Hypergraph Grammar-Based Model of Adaptive Bitmap Compression

Abstract

JPEG algorithm defines a sequence of steps (essential and optional) executed in order to compress an image. The first step is an optional conversion of the image color space from RBG (red-blue-green) to YCbCr (luminance and two chroma components). This step allows to discard part of chrominance information, a useful gain due to the fact, that the chrominance resolution of the human eye is much lower than the luminance resolution. In the next step, the image is divided into 8 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times $$\end{document} 8 blocks, called MCUs (Minimum Coded Units). In this paper we present a new adaptive bitmap compression algorithm, and we compare it to the state-of-the-art of JPEG algorithms. Our algorithm utilizes hypergraph grammar model, partitioning the bitmap into a set of adaptively selected rectangles. Each rectangle approximates a bitmap using MCUs with the size selected according to the entire rectangular element. The hypergraph grammar model allows to describe the whole compression algorithm by a set of five productions. They are executed during the compression stage, and they partition the actual rectangles into smaller ones, until the required compression rate is obtained. We show that our method allows to compress bitmaps with large uniform areas in a better way than traditional JPEG algorithms do.