Vector quantizer based on brightness maps for image compression with the polynomial transform

Abstract

We present a vector quantization scheme acting on brightness fields based on distance/distortion criteria correspondent with psycho-visual aspects. These criteria quantify sensorial distortion between vectors that represent either portions of a digital image or alternatively, coefficients of a transform-based coding system. In the latter case, we use an image representation model, namely the Hermite transform, that is based on some of the main perceptual characteristics of the human vision system (HVS) and in their response to light stimulus. Energy coding in the brightness domain, determination of local structure, code-book training and local orientation analysis are all obtained by means of the Hermite transform. This paper, for thematic reasons, is divided in four sections. The first one will shortly highlight the importance of having newer and better compression algorithms. This section will also serve to explain briefly the most relevant characteristics of the HVS, advantages and disadvantages related with the behavior of our vision in front of ocular stimulus. The second section shall go through a quick review of vector quantization techniques, focusing their performance on image treatment, as a preview for the image vector quantizer compressor actually constructed in section 5. Third chapter was chosen to concentrate the most important data gathered on brightness models. The building of this so-called brightness maps (quantification of the human perception on the visible objects reflectance), in a bi-dimensional model, will be addressed here. The Hermite transform, a special case of polynomial transforms, and its usefulness, will be treated, in an applicable discrete form, in the fourth chapter. As we have learned from previous works ¹, Hermite transform has showed to be a useful and practical solution to efficiently code the energy within an image block, deciding which kind of quantization is to be used upon them (whether scalar or vector). It will also be a unique tool to structurally classify the image block within a given lattice. This particular operation intends to be one of the main contributions of this work. The fifth section will fuse the proposals derived from the study of the three main topics- addressed in the last sections- in order to propose an image compression model that takes advantage of vector quantizers inside the brightness transformed domain to determine the most important structures, finding the energy distribution inside the Hermite domain. Sixth and last section will show some results obtained while testing the coding-decoding model. The guidelines to evaluate the image compressing performance were the compression ratio, SNR and psycho-visual quality. Some conclusions derived from the research and possible unexplored paths will be shown on this section as well.