Fractal image compression using a fast affine transform and hierarchical classification scheme

• Published in: The Visual computer Vol. 38; no. 11; pp. 3867 - 3880
• Main Author: Nandi, Utpal
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2022; Springer Nature B.V
• Subjects: Affine transformations; Algorithms; Artificial Intelligence; Classification; Classification schemes; Coding; Coding standards; Compression ratio; Computation; Computer Graphics; Computer Science; Fractals; Image classification; Image coding; Image compression; Image Processing and Computer Vision; Image quality; Image reconstruction; Multiplication; Original Article; Image quality; Iterated function system; Compression ratio; Encoding time; Fractal image compression; Affine transform
• ISSN: 0178-2789; 1432-2315
• DOI: 10.1007/s00371-021-02226-y

Fractal image compression is one of the efficient structure-based methods in applications where images are compressed only once but decoded several times due to its resolution-independent feature and fast reconstruction time. However, it has high computational complexity restricting practical use most of the time. Although several methods have been developed to speed up the compression process, these do not satisfy the compression time or the decoded image quality requirements. The affine transforms of image blocks used in fractal coding require a huge number of multiplications and additions and are very expensive in computation that may also slow down the compression process. This paper presents a novel fractal image compression using a fast affine transform and hierarchical classification scheme. The applied affine transform computation algorithm of image blocks uses relationships among neighboring pixels of transformed image block that significantly reduces the number of multiplication and addition operations. Then, this strategy with hierarchical classification and class-wise domain sorting is applied in fractal coding with quad-tree and horizontal vertical partitioning schemes to reduce compression time. Experimental results show that the quad-tree-based fractal coding with the proposed scheme can significantly speed up the compression process keeping image quality and compression ratio almost unchanged.