Subhash Chandra Shrivastava, and Ritu Shrivastava,
A Comparative Study of Different Methods for Fractal Image Compression,
Indian Journal of Mathematics,
Volume 67,
Issue 02,
2025,
Pages 253--266,
ISSN 0019-5324,
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.