resolution Texture Analysis and Classification , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[35]  F. Arduini,et al.  A multifractal-based approach to natural scene analysis , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

[36]  S. C. Kwatra,et al.  A data compression algorithm for color images based on run-length coding and fractal geometry , 1988, IEEE International Conference on Communications, - Spanning the Universe..

[37]  Jarkko Kari,et al.  Inference algorithms for WFA and image compression , 1995 .

[38]  James A. Storer,et al.  DCC '92 : Data Compression Conference , 1991 .

[39]  James M. Keller,et al.  Characteristics of Natural Scenes Related to the Fractal Dimension , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[40]  Arnaud E. Jacquin,et al.  A novel fractal block-coding technique for digital images , 1990, International Conference on Acoustics, Speech, and Signal Processing.

[41]  Y. Fisher Fractal image compression: theory and application , 1995 .

[42]  D. Malah,et al.  Fractal representation of images via the discrete wavelet transform , 1995, Eighteenth Convention of Electrical and Electronics Engineers in Israel.

[43]  Rae-Hong Park,et al.  Image coding based on fractal approximation and vector quantization , 1994, Proceedings of 1st International Conference on Image Processing.

[44]  Donald M. Monro,et al.  Fractal block coding of images , 1992 .

[45]  R. J. Stevens,et al.  Manipulation and Presentation of Multidimensional Image Data Using the Peano Scan , 1983, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[46]  Edward R. Vrscay,et al.  Solving The Inverse Problem For Function/image Approximation Using Iterated Function Systems Ii. Alg , 1994 .

[47]  Oleg Kiselyov,et al.  Self-similarity of the multiresolutional image/video decomposition: smart expansion as compression of still and moving pictures , 1994, Proceedings of IEEE Data Compression Conference (DCC'94).

[48]  Dietmar Saupe,et al.  Accelerating fractal image compression by multi-dimensional nearest neighbor search , 1995, Proceedings DCC '95 Data Compression Conference.

[49]  M. Barnsley,et al.  Invariant measures for Markov processes arising from iterated function systems with place-dependent , 1988 .

[50]  Kenneth Falconer,et al.  Fractal Geometry: Mathematical Foundations and Applications , 1990 .

[51]  Erich Kaltofen,et al.  Computers and Mathematics , 1989, Springer US.

[52]  D. Field,et al.  Human discrimination of fractal images. , 1990, Journal of the Optical Society of America. A, Optics and image science.

[53]  Roberto Rinaldo,et al.  Inverse and approximation problem for two-dimensional fractal sets , 1994, IEEE Trans. Image Process..

[54]  R. Devaney,et al.  Chaos and Fractals: The Mathematics Behind the Computer Graphics , 1989 .

[55]  S. A. Rajala,et al.  Texture segmentation-based image coder incorporating properties of the human visual system , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

[56]  M. Barnsley,et al.  Recurrent iterated function systems , 1989 .

[57]  Edward R. Vrscay,et al.  SOLVING THE INVERSE PROBLEM FOR FUNCTION/IMAGE APPROXIMATION USING ITERATED FUNCTION SYSTEMS I: THEORETICAL BASIS , 1994 .

[58]  Donald M. Monro,et al.  REAL TIME FRACTAL VIDEO FOR PERSONAL COMMUNICATIONS , 1994 .

[59]  Yuval Fisher,et al.  Fractal encoding with HV partitions , 1995 .

[60]  N. D. Durie,et al.  Digest of papers , 1976 .

[61]  Kiyoharu Aizawa,et al.  Structural edge detection based on fractal analysis for image compression , 1992, [Proceedings] 1992 IEEE International Symposium on Circuits and Systems.

[62]  E. Reusens Overlapped partitioning for sequence coding based on the fractal theory of iterated transformations systems , 1994 .

[63]  Lyman P. Hurd,et al.  Fractal image compression , 1993 .

[64]  A. Jacquin A fractal theory of iterated Markov operators with applications to digital image coding , 1989 .

[65]  I. Good,et al.  Fractals: Form, Chance and Dimension , 1978 .

[66]  Heinz-Otto Peitgen,et al.  The science of fractal images , 2011 .

[67]  E. Bacry,et al.  Solving the Inverse Fractal Problem from Wavelet Analysis , 1994 .

[68]  Arnaud E. Jacquin,et al.  Application Of Recurrent Iterated Function Systems To Images , 1988, Other Conferences.

[69]  E. W. Jacobs,et al.  Fractal-Based Image Compression , 1989 .

[70]  Jerome M. Shapiro,et al.  Embedded image coding using zerotrees of wavelet coefficients , 1993, IEEE Trans. Signal Process..

[71]  Michael Mills,et al.  Fractal based image coding scheme using Peano scan , 1988, 1988., IEEE International Symposium on Circuits and Systems.

[72]  Y. Fisher,et al.  Image compression: A study of the iterated transform method , 1992, Signal Process..

[73]  Gregory K. Wallace,et al.  The JPEG still picture compression standard , 1992 .

[74]  Roberto Rinaldo,et al.  Image coding by block prediction of multiresolution subimages , 1995, IEEE Trans. Image Process..

[75]  F. Arduini,et al.  Fractal dimension estimation by adaptive mask selection , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[76]  Jiaxiong Peng,et al.  Fractal approximation of image block in its neighbor and fractal coding , 1997, 1997 IEEE International Conference on Intelligent Processing Systems (Cat. No.97TH8335).

[77]  Zheng Yan,et al.  Approximation of measures by Markov processes and homogeneous affine iterated function systems , 1989 .

[78]  Ari M. Vepsalainen,et al.  Estimating of Fractal and Correlation Dimension from 2D and 3D-Images , 1989, Other Conferences.

[79]  S Abenda Inverse problem for one-dimensional fractal measures via iterated function systems and the moment method , 1990 .

[80]  Walter S. Kuklinski UTILIZATION OF FRACTAL IMAGE MODELS IN MEDICAL IMAGE PROCESSING , 1994 .

[81]  G. A. Edgar Measure, Topology, and Fractal Geometry , 1990 .

[82]  Daniel N. Rogovin,et al.  Fractal (self-VQ) encoding of video sequences , 1994, Other Conferences.

[83]  D. Saupe,et al.  Complexity Reduction Methods for Fractal Image Compression , 1994 .

[84]  H. K. Ramapriyan Proceedings of the Scientific Data Compression Workshop , 1989 .

[85]  Edward R. Vrscay,et al.  Iterated fuzzy set systems: A new approach to the inverse problem for fractals and other sets , 1992 .

[86]  Michael F. Barnsley MAKING CHAOTIC DYNAMICAL SYSTEMS TO ORDER , 1986 .

[87]  Roberto Rinaldo,et al.  Inverse problem for two-dimensional fractal sets using the wavelet transform and the moment method , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[88]  E. Walach,et al.  A fractal based approach to image compression , 1986, ICASSP '86. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[89]  Roberto Rinaldo,et al.  An image coding scheme using block prediction of the pyramid subband decomposition , 1994, Proceedings of 1st International Conference on Image Processing.

[90]  A. Jacquin Fractal image coding: a review , 1993, Proc. IEEE.

[91]  J. L. Véhel,et al.  MULTIFRACTAL SEGMENTATION OF IMAGES , 1994 .

[92]  G. Davis,et al.  Self-quantized wavelet subtrees: a wavelet-based theory for fractal image compression , 1995, Proceedings DCC '95 Data Compression Conference.

[93]  Thomas S. Huang,et al.  Fractal-based techniques for a generalized image coding method , 1994, Proceedings of 1st International Conference on Image Processing.

[94]  Alexandru Bogdan Multiscale (inter/intra-frame) fractal video coding , 1994, Proceedings of 1st International Conference on Image Processing.

[95]  D. M. Monro,et al.  Fractal approximation of image blocks , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[96]  Michael T. Orchard,et al.  Wavelet packets-based image coding using joint space-frequency quantization , 1994, Proceedings of 1st International Conference on Image Processing.

[97]  Sarah A. Rajala,et al.  Segmentation based image coding using fractals and the human visual system , 1990, International Conference on Acoustics, Speech, and Signal Processing.

[98]  Farzin Deravi,et al.  Pruning of the transform space in block-based fractal image compression , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[99]  S. Chatterjee,et al.  Fractal scanning for image compression , 1991, [1991] Conference Record of the Twenty-Fifth Asilomar Conference on Signals, Systems & Computers.

[100]  Benoit B. Mandelbrot,et al.  Les objets fractals : forme, hasard et dimension , 1989 .

[101]  Miodrag Temerinac,et al.  AN EFFICIENT IMAGE COMPRESSION ALGORITHM BASED ON FILTER BANK ANALYSIS AND FRACTAL THEORY , 1992 .

[102]  Thomas S. Huang,et al.  Fractal image coding using rate-distortion optimized matching pursuit , 1996, Other Conferences.

[103]  Farzin Deravi,et al.  Region-based fractal image compression using heuristic search , 1995, IEEE Trans. Image Process..

[104]  Tariq S. Durrani,et al.  IFS fractals and the wavelet transform , 1990, International Conference on Acoustics, Speech, and Signal Processing.

[105]  Michael F. Barnsley,et al.  A better way to compress images , 1988 .

[106]  Joan L. Mitchell,et al.  JPEG: Still Image Data Compression Standard , 1992 .

[107]  Thomas S. Huang,et al.  A fractal-based image block-coding algorithm , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[108]  Michael F. Barnsley,et al.  Fractal functions and interpolation , 1986 .

[109]  T. Peli,et al.  Multi-Scale Fractal and Correlation Signatures for Image Screening and Natural Clutter Suppression , 1989, Other Conferences.

[110]  C. Sparrow The Fractal Geometry of Nature , 1984 .

[111]  R. Garigliano,et al.  Evolutionary algorithms and a fractal inverse problem. , 1994, Bio Systems.

[112]  Arnaud E. Jacquin,et al.  Fractal image coding based on a theory of iterated contractive image transformations , 1990, Other Conferences.

[113]  Kannan Ramchandran,et al.  Joint thresholding and quantizer selection for decoder-compatible baseline JPEG , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[114]  Alex Pentland,et al.  A practical approach to fractal-based image compression , 1991, [1991] Proceedings. Data Compression Conference.

[115]  Tor A. Ramstad,et al.  An inner product space approach to image coding by contractive transformations , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

[116]  Mohammad Gharavi-Alkhansari,et al.  Generalized Image Coding Using Fractal-Based Methods , 1994 .

[117]  Arnaud Jacquin,et al.  Harnessing chaos for image synthesis , 1988, SIGGRAPH.

[118]  M. Barnsley,et al.  Iterated function systems and the global construction of fractals , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[119]  Y. Zeevi,et al.  Generalized scanning and multiresolution image compression , 1991, [1991] Proceedings. Data Compression Conference.

[120]  Edward R. Vrscay,et al.  Solving the inverse problem for measures using iterated function systems: a new approach , 1995, Advances in Applied Probability.

[121]  G Turchetti,et al.  Local moments and inverse problem of fractal measures , 1992 .

[122]  James Theiler,et al.  Estimating fractal dimension , 1990 .

[123]  Monson H. Hayes,et al.  Fractal-based compression of motion video sequences , 1994, Proceedings of 1st International Conference on Image Processing.

[124]  A. Ait-Kheddache,et al.  Texture classification based on higher-order fractals , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[125]  David L. Wilson,et al.  Rate buffered fractal video , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

[126]  George G. Lorentz,et al.  Constructive Approximation , 1993, Grundlehren der mathematischen Wissenschaften.

[127]  Haibo Li,et al.  Fractal-based image sequence compression scheme , 1993 .

[128]  G. Lu,et al.  Image compression using quadtree partitioned iterated function systems , 1994 .

[129]  John D. Kalbfleisch,et al.  INVERSE PROBLEMS IN FRACTAL CONSTRUCTION : HELLINGER DISTANCE METHOD , 1994 .