Isometry-Based Shape-Adaptive Fractal Coding for Images

Fractal image coding is an effective method to eliminate the image redundancy through piecewise self-transformability. The fractal code consists of a set of contractive affine transforms. To improve the performance when a range block experiences large error, we usually partition the range block into square or nonsquare subrange blocks for two- or multilevel fractal coding. In this paper, we find an inherent property of fractal coding that can be used to decide the edge orientation of a range block. Then this property is used for shape-adaptive fractal coding (SAFC). In SAFC, the top-level range block is partitioned into square or nonsquare (rectangle or triangle) subrange blocks for multilevel fractal encoding. Here, the maximum size of the range block can be the same as that of the whole image size while the minimum size is 4×4. In SAFC, no additional computations are required to obtain the edge orientation of a range block. Instead, we propose an edge-orientation detector, where the edge orientation of a range block is obtained during the fractal encoding process. According to our simulation results, SAFC can reduce the bit rate requirement of the conventional fractal coding scheme.