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Original Articles

Partitioned Iterative Function System: A New Tool for Digital Imaging

, & , FIETE
Pages 279-298 | Published online: 26 Mar 2015

REFERENCES

  • M F Barnsley. Fractals everywhere. Now York. Academic Press 1998.
  • A E Jacquin, Image coding based on a fractal theory of iterated contractive image transformations. IEEE Trans on linage Processing, vol 1. pp 18–30. 1992.
  • S K Mitra, C A Murthy & M K Kundu, Fractal based image coding using genetic algorithm, in Pattern Recognition, Image Processing and Computer Vision. Recent Advances (P P Das & B N Chatterji, eds), pp 86–96. New Delhi, Narosa Publishing House. 1995.
  • S K Mitra, C A Murthy & M K Kundu. Technique for fractal image compression using genetic algorithm, IEEE Transaction on Image Processing, vol 7. pp 586–593. 1998.
  • D E Goldberg, Genetic Algorithms: Search, Optimization and Machine Learning, Reading, Addison-Wesley. 1989.
  • L Davis, Handbook of Genetic Algorithms, New York, Van Nostrand Reinhold, 1991.
  • Z Michalewicz, Genetic Algorithms + Data Structure = Evolution Programs, Berlin. Springer Verlag. 1992.
  • P S Chave (Jr), Digital merging of landsat TM and digitised NHAP data for 1:24000 scale image mapping, Photogrammetric Engineering and Remote Sensing, vol 52, pp 1637–1646, 1986.
  • R Welch & M Ehlers. Merging multi resolutions SPOT HRV and Landsat TM data. Photogrammetric Engineering and Remote Sensing, vol 53. pp 310–303. 1987.
  • R C Gonzalez & R R Wood. Digital Image Processing, Reading. Addison Wesley. 1993.
  • R G Keys Cubic convolution interpolation for digital image processing. IEEE Transactions on Acoustics. Speech and Signal Processing, vol 29. pp 1153–1160. 1981.
  • S K Park & R A Schowengerdt, Image reconstruction using parametric cubic convolution. Computer Vision, Graphics, and Image Processing, vol 23, pp 258–272. 1983.
  • R A Schowengerdt, S K Park, & R Gray. Topics in two dimensional sampling and reconstruction of images. International Journal of Remote Sensing, vol 5. pp 333–347, 1984.
  • W K Pratt. Digital Image Processing, New York. John Wiley and Sons Inc. 1991.
  • J Canny. A computational approach to edge detection. IEEE Transaction on Pattern Analysis and Machine Intelligence, vol 8. pp 679–698. 1986.
  • D Marr & E C Hilderth, Theory of edge detection, in Proceedings of Royal Society, Series B, (London. UK), pp 187–217, 1980.
  • R M Haralick, Digital step edge from zero crossing of second directional derivatives, IEEE Trans on Pattern Analysis and Machine Intelligence, vol 6, pp 58–86. 1984.
  • A E Jacquin, Fractal Theory of Iterated Markov Operators with Applications to Digital Image Coding. PhD thesis. Georgia Institute of Technology. Atlanta USA. 1989
  • A E Jacquin, A novel fractal block-coding technique for digital images, in Proceedings of International Conference on Acoustics. Speech and Signal Processing (ICASSP'90), (Alberquerque. USA), pp 2225–2228, 1990.
  • F Dudbridge. Image Approximation by Self Affine Fractals. PhD thesis, Imperial College. London, UK, 1992.
  • Y Fisher. Fractal Image Compression: Theory and Application. New York. Springer Verlag, 1995.
  • Y Fisher, Fractal Image Encoding and Analysis, NATO ASI Series F, vol 159, New York. Springer Verlag, 1998
  • B Ramamurthi & A Gersho, Classified vector quantization of images, IEEE Trans on Communications, vol COM-34, pp 1105–1115, 1986.
  • A D Sloan. Low-bit-rate fractal image coding, in Visual Information Processing III, Volume 2239 of SPIE Proceedings (F O Huck & R D Juday, eds), pp 210–213. 1994.
  • H Lin & A N Venetsanopoulos, Perceptually lossless fractal image compression, in Visual Communication and Image Processing, volume 2727 of SPIE Proceedings (R Ansari & M J Smith eds), pp 1394–1399, 1996.
  • Y Fisher, E W Jacobs, & R D Boss, Fractal image compression using iterated transforms, in Image and Text Compression (J A Storer, ed), Kulwer Academic Publishers, pp 35–61, 1992.
  • D Saupe & S Jacob, Variance based quadtree in fractal image compression. Electronic Letters, vol 33. pp 46–48. 1997.
  • F Davoine, J Sevesson, & J M Chessary. A mixed triangular and quadrilateral partition for fractal image coding, in Proceedings of IEEE International Conference on Image Processing (ICIP'95), (Washington DC, USA), pp 284–287, 1995.
  • H L Ho & W K Cham. Attractor image coding using lapped partitioned iterated function systems, in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 97), (Munich. Germany), pp 2917–2920, 1997.
  • L Thomas & F Deravi, Region-based fractal image compression using heuristic search, IEEE Transactions on Image Processing, vol 4, pp 832–838, 1995.
  • M H Loew, D Li & R L Pickholtz, Adaptive PIFS model in fractal image compression, in Medical Imaging 1996: Image Display, volume 2707 of SPIE Proceedings (Y Kim, ed.), pp 284–293, 1996.
  • M Tanimoto, H Ohyama, & T Kimoto, A new fractal image coding scheme employing blocks of variable shapes, in Proceedings of IEEE International Conference on Image Processing (ICIP'96), (Lausanne, Switzerland), pp 137–140, 1996.
  • D Saupe & M Ruhl, Evolutionary fractal image compression, in Proceeding of IEEE International Conference on Image Processing (ICIP'96), (Lausanne, Switzerland), pp 161–164, 1996.
  • M Ruhl, H Hatrenstein, & D Saupe, Adaptive partitionings for fractal image compression, in IEEE International Conference on Image Processing (ICIP'97), (Santa Barbara, USA), 1997.
  • E Reusens, Overlapped adaptive partitioning for image coding based on the theory of iterated function systems, in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP'94), (Adelaide, Australia), pp 569–572, 1994.
  • J S Chen, Fractal image compression based on visual perception, in Human Vision, Visual Processing and Digital Display VI, Volume 2411 of SPIE Proceedings (BE Rogowitz & J P Allebach, eds), pp 92–99, 1995.
  • K U Barthel, Entropy constrained fractal image coding, Fractal, vol 5, pp 17–26, 1997.
  • R Rinaldo & G Calvango, Image coding by block prediction of multiresolution subimages, IEEE Trans on Image Processing, vol 4, pp 909–920, 1995.
  • M G Alkhansari & T S Huang, Fractal-based techniques for a generalized image coding method, in Proceedings of IEEE International Conference on Image Processing (IC1P'94), (Austin, USA), pp 122–126, 1994.
  • D Saupe, Fractal image compression via nearest neighbour search, in NATO ASI on Fractal Image Encoding and Analysis, (Trondheim, Norway), 1995.
  • H Lin & A N Venetsanopoulos, A pyramid algorithm for fast fractal image compression, in Proceedings of IEEE International Conference on Image Processing (ICIP'95), (Washington DC, USA), pp 596–599, 1995.
  • B Simon. A pyramid algorithm for fast fractal image compression, in Proceedings of IEEE International Conference on Image Processing (ICIP '95), (Washington DC USA), pp 278–281. 1995.
  • L Lepsoy & G E Oein, Fast attractor image encoding by adaptive codebook clustering, in Fractal Image Compression: Theory and Applications (Y Fisher, ed.), pp 177–197, New York, Springer Verlag, 1995.
  • C J Wein & I F Blake, On the performance of fractal compression with clustering, IEEE Transactions on Image Processing, vol 5, pp 522–526, 1996.
  • J Komkinek, Codebook reduction in fractal image compression, in Still Image Compression II, Volume 2669 of SPIE Proceedings (R L Stevenson, A I Drukarev & T R Gardos, eds), pp 33–41, 1995.
  • M E Haziti, H Cherifi & D Aboutajdine, Complexity reduction in fractal image compression, in Proceedings of the IASTED International Conference on Signal and Image Processing (SIP '97), (New Orleans, USA), pp 245–250, 1997.
  • J Signes, Reducing the codebook size in fractal image compression by geometrical analysis, in Visual Communication and Image Processing, volume 2727 of SPIE Proceedings (R Ansari & M J Smith, eds), pp 1400–1409, 1996.
  • B E Wohlberg & G De Jager, On reduction of fractal compression encoding time, in IEEE South African symposium on Communications and Signal processing (COMSIG '94), (University of Stellenbosch), pp 158–161, 1994.
  • Z Baharav, D Malah & E Karnin, Hierarchical interpretation of fractal image coding and its application to fast decoding, in Proceedings of the IEEE International Conference on Digital Signal Processing, (Nicosia, Cyprus), pp 190–195, 1993.
  • B Bani-Eqbal, Speeding up fractal image compression, in Still Image Compression, Volume 2418, SPIE Proceedings (M Rabbani, E J Delp & S A Rajala, eds), pp 67–74, San Jose, USA, 1995.
  • K Belloulata, A Buskurt & R Prost, Fast directional fractal coding of subbands using decision directed clustering for block classification, in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP'97), (Munich, Germany), pp 3121–3124, 1997.
  • G Caso, P Obrador & C C J Kuo, Fast method for fractal image encoding, in Visual Communication and Image Processing, vol 2501 of SPIE Proceedings (L T Wu. ed), pp 583–594, Taipei, Taiwan, 1996.
  • B Hurtgen & C Stiller, Fast hierarchical codebook search for fractal coding of still images, in Video Communications and PACS for Medical Applications, vol 1977 of SPIE Proceedings, (R A Mattheus, A J Duerinckx & P J V Ptterloo, eds), pp 397–408, 1993.
  • B S Everitt, Unresolved problem in cluster analysis. Biometrics, vol 35, pp 169–181, 1979.
  • W Skarbek, On convergence of affine fractal operators. Image Processing and Communications, vol 1, pp 33–44, 1995.
  • W Skarbek, Analysis of fractal operator convergence by graph method, Fundameta Informaticae, vol 34, p 429–440, 1998.
  • M G Alkhansari & T S Huang, A system/graph theoretical analysis of attractor coders, in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '97). (Munich, Germany), pp 2705–2708, 1997.
  • B Hurtgen & S F Simon, On the problem of convergence in fractal coding schemes, in Proceedings of IEEE International Conference on Image Processing (ICIP '94) (Austin, USA), pp 103–106. 1994.
  • B Hurtgen & T Hain, On the convergence of fractal transforms, in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '94), pp 561–564, 1994.
  • G Davis, Self quantized wavelet subtree: A wavelet based theory fractal image compression, in Wavelet Application II, vol 2491 of SPIE Proceedings (H H Szu, ed), pp 141–152, 1995.
  • G Davis, A wavelet based analysis of fractal image compression, IEEE Trans on Image Processing, vol 7, pp 141–154. 1998.
  • G Davis, Why fractal block coders work, in Fractal image Encoding and Analysis. NATO ASI Series F, vol 159 (Y Fissher, ed). pp 3–19. New York, Springer Verlag, 1998.
  • M Dekking, Fractal image coding: Some mathematical remarks on its limits and its prospects, in Fractal Image Encoding and Analysis. NATO ASI Series F, vol 159 (Y Fisher, ed), pp 117–131, New York, Springer Verlag, 1998.
  • J H Elton, An ergodic theorem for iterated maps. Ergodic theory and Dynamical Systems, vol 7. pp 481–488, 1987.
  • B Forte & E R Vrscay, Solving the inverse problem function and image approximation using iterated function systems, I: Theoretical basis. Fractals, vol 3. pp 325–334, 1994.
  • D M Monro. Generalized fractal transform: Complexity issues, in Proceedings of IEEE Data Compression Conference. (DCC '93) (J A Storer & M Cohn, eds), pp 254–261, 1993.
  • G E Oien, Z Baharav, S Lepsoy, E Karnin & D Malah, A new improved collage theorem with application to multiresolution fractal image coding, in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '94), pp 565–568, 1994.
  • K Kim & R H Park, Image coding based on fractal approximation and vector quantization, in Proceedings of IEEE international Conference on Image Processing (ICIP '94) (Austin, USA), pp 132–136, 1994.
  • K Kim & R H Park, Still image coding based on vector quantization and fractal approximation, IEEE Trans on Processing, vol 4, pp 587–597. 1996.
  • A Bogdan & H Meadows, Kohonen neural network for image coding based on iteration transform theory, in Neural and Stochastic Methods in Image and Signal Processing (S S Chen, ed), pp 425–436. Vol 1776 of SPIE Proceedings, 1992.
  • W Skarbek, Image compression using pixel network, in Soft-computing for Image Processing (S K Pal, A Ghosh & M K Kundu, eds), Heidelberg, Physica Verlag, 1999.
  • A V deWalle, Merging fractal image compression and wavelet transform methods, in NATO ASI on Fractal Image Encoding and Analysis, (Trondheim. Norway), 1995.
  • N T Thao, A hybrid fractal-DCT coding scheme for image compression, in Proceedings of IEEE International Conference on Image Processing (ICIP '96), (Lausanne, Switzerland), pp 169–172, 1996.
  • B E Wohlberg & G De Jager, Fast image domain fractal compression by DCT domain block matching, Electronic Utters, vol 31, pp 869–870, 1995.
  • K U Barthel, J Schuttemeyer, T Voyi & P Noll, A new image coding technique unifying fractal and transform coding, in Proceedings of IEEE International Conference on Image Processing (ICIP '94), pp 112–116, 1994.
  • D M Monro, A hybrid fractal transform, in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '93), pp 169–172, 1993.
  • V Ratnakar, E Feig & P Tiwari, Fractal based hybrid compression scheme, in Visual Communication and Image processing, vol 2308 of SPIE Proceedings (A K Katsaggelos, ed), pp 448–454, 1994.
  • P D Wakefield, D M Bethel & D M Monro, Hybrid image compression with implicit fractal terms, in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '97), (Munich, Germany), pp 2933–2936, 1997.
  • N Zhang & H Yan, Hybrid image compression method based on fractal geometry, Electronics Letters, vol 27, pp 406–408, 1991.
  • J Domaszewich, S Kullinski & V A Vaishampayan, Fractal coding versus classified transform coding, in Proceedings of IEEE International Conference on Image Processing (ICIP “96), (Lausanne, Switzerland), pp 149–152, 1996.
  • Y F Fisher, T P Shen & D Rogovin, Comparison of fractal methods with discrete cosine transform (DCT) and wavelets, in Neural and Stochastic Methods in Image and Signal Processing III, vol 2308 of SPIE Proceedings (S S Chen, ed), pp. 132–143, 1994.
  • D W Lin & R H Park, Fractal image coding as generalized predictive coding, in Processing of IEEE International Conference on Image Processing (ICIP '94), (Austin, USA), pp 117–121, 1994.
  • J Scharinger, F Pichler, H G Feichtinger & F Leberl, Comparison of lossy image compression techniques with respect to their impact on edge detection, in Application of digital Image Processing XIX, vol 2847 of SPIE Proceedings, (Denver, USA), p 479–490, 1996.
  • F Dudbridge, Least-squares block coding by fractal functions, in Fractal Image Compression: Theory and Applications (Y Fisher, ed). pp 229–241. New York, Springer Verlag. 1995.
  • H Lin & A N Venetsanopoulos, Incorporating nonlinear contractive functions into the fractal coding, in Proceedings of IEEE International Workshop on Intelligent Signal Processing and Communication Systems. (Seoul. Korea), pp 169–172, 1994.
  • G E Oien & G Narstad. Fractal compression of ECG Signals, in Fractal Image Encoding and Analysis (Y Fisher, ed), pp 201–226, New York, Springer Verlag, 1998.
  • G Vines, Orthogonal basis of IFS, in Fractal Image Compression: Theory and Applications (Y Fisher, ed), pp 199–214, New York, Springer Verlag, 1995.
  • C S Kim, R C Kim & S U Lee. Novel Fractal Image Compression with non iterative Decoder, in Proceedings of IEEE International Conference on Image Processing (ICIP '95), (Washington DC, USA), pp 268–271. 1995.
  • R Hamzaoui, A new decoding algorithm for fractal image compression. Electronics Letters, vol 14, pp 1273–1274, 1996.
  • M F Barnsley & L P Hurd. Fractal Image Compression, Wellesley, A K Peters Ltd, 1993.
  • S K Mitra & C A Murthy, Mathematical framework to show the existence of the attractor of the partitioned iterative function systems. Pattern Recognition, (Accepted).
  • D Bhandari, C A Murthy & S K Pal. Genetic algorithm with elitist model and its convergence. International Journal of Pattern Recognition and Artificial Intelligence, vol 10, pp 731–747, 1996.
  • S Bandyopadhyay, Pattern Classification Using Genetic Algorithm. PhD thesis. Indian Statistical Institute. Calcutta, India. 1998.
  • S K Pal. D Bhandari & M K Kundu. Genetic algorithms for optimal image enhancement. Pattern Recognition Letters, vol 15. pp 261–271. 1994.
  • N R Pal, S Nandi & M K Kundu. Self crossover—A new genetic operator and its application to feature selection. International Journal of Systems Science, vol 29. pp 207–212, 1998.
  • S K Mitra, C A Murthy & M K Kundu. A technique for image magnification using partitioned iterative function system. Pattern Recognition, (accepted).
  • S K Mitra, C A Murthy & M K Kundu. Digital image magnification using fractal operators and genetic algorithm, in Computational Intelligence and Applications (P S Szczepaniak, ed). pp 250–259. Heidelberg. Physica Verlag. 1998.
  • S K Mitra, C S Murhty & M K Kundu, A study on partitioned iterative function systems for image compression, Fundamenta Informaticae. vol 34. pp 413–428. 1998.
  • S K Pal & D D Majumder. Fuzzy Mathematical Approach to Pattern Recognition. New York. John Wiley (Halsted Press), 1986.
  • C A Murthy & N Chowdhury. In search of optimal clusters using genetic algorithm. Pattern Recognition Letters, vol 17, pp 825–832, 1996.
  • S K Mitra, C A Murthy & M K Kundu, Edge extraction in the compressed domain using fractal reconstruction, IEEE Transactions on Image Processing, (Communicated).

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