A Comparative Study of Different Methods for Fractal Image Compression

Shrivastava, Subhash Chandra; Shrivastava, Ritu

Indian Journal of Mathematics

A Comparative Study of Different Methods for Fractal Image Compression

Author(s): Subhash Chandra Shrivastava Subhash Chandra Shrivastava Department of Mathematics,
Rungta College of Engineering and Technology,
Rungta International Skills University,
Bhilai, Durg, 490024, Chhattisgarh, India. suhash_2911@rediffmail.com , Ritu Shrivastava Ritu Shrivastava Department of Physics,
Government Naveen College Risali,
Bhilai, Durg, 490006, Chhttisgarh, India. ritu_10101010@rediffmail.com

Vol. 67, No. 2 (2025) • pp. 253–266

Published 09-07-2026 Article History Received 17-11-2025 Revised 11-05-2026 Published 09-07-2026

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Abstract

Fractal image compression can be done by partitioning of an image into different domains, and for each domain there is a transformation into range element. The normal algorithm produces for this purpose is known as Recurrent Iterated Function System. The domain-range equivalence also applied to the general inverse problem of RIFS. The method of fractal image compression through RIFS is better than general fractal image compression technique. RIFS are improvements of IFS using elements of the theory of Marcovian stochastic processes which can produce more natural looking images. New RIFs consists of vertical contraction factor function and nonlinear transformations. A very fast fractal-based image compression encoding technique is the theory of IFS with probabilities. In this approach a Markov operator associated with the probability operator. One more extension of IFS theory for image compression is partitioned or local iterative function system (PIFS) for coding the gray level images. The difference between PIFS and IFS technique for image compression is in the application domain and computational cost.

Keywords

Fractal Image Compression; Iterated Function System; Partial Iterated Function System; Fractal Dimension

2020 Mathematics Subject Classification

28A80, 47H10, 54E50

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Allahabad Mathematical Society

A Comparative Study of Different Methods for Fractal Image Compression

Abstract

Keywords

2020 Mathematics Subject Classification

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