Affiliations: Dhirubhai Ambani Institute of Information and
Communication Technology, Near Indroda Circle, Gandhinagar 382 007, Gujarat,
India. suman mitra@daiict.ac.in | Indian Statistical Institute, 203, B. T. Road, Calcutta
700108, India. {malay,murthy,bhargab}@isical.ac.in | Avisere, Chandler, AZ 85226, USA.
tinku.acharya@ieee.org
Note: [] Address for corespondence: Machine Intelligence Unit, Indian
Statistical Institute, 203, B. T. Road, Calcutta 700108, India
Abstract: Approximation of an image by the attractor evolved through
iterations of a set of contractive maps is usually known as fractal image
compression. The set of maps is called iterated function system (IFS). Several
algorithms, with different motivations, have been suggested towards the
solution of this problem. But, so far, the theory of IFS with probabilities, in
the context of image compression, has not been explored much. In the present
article we have proposed a new technique of fractal image compression using the
theory of IFS and probabilities. In our proposed algorithm, we have used a
multiscaling division of the given image up to a predetermined level or up to
that level at which no further division is required. At each level, the maps
and the corresponding probabilities are computed using the gray value
information contained in that image level and in the image level higher to that
level. A fine tuning of the algorithm is still to be done. But, the most
interesting part of the proposed technique is its extreme fastness in image
encoding. It can be looked upon as one of the solutions to the problem of huge
computational cost for obtaining fractal code of images.
Keywords: Iterated function System (IFS), Collage theorem, measure, Markov operator, image compression
