Vector quantization of images with variable block size

We proposed a vector quantization (VQ) with variable block size using local fractal dimensions (LFDs) of an image. A VQ with variable block size has so far been implemented using a quad tree (QT) decomposition algorithm. QT decomposition carries out image partitioning based on the homogeneity of local regions of an image. However, we think that the complexity of local regions of an image is more essential than the homogeneity, because we pay close attention to complex region than homogeneous region. Therefore, complex regions are essential for image compression. Since the complexity of regions of an image is quantified by values of LFD, we implemented variable block size using LFD values and constructed a codebook (CB) for a VQ. To confirm the performance of the proposed method, we only used a discriminant analysis and FGLA to construct a CB. Here, the FGLA is the algorithm to combine generalized Lloyd algorithm (GLA) and the fuzzy k means algorithm. Results of computational experiments showed that this method correctly encodes the regions that we pay close attention. This is a promising result for obtaining a well-perceived compressed image. Also, the performance of the proposed method is superior to that of VQ by FGLA in terms of both compression rate and decoded image quality. Furthermore, 1.0 bpp and more than 30 dB in PSNR by a CB with only 252 code-vectors were achieved using this method.