A Review of the Fractal Image Coding Literature
Inhaltsverzeichnis
Reference
Brendt Wohlberg, Gerhard de Jager: A Review of the Fractal Image Coding Literature. IEEE Transactions on Image Processing, vol. 8, no. 12 pp. 1716--1729.
DOI
http://dx.doi.org/10.1109/83.806618
Abstract
Fractal image compression is a technique based on the representation of an image by a contractive transform, on the space of images, for which the fixed point is close to the original image. This broad principle encompasses a very wide variety of coding schemes, many of which have been explored in the rapidly growing body of published research. While certain theoretical aspects of this representation are well established, relatively little attention has been given to the construction of a coherent underlying image model that would justify its use. Most purely fractal-based schemes are not competitive with the current state of the art, but hybrid schemes incorporating fractal compression and alternative techniques have achieved considerably greater success. This review represents a survey of the most significant advances, both practical and theoretical, since the publication of Jacquin's (1990) original fractal coding scheme
Extended Abstract
Bibtex
Used References
E. Kreyszig, Introductory Functional Analysis with Applications, 1978 :Wiley
W. K. Pratt, "Vector space formulation of two-dimensional signal processing operations", Comput. Graph. Image Process., vol. 4, pp.1 -24 1975 http://dx.doi.org/10.1016/0146-664X(75)90018-0
Y. Fisher, Fractal Image Compression: Theory and Application, 1995 :Springer-Verlag http://dx.doi.org/10.1007/978-1-4612-2472-3
M. Barnsley, Fractals Everywhere, 1988 :Academic
H.-O. Peitgen, H. Jürgens, and D. Saupe, Chaos and Fractals: New Frontiers of Science, 1992 :Springer-Verlag
T. Bedford, F. M. Dekking, and M. S. Keane, "Fractal image coding techniques and contraction operators", Nieuw Archief Voor Wiskunde, vol. 10, pp.185 -217 1992
M. F. Barnsley and L. P. Hurd, Fractal Image Compression, 1993 :A. K. Peters
K. Belloulata, A. M. Baskurt, H. Benoit-Cattin, and R. Prost, Y. Kim, "Fractal coding of medical images", Proc. SPIE: Med. Imag. X: Image Display, vol. 2707, pp.598 -609 1996 http://dx.doi.org/10.1117/12.238491
B. Hürtgen, P. Mols, and S. F. Simon, A. K. Katsaggelos, "Fractal transform coding of color images", SPIE Proc.: Vis. Commun. Image Process., vol. 2308, pp.1683 -1691 1994
Y. Zhang and L.-M. Po, "Fractal color image compression using vector distortion measure", Proc. IEEE Int. Conf. Image Processing, vol. III, pp.284 -287 1995 http://dx.doi.org/10.1109/ICIP.1995.538544
M. S. Lazar and L. T. Bruton, "Fractal block coding of digital video", IEEE Trans. Circuits Syst. Video Technol., vol. 4, pp.297 -308 1994 http://dx.doi.org/10.1109/76.305874
Y. Fisher, D. N. Rogovin, and T.-P. J. Shen, A. K. Katsaggelos, "Fractal (self-VQ) encoding of video sequences", Proc. SPIE Vis. Commun. Image Process., vol. 2308, pp.1359 -1370 1994 http://dx.doi.org/10.1117/12.185894
D. L. Wilson, J. A. Nicholls, and D. M. Monro, "Rate buffered fractal video", Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing, vol. 5, pp.505 -508 1994 http://dx.doi.org/10.1109/ICASSP.1994.389460
Y. Fisher and F. Dudbridge, Proc. 1995 NATO ASI on Fractal Image Encoding and Analysis: Fractals, vol. 5, Suppl., 1997
Y. Fisher, Fractal Image Encoding and Analysis, vol. 159, 1997 :Springer-Verlag
N. Lu, Fractal Imaging, 1997 :Academic
G. E. Øien, S. Lepsøy, and T. A. Ramstad, "An inner product space approach to image coding by contractive transformations", Proc. IEEE Int. Conf. Acoustics, Speech, and Signal Processing, vol. 4, pp.2773 -2776 1991 http://dx.doi.org/10.1109/ICASSP.1991.150977
D. M. Monro, "Class of fractal transforms", Electron. Lett., vol. 29, pp.362 -363 1993 http://dx.doi.org/10.1049/el:19930244
N. T. Thao, "A hybrid fractal-DCT coding scheme for image compression", Proc. IEEE Int. Conf. Image Processing, vol. I, pp.169 -172 1996 http://dx.doi.org/10.1109/ICIP.1996.559460
W. B. Pennebaker and J. L. Mitchell, JPEG Still Image Data Compression Standard, 1993 :Van Nostrand Reinhold
G. Lu and T.-L. Yew, M. Rabbani and R. J. Safranek, "Image compression using partitioned iterated function systems", Proc. SPIE: Image Video Compress., vol. 2186, pp.122 -133 1994 http://dx.doi.org/10.1117/12.173912
D. Saupe and S. Jacob, "Variance-based quadtrees in fractal image compression", Electron. Lett., vol. 33, pp.46 -48 1997 http://dx.doi.org/10.1049/el:19970052
D. J. Jackson, W. Mahmoud, W. A. Stapleton, and P. T. Gaughan, "Faster fractal image compression using quadtree recomposition", Image Vis. Comput., vol. 15, pp.759 -767 1997 http://dx.doi.org/10.1016/S0262-8856(97)00020-6
A. E. Jacquin, M. Kunt, "Fractal image coding based on a theory of iterated contractive image transformations", Proc. SPIE: Vis. Commun. Image Process., vol. 1360, pp.227 -239 1990 http://dx.doi.org/10.1109/83.128028
A. E. Jacquin, "A novel fractal block-coding technique for digital images", Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing, vol. 4, pp.2225 -2228 1990 http://dx.doi.org/10.1109/ICASSP.1990.116007
A. E. Jacquin, "Image coding based on a fractal theory of iterated contractive image transformations", IEEE Trans. Image Processing, vol. 1, pp.18 -30 1992 http://dx.doi.org/10.1109/83.128028
Y. Fisher, E. W. Jacobs, and R. D. Boss, J. A. Storer, "Fractal image compression using iterated transforms", Image and Text Compression, pp.35 -61 1992 :Kluwer
D. Saupe, et al., "Optimal hierarchical partitions for fractal image compression", Proc. IEEE Int. Conf. Image Processing, vol. 1, pp.737 -741 1998 http://dx.doi.org/10.1109/ICIP.1998.723601
L. Thomas and F. Deravi, "Region-based fractal image compression using heuristic search", IEEE Trans. Image Processing, vol. 4, pp.832 -838 1995 http://dx.doi.org/10.1109/83.388086
D. Saupe and M. Ruhl, "Evolutionary fractal image compression", Proc. IEEE Int. Conf. Image Processing, vol. I, pp.129 -132 1996 http://dx.doi.org/10.1109/ICIP.1996.559449
M. Tanimoto, H. Ohyama, and T. Kimoto, "A new fractal image coding scheme employing blocks of variable shapes", Proc. IEEE Int. Conf. Image Processing, vol. 1, pp.137 -140 1996 http://dx.doi.org/10.1109/ICIP.1996.560621
M. Ruhl, H. Hartenstein, and D. Saupe, "Adaptive partitionings for fractal image compression", Proc. IEEE Int. Conf. Image Processing, vol. II, pp.310 -313 1997 http://dx.doi.org/10.1109/ICIP.1997.638753
Y.-C. Chang, B.-K. Shyu, and J.-S. Wang, "Region-based fractal image compression with quadtree segmentation", Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing, vol. 4, pp.3125 -3128 1997 http://dx.doi.org/10.1109/ICASSP.1997.595454
M. Novak, "Attractor coding of images", Proc. Int. Picture Coding Symp., pp.15.6 1993
M. Novak, Attractor coding of images, 1993 :Linko¨,ping Univ.
F. P. Preparata and M. I. Shamos, Computational Geometry: Texts and Monographs in Computer Science, 1985 :Springer-Verlag
F. Davoine, M. Antonini, J.-M. Chassery, and M. Barlaud, "Fractal image compression based on Delaunay triangulation and vector quantization", IEEE Trans. Image Processing, vol. 5, pp.338 -346 1996 http://dx.doi.org/10.1109/83.480769
F. Davoine, E. Bertin, and J.-M. Chassery, "From rigidity to adaptive tessellations for fractal image compression: Comparative studies", Proc. 8th IEEE Workshop on Image and Multidimensional Signal Processing, pp.56 -57 1993
F. Davoine and J.-M. Chassery, "Adaptive Delaunay triangulation for attractor image coding", Proc. 12th Int. Conf. Pattern Recognition, pp.801 -803 1994 http://dx.doi.org/10.1109/ICPR.1994.576449
E. Reusens, "Partitioning complexity issue for iterated functions systems based image coding", Proc. Eur. Signal Processing Conf., vol. 1, pp.171 -174 1994 http://dx.doi.org/10.1109/ICASSP.1994.389448
F. Davoine, J. Svensson, and J.-M. Chassery, "A mixed triangular and quadrilateral partition for fractal image coding", Proc. IEEE Int. Conf. Image Processing, vol. III, pp.284 -287 1995 http://dx.doi.org/10.1109/ICIP.1995.537633
E. Reusens, "Overlapped adaptive partitioning for image coding based on the theory of iterated functions systems", Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing, vol. 5, pp.569 -572 1994 http://dx.doi.org/10.1109/ICASSP.1994.389448
D. J. Bone, "Orthonormal fractal image encoding using overlapping blocks", Fractals, vol. 5, Suppl., pp.187 -199 1997
H.-L. Ho and W.-K. Cham, "Attractor image coding using lapped partitioned iterated function systems", Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing, vol. 4, pp.2917 -2920 1997 http://dx.doi.org/10.1109/ICASSP.1997.595400
Y. Fisher, T. P. Shen, and D. Rogovin, S.-S. Chen, "Comparison of fractal methods with discrete cosine transform (DCT) and wavelets", Proc. SPIE: Neural Stochast. Methods Image Signal Process. III, vol. 2304, pp.132 -143 1994
H. Kuroda, D. C. Popescu, and H. Yan, L. T. Wu, "Fast block matching method for image data compression based on fractal models", Proc. SPIE: Vis. Commun. Image Process., vol. 2501, pp.1257 -1266 1995 http://dx.doi.org/10.1117/12.206659
S. Lepsøy, Attractor Image Compression&mdash,Fast Algorithms and Comparisons to Related Techniques, 1993 :Norwegian Inst. Technol.
J. M. Beaumont, "Advances in block based fractal coding of still pictures", Proc. IEE Colloq.: The Application of Fractal Techniques in Image Processing, pp.3.1 -3.6 1990
K. U. Barthel and T. Voye´,, "Adaptive fractal image coding in the frequency domain", Proc. Int. Workshop Image Processing, pp.33 -38 1994
C. Frigaard, J. Gade, T. Hemmingsen, and T. Sand, Image compression based on a fractal theory, 1994 :Inst. Electron. Syst., Aalborg Univ.
D. M. Monro and S. J. Woolley, "Rate/distortion in fractal compression: Order of transform and block symmetries", Proc. Int. Symp. Speech, Image Processing and Neural Networks, vol. 1, pp.168 -171 1994 http://dx.doi.org/10.1109/SIPNN.1994.344940
A. E. Jacquin, "Fractal image coding: A review", Proc. IEEE, vol. 81, pp.1451 -1465 1993 http://dx.doi.org/10.1109/5.241507
H. A. Kaouri, "Fractal coding of still images", IEE 6th Int. Conf. Digital Processing of Signals in Communications, pp.235 -239 1991
D. Saupe, "The futility of square isometries in fractal image compression", Proc. IEEE Int. Conf. Image Processing, vol. I, pp.161 -164 1996 http://dx.doi.org/10.1109/ICIP.1996.559458
S. J. Woolley and D. M. Monro, "Rate-distortion performance of fractal transforms for image compression", Fractals, vol. 2, pp.395 -398 1994 http://dx.doi.org/10.1142/S0218348X9400051X
D. C. Popescu, A. Dimca, and H. Yan, "A nonlinear model for fractal image coding", IEEE Trans. Image Processing, vol. 6, pp.373 -382 1997 http://dx.doi.org/10.1109/83.557339
G. E. Øien, et al., "A new improved collage theorem with applications to multiresolution fractal image coding", Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing, vol. 5, pp.565 -568 1994 http://dx.doi.org/10.1109/ICASSP.1994.389449
K. U. Barthel, J. Sch ̈uttemeyer, T. Voy ́e, and P. Noll, "A new image coding technique unifying fractal and transform coding", Proc. IEEE Int. Conf. Image Processing, vol. III, pp.112 -116 1994 http://dx.doi.org/10.1109/ICIP.1994.413877
K. U. Barthel, "Entropy constrained fractal image coding", Fractals, vol. 5, Suppl., pp.17 -26 1997
Y. Zhao and B. Yuan, "Image compression using fractals and discrete cosine transform", Electron. Lett., vol. 30, pp.474 -475 1994 http://dx.doi.org/10.1049/el:19940321
D. M. Monro and F. Dudbridge, "Fractal block coding of images", Electron. Lett., vol. 28, pp.1053 -1055 1992 http://dx.doi.org/10.1049/el:19920667
D. M. Monro and F. Dudbridge, "Fractal approximation of image blocks", Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing, vol. 3, pp.485 -488 1992 http://dx.doi.org/10.1109/ICASSP.1992.226170
D. M. Monro and S. J. Woolley, "Fractal image compression without searching", Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing, vol. 5, pp.557 -560 1994 http://dx.doi.org/10.1109/ICASSP.1994.389451
S. J. Woolley and D. M. Monro, "Optimum parameters for hybrid fractal image coding", Proc. IEEE Int. Conf. Acoustics, Speech, and Signal Processing, vol. 4, pp.2571 -2574 1995 http://dx.doi.org/10.1109/ICASSP.1995.480074
P. D. Wakefield, D. M. Bethel, and D. M. Monro, "Hybrid image compression with implicit fractal terms", Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing, vol. 4, pp.2933 -2936 1997 http://dx.doi.org/10.1109/ICASSP.1997.595404
G. Melnikov and A. K. Katsaggelos, "Non uniform segmentation optimal hybrid fractal/DCT image compression algorithm", Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing, vol. 5, pp.2573 -2576 1998 http://dx.doi.org/10.1109/ICASSP.1998.678048
M. Gharavi-Alkhansari and T. S. Huang, "Generalized image coding using fractal-based methods", Proc. Int. Picture Coding Symp., pp.440 -443 1994
M. Gharavi-Alkhansari and T. S. Huang, "Fractal-based techniques for a generalized image coding method", Proc. IEEE Int. Conf. Image Processing, vol. III, pp.122 -126 1994 http://dx.doi.org/10.1109/ICIP.1994.413875
M. Gharavi-Alkhansari and T. S. Huang, R. Ansari and M. J. Smith, "Fractal image coding using rate-distortion optimized matching pursuit", Proc. SPIE: Vis. Commun. Image Process., vol. 2727, pp.1386 -1393 1996
A. Gersho and R. M. Gray, Vector Quantization and Signal Compression, 1992 :Kluwer
B. Hu¨,rtgen and C. Stiller, R. A. Mattheus, A. J. Duerinckx, and P. J. van Otterloo, "Fast hierarchical codebook search for fractal coding of still images", SPIE Proc.: Video Commun. PACS Med. Applic., vol. 1977, pp.397 -408 1993
C.-S. Kim, R.-C. Kim, and S.-U. Lee, "Fractal vector quantizer for image coding", IEEE Trans. Processing, vol. 7, pp.1598 -1602 1998 http://dx.doi.org/10.1109/83.725366
K. Kim and R.-H. Park, "Image coding based on fractal approximation and vector quantization", Proc. IEEE Int. Conf. Image Processing, vol. III, pp.132 -136 1994 http://dx.doi.org/10.1109/ICIP.1994.413873
K. Kim and R.-H. Park, "Still image coding based on vector quantization and fractal approximation", IEEE Trans. Image Processing, vol. 5, pp.587 -597 1996 http://dx.doi.org/10.1109/83.491335
R. Hamzaoui, M. Müller, and D. Saupe, "VQ-enhanced fractal image compression", Proc. IEEE Int. Conf. Image Processing, vol. I, pp.153 -156 1996 http://dx.doi.org/10.1109/ICIP.1996.559456
B. Wohlberg, Fractal image compression and the self-affinity assumption: A stochastic signal modeling perspective, 1996 :Univ. Cape Town
G. Davis, H. H. Szu, "Self-quantized wavelet subtrees: A wavelet-based theory of fractal image compression", Proc. SPIE: Wavelet Applic. II, vol. 2491, pp.141 -152 1995
B. Hürtgen and T. Hain, "On the convergence of fractal transforms", Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing, vol. 5, pp.561 -564 1994 http://dx.doi.org/10.1109/ICASSP.1994.389450
B. Hürtgen, "Statistical evaluation of fractal coding schemes", Proc. IEEE Int. Conf. Image Processing, vol. III, pp.280 -283 1995 http://dx.doi.org/10.1109/ICIP.1995.537632
J. Kominek, J. A. Storer and M. Cohn, "Convergence of fractal encoded images", Proc. IEEE Data Compression Conf., pp.242 -251 1995 http://dx.doi.org/10.1109/DCC.1995.515514
M. Gharavi-Alkhansari and T. S. Huang, "A system/graph theoretical analysis of attractor coders", Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing, vol. 4, pp.2705 -2708 1997 http://dx.doi.org/10.1109/ICASSP.1997.595347
B. Hürtgen, "Contractivity of fractal transforms for image coding", Electron. Lett., vol. 29, pp.1749 -1750 1993 http://dx.doi.org/10.1049/el:19931165
B. Hürtgen and S. F. Simon, "On the problem of convergence in fractal coding schemes", Proc. IEEE Int. Conf. Image Processing, vol. III, pp.103 -106 1994 http://dx.doi.org/10.1109/ICIP.1994.413879
M. Ruhl and H. Hartenstein, "Optimal fractal coding is NP-hard", Proc. IEEE Data Compression Conf., pp.261 -270 1997 http://dx.doi.org/10.1109/DCC.1997.582049
J. Domaszewicz and V. A. Vaishampayan, "Iterative collage coding for fractal compression", Proc. IEEE Int. Conf. Image Processing, vol. III, pp.127 -131 1994 http://dx.doi.org/10.1109/ICIP.1994.413874
B. Hürtgen, "Performance bounds for fractal coding", Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing, vol. 4, pp.2563 -2566 1995 http://dx.doi.org/10.1109/ICASSP.1995.480072
D. Saupe and R. Hamzaoui, J. M. Blackledge, "Complexity reduction methods for fractal image compression", Proc. IMA Conf. Image Processing: Mathematical Methods and Applications, pp.211 -229 1994
D. Saupe, J. A. Storer and M. Cohn, "Accelerating fractal image compression by multi-dimensional nearest neighbor search", Proc. IEEE Data Compression Conf., pp.222 -231 1995 http://dx.doi.org/10.1109/DCC.1995.515512
D. C. Popescu and H. Yan, "MR image compression using iterated function systems", Magn. Reson. Imag., vol. 11, pp.727 -732 1993 http://dx.doi.org/10.1016/0730-725X(93)90015-6
D. Go¨,tting, A. Ibenthal, and R.-R. Grigat, "Fractal image coding and magnification using invariant features", Fractals, vol. 5, Suppl., pp.65 -74 1997
B. Wohlberg and G. de Jager, "Fast image domain fractal compression by DCT domain block matching", Electron. Lett., vol. 31, pp.869 -870 1995 http://dx.doi.org/10.1049/el:19950582
D. Saupe, "Fractal image compression via nearest neighbor search", Proc. NATO ASI on Fractal Image Encoding and Analysis, 1995
D. Saupe, R. L. Stevenson, A. I. Drukarev, and T. R. Gardos, "Lean domain pools for fractal image compression", Proc. SPIE: Still-Image Compress. II, vol. 2669, pp.150 -157 1996
J. Signes, "Geometrical interpretation of IFS based image coding", Fractals, vol. 5, Suppl., pp.133 -143 1997 http://dx.doi.org/10.1142/S0218348X9700070X
G. Caso, P. Obrador, and C.-C. J. Kuo, L. T. Wu, "Fast methods for fractal image encoding", Proc. SPIE: Vis. Commun. Image Process., vol. 2501, pp.583 -594 1996 http://dx.doi.org/10.1117/12.206767
M. Kawamata, M. Nagahisa, and T. Higuchi, "Multi-resolution tree search for iterated transformation theory-based coding", Proc. IEEE Int. Conf. Image Processing, vol. III, pp.137 -141 1994 http://dx.doi.org/10.1109/ICIP.1994.413872
H. Lin and A. Venetsanopoulos, "A pyramid algorithm for fast fractal image compression", Proc. IEEE Int. Conf. Image Processing, vol. III, pp.596 -599 1995 http://dx.doi.org/10.1109/ICIP.1995.537705
F. M. Dekking, Fractal image coding: some mathematical remarks on its limits and its prospects, 1995 :Fac. Tech. Math. Informat., Delft Univ. Technol.
C. J. Wein and I. F. Blake, "On the performance of fractal compression with clustering", IEEE Trans. Image Processing, vol. 5, pp.522 -526 1996 http://dx.doi.org/10.1109/83.491325
R. Hamzaoui, "Codebook clustering by self-organizing maps for fractal image compression", Fractals, vol. 5, Suppl., pp.27 -38 1997
D. Saupe and H. Hartenstein, "Lossless acceleration of fractal image compression by fast convolution", Proc. IEEE Int. Conf. Image Processing, vol. I, pp.185 -188 1996 http://dx.doi.org/10.1109/ICIP.1996.559464
H. Samet, The Design and Analysis of Spatial Data Structures, 1989 :Addison-Wesley
S. Arya and D. M. Mount, J. Storer and M. Cohn, "Algorithms for fast vector quantization", Proc. IEEE Data Compression Conf., pp.381 -390 1993 http://dx.doi.org/10.1109/DCC.1993.253111
D. Saupe, Breaking the time complexity of fractal image compression, 1994 :Inst. Informat., Univ. Freiburg
J. Kominek, A. A. Rodriguez, R. J. Safranek, and E. J. Delp, "Algorithm for fast fractal image compression", Proc. SPIE: Digital Video Compress.: Algor. Technol., vol. 2419, pp.296 -305 1995 http://dx.doi.org/10.1117/12.206368
B. Bani-Eqbal, M. Rabbani, E. J. Delp, and S. A. Rajala, "Speeding up fractal image compression", Proc. SPIE: Still-Image Compress., vol. 2418, pp.67 -74 1995 http://dx.doi.org/10.1049/ic:19950017
B. Bani-Eqbal, "Enhancing the speed of fractal image compression", Opt. Eng., vol. 34, pp.1705 -1710 1995 http://dx.doi.org/10.1117/12.203134
H. T. Chang and C. J. Kuo, "Finite-state fractal block coding of images", Proc. IEEE Int. Conf. Image Processing, vol. I, pp.133 -136 1996 http://dx.doi.org/10.1109/ICIP.1996.559450
G. E. Ø,ien, "Parameter quantization in fractal image coding", Proc. IEEE Int. Conf. Image Processing, vol. III, pp.142 -146 1994 http://dx.doi.org/10.1109/ICIP.1994.413871
K. U. Barthel, T. Voye´,, and P. Noll, "Improved fractal image coding", Proc. Int. Picture Coding Symp., pp.1.5 1993
H. Hartenstein, D. Saupe, and K.-U. Barthel, "VQ-encoding of luminance parameters in fractal coding schemes", Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing, vol. 4, pp.2701 -2704 1997 http://dx.doi.org/10.1109/ICASSP.1997.595346
G. Strang, Linear Algebra and its Applications, 1988 :Harcourt Brace Jovanovich
H.-S. Kang and S.-D. Kim, "Fractal decoding algorithm for fast convergence", Opt. Eng., vol. 35, pp.3191 -3198 1996 http://dx.doi.org/10.1117/1.601058
R. Hamzaoui, "Decoding algorithm for fractal image compression", Electron. Lett., vol. 32, pp.1273 -1274 1996 http://dx.doi.org/10.1049/el:19960831
R. Hamzaoui, "Ordered decoding algorithm for fractal image compression", Proc. Int. Picture Coding Symp., pp.91 -95 1997
Z. Barahav, D. Malah, and E. Karnin, "Hierarchical interpretation of fractal image coding and its application to fast decoding", Proc. IEEE Int. Conf. Digital Signal Processing, pp.190 -195 1993
D. M. Monro and F. Dudbridge, "Rendering algorithms for deterministic fractals", IEEE Comput. Graph. Appl., vol. 15, pp.32 -41 1995 http://dx.doi.org/10.1109/38.364961
R. Dettmer, "Form and function: Fractal-based image compression", Inst. Elec. Eng. Rev., vol. 38, pp.323 -327 1992
E. Polidori and J.-L. Dugelay, "Zooming using iterated function systems", Fractals, vol. Suppl., pp.111 -123 1997 http://dx.doi.org/10.1142/S0218348X97000681
M. Gharavi-Alkhansari, R. DeNardo, Y. Tenda, and T. S. Huang, J. Biemond and E. J. Delp, "Resolution enhancement of images using fractal coding", Proc. SPIE: Vis. Commun. Image Process., vol. 3024, pp.1089 -1100 1997
H. Krupnik, D. Malah, and E. Karnin, "Fractal representation of images via the discrete wavelet transform", Proc. 18th IEEE Conv. Electrical and Electronics Engineers in Israel, pp.2.2.2/1 -5 1995 http://dx.doi.org/10.1109/ICIP.1995.529700
B. Simon, "Explicit link between local fractal transform and multiresolution transform", Proc. IEEE Int. Conf. Image Processing, vol. I, pp.278 -281 1995 http://dx.doi.org/10.1109/ICIP.1995.529700
A. van de Walle, "Merging fractal image compression and wavelet transform methods", Fractals, vol. 5, Suppl., pp.3 -15 1997 http://dx.doi.org/10.1142/S0218348X97000590
I. Daubechies, Ten Lectures on Wavelets, 1992 :SIAM http://dx.doi.org/10.1137/1.9781611970104
G. Davis, A. F. Laine, M. A. Unser, and M. V. Wickerhauser, "Adaptive self-quantization of wavelet subtrees: A wavelet-based theory of fractal image compression", Proc. SPIE: Wavelet Appl. Signal Image Process. III, vol. 2569, pp.294 -307 1995
G. Davis, "A wavelet-based analysis of fractal image compression", IEEE Trans. Image Processing, vol. 7, pp.141 -154 1998 http://dx.doi.org/10.1109/83.660992
G. Caso and C.-C. J. Kuo, R. Ansari and M. J. Smith, "New results for fractal/wavelet image compression", Proc. SPIE: Vis. Commun. Image Process., vol. 2727, pp.536 -547 1996
A. van de Walle, Relating fractal image compression to transform methods, 1995 :Univ. Waterloo
J. Li and C.-C. J. Kuo, "Fractal wavelet coding using a rate-distortion constraint", Proc. IEEE Int. Conf. Image Processing, vol. II, pp.81 -84 1996 http://dx.doi.org/10.1109/ICIP.1996.560607
R. Rinaldo and G. Calvagno, "An image coding scheme using block prediction of the pyramid subband decomposition", Proc. IEEE Int. Conf. Image Processing, vol. II, pp.878 -882 1994 http://dx.doi.org/10.1109/ICIP.1994.413481
R. Rinaldo and G. Calvagno, "Image coding by block prediction of multiresolution subimages", IEEE Trans. Image Processing, vol. 4, pp.909 -920 1995 http://dx.doi.org/10.1109/83.392333
K. Belloulata, A. M. Baskurt, H. Benoit-Cattin, and R. Prost, "Fractal coding of subbands with an oriented partition", Signal Process.: Image Commun., vol. 12, pp.243 -252 1998 http://dx.doi.org/10.1016/S0923-5965(97)00040-4
J. M. Shapiro, "Embedded image coding using zerotrees of wavelet coefficients", IEEE Trans. Signal Processing, vol. 41, pp.3445 -3462 1993 http://dx.doi.org/10.1109/78.258085
R. J. Clarke and L. M. Linnett, "Fractals and image representation", Electron. Commun. Eng. J., vol. 5, pp.233 -239 1993
D. W. Lin, "Fractal image coding as generalized predictive coding", Proc. IEEE Int. Conf. Image Processing, vol. III, pp.117 -121 1994 http://dx.doi.org/10.1109/ICIP.1994.413876
J. Domaszewicz, S. Kuklinski, and V. A. Vaishampayan, "Fractal coding versus classified transform coding", Proc. IEEE Int. Conf. Image Processing, vol. I, pp.149 -152 1996 http://dx.doi.org/10.1109/ICIP.1996.559455
B. Wohlberg and G. de Jager, "A class of multiresolution stochastic models generating self-affine images", IEEE Trans. Signal Processing, vol. 47, pp.1739 -1742 1999 http://dx.doi.org/10.1109/78.765153
S. Lepsø,y, P. Carlini, and G. E. Ø,ien, Y. Fisher, "On fractal compression and vector quantization", Fractal Image Encoding and Analysis, vol. 159, 1997 :Springer-Verlag
B. Wohlberg and G. de Jager, "Fractal coding performance for first-order Gauss-Markov models", Electron. Lett., vol. 32, pp.441 -442 1996 http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=491137&navigation=1
Links
Full Text
http://math.lanl.gov/~brendt/Publications/Docs/wohlberg-1999-review.pdf