Isometry-based shape-adaptive fractal coding for images

Fractal image coding is an effective method to eliminate the image redundancy through piecewise self transformability called fractal codes on a block-wise sequence. The fractal code is a set of contractive affine transforms defined as a sequence of parent and child block transformations. To improve the performance when a parent range block experiences large error, we usually partition the parent range block into four children (smaller) square blocks. In this paper, a shape-adaptive fractal coding (SAFC) based on the edge information is proposed. In SAFC, each parent range block is first partitioned into nonsquare (rectangle or triangle) children blocks which are to be fractal encoded. If the coded image quality does not improve, then the traditional square partition is executed. In SAFC, no additional computations are required to obtain the edge orientation of a range block. Instead, the edge orientation (of a range block) is obtained during the isometries calculation between a range block and all its possible domain blocks. According to our simulation, SAFC achieve 33.9 dB PSNR at 0.49 bit/pixel (bpp), while the conventional fractal coding achieves 34.0 dB at 0.55 bpp. In addition, we mathematically show that the proposed detector does find the correct edge orientation of blocks under certain conditions