Competitive Improvement of the Time Complexity to Encode Fractal Image: By Applying Symmetric Central Pixel of the Block

Abstract

By combining the basics of self-similarity, scaling correlation, and statistical components, Benoit Mandelbrot formulated the idea of a natural fractal entity, an entity described by those fundamentals. As a result of these principles, fractal image codings are being used in many substantial applications already, such as image compression, image signature, image watermarking, image attribute extraction, and even image texture segmentation. Thus, while fractal image coding is relatively new in the field of image encoding, it has gained broad acceptance at a rapid pace. In light of its beneficial qualities, such as quick decomposition, high compression ratio, and the independence of resolution at any size make these applications conceivable. However, compared to its advantages, fractal image coding is extremely time-complex and so remarkably expensive, which hinders its prevalence. A wide hunting domain blocks for the relevant range blocks caused this difficulty. We proposed several improvements to the Jacquin design in this paper. We first used max-pooling as an alternative for the medium bonding of spatial contractions to validate the value of the edge textures of the block. Secondly, we construct the odd-size pixel block alternative to an even-size pixel block for validation of the symmetric central pixel (CP). Finally, before the search started, we proposed a shortening of block space, using the central pixel of the block to convert each eight-bit pixel to a two-bit pixel. As a consequence, the symmetrical CP of odd pixels block, reduction of block space, and edge pixel selection accomplished faster coding and competitive image quality than existing known exhaustive search algorithms.