Fuzzy Vector Quantization of Images Based on Local Fractal Dimensions

Telecommunication networks are spreading worldwide. People can communicate with each other beyond spacial restrictions using the Internet. In this situation, the demand for transmission bandwidth and storage space continues to outstrip the capacity of existing technologies. Image and video compression technology is therefore essential for the effective use of communication networks. In this paper, we propose a new method to compress images using vector quantization. Dimensions of the training vectors to prepare a codebook are determined on the basis of local fractal dimensions (LFDs) of a learning image. This means that each block size to divide the learning image is specified by the LFDs. In principle, the smaller the number of pixels in a training vector is, the larger is a codebook (low bit rate). Furthermore, the smaller the number of pixels in a codebook is, the higher is the quality of the encoded image. This is a tradeoff between compression rate and quality of the encoded image. The tradeoff can be solved by the division of images with different block sizes. Furthermore, the code-vectors are computed from the training vectors using a fuzzy k-means clustering algorithm. The performance of the proposed algorithm was evaluated by compression rate and quality of encoded images in comparison with those using fuzzy generalized Lloyd algorithm. The experiments showed that the proposed algorithm solved the tradeoff between compression rate and quality of image.