Gradient based fractal image compression using Cayley table

Abstract

Encoding complexity reduction is an active area of research in the field of fractal image compression. In this proposed method, affine transformation is predicted to reduce the computational complexity and score value is calculated to further minimise the number of computations in the exhaustive process of encoding. In this hybrid wavelet- fractal image compression, relative geometric transformation of range and domain blocks is determined using a reference matrix as GR and GD respectively. Then affine transformation is predicted as the geometric composition of GR and GD, using Cayley table. Score value is defined individually for domain and range blocks. It is the absolute value of maximum change in the intensity in the respective block. An important merit of this proposed method is that the encoding time is highly reduced in comparison to other recent fractal coding techniques, with a better value of PSNR. This method is 641 times faster than Standard fractal image compression method (SFIC). Cayley table is utilized for the first time in fractal image compression. This lossy compression technique can be used in multimedia applications to handle the situation of limited storage space and bandwidth and also to transmit enormous amount of data with acceptable value of PSNR. As the medical images are huge in size a good lossy compression technique is required to store them in medical archives in an economical manner. Since this proposed method provides a good trade-off between compression ratio and the quality of reconstructed image, it is a better solution for the storage of medical images in an efficient manner.