Uniform image partitioning for fractal compression on virtual hexagonal structure

Hexagonal structure is different from the traditional square structure for image representation. The geometrical arrangement of pixels on hexagonal structure can be described in terms of a hexagonal grid. Uniformly separating image into seven similar copies with a smaller scale has commonly been used for parallel and accurate image processing including image compression on hexagonal structure. However, all the existing hardware for capturing image and for displaying image are produced based on square architecture. It has become a serious problem affecting the advanced research based on hexagonal structure. Furthermore, the current techniques used for uniform separation of images on hexagonal structure do not coincide with the rectangular shape of images. This has been an obstacle in the use of hexagonal structure for image processing. In this paper, we briefly review a newly developed virtual hexagonal structure that is scalable. Based on this virtual structure, algorithms for uniform image separation are presented. The virtual hexagonal structure retains image resolution during the process of image separation, and does not introduce distortion. Furthermore, images can be smoothly and easily transferred between the traditional square structure and the hexagonal structure while the image shape is kept in rectangle. As an application of image partitioning, we present a Fractal Image Compression (FIC) method on the virtual image structure by adopting Fisher's basic FIC method on the traditional square image structure. The modification on the definition of range block and domain block is implemented in order to utilize the enhanced image structure. The results of the FIC approach applied to testing images are analyzed and show higher fidelity.