Partitioned Iterative Function System: A New Tool for Digital Imaging

AbstractThis article deals with the fractal based representation of image to perform various image processing tasks like image compression, image magnification and image edge extraction. Representation of an image in terms of a set of affine contractive maps has been regarded as the fractal representation. The set of transformations is called iterative function system (IFS). However, the contribution of the article is based on partitioned iterative function system (PIFS). The basic difference between IFS and PIFS exist in the domain of application of their respective transformation. The cost of generating PIFS code of an image is reduced by using Genetic Algorithms (GAs) based search technique. Image compression is a direct consequence of the PIFS code. On the other hand two other operations, viz, image magnification and edge extraction can also be performed using the PIFS code obtained by the GA based method.Indexing terms: Iterative function system (IFS)Partitioned iterative function system (PIFS)Genetic algorithms (GAs)Image compressionImage magnificationImage edge extraction Additional informationNotes on contributorsS K MitraSuman Kumar Mitra was born in India on February 15, 1968. He received BSc and MSc degrees in Statistics from the University of Calcutta in the year 1988 and 1990 respectively. He was a junior research fellow at the Indian Statistical Institute during 1994–1996 and was also a senior research fellow of the same Institute during 1996–1999. Presently, he is a project linked personnel at the Machine Intelligence Unit of the Indian Statistical Institute, Calcutta under INTEL, USA-ISI project. He has submitted his thesis at the Indian Statistical Institute in 1999. His research interests includes fractal modeling of real life images, image processing, digital image watermaking, wavelets, genetic algorithms and pattern recognition. He has contributed about 15 research papers in prestigious journals, international refereed conferences and as chapters in edited volumes.C A MurthyC A Murthy was born in Ongle, India in 1958. He received his MStat and PhD Degrees from the Indian Statistical Institute, Calcutta. He is currently a Professor in the Machine Intelligence Unit of the Indian Statistical Institute. He visited The Michigan State University, East Lansing, in 1991–1992, for six months. He also visited the Pennsylvania State University, Park, in 1996–1997. His fields of interests include Pattern Recognition, Image Processing, Fuzzy Sets, Neural Networks, Fractal and Genetic Algorithms.M K KunduMalay K Kundu received his BTech, MTech and PhD (Tech) degrees all in Radio Physics and Electronics from the University of Calcutta. In 1982, he joined the Indian Statistical Institute, Calcutta, as a faculty member. He had been the Head of the Machine Intelligence Unit of the Institute during September 1993 to November 1995. Currently he is a professor and is working in the same Unit. During 1988–89, he was at the A I Laboratory of the Massachusetts Institute of Technology, Cambridge, USA, as a visiting scientist under UN Fellowship program. His current research interest includes image processing, data compression, computer vision, genetic algorithms, fractals, wavelets, VLSI design for digital imaging and soft Computing.He has contributed about 50 research papers in well known & prestigious archival journals, international refereed conferences and as chapters in monographs & edited volumes. He is co-author of the book titled Soft Computing for Image Processing published from Physica-Verlag, Heidelberg. He is a senior member of the IEEE, USA, a fellow of the National Academy of Science, India and a fellow of the Institution of Electronics and Telecommunication Engineers, India.