Data Compression Using Image Contours

Abstract

This paper proposes an approach to waveform coding that generates a family of one dimensional waveforms from a two dimensional image, transform codes the waveforms by fitting a low rank approximation to them, and codes the approximation parameters into variable length binary codes that reflect the probabilistic structure of the image. We argue that contour lines are the most natural one dimensional lines to pass through an image. As readers of topographic maps know, a relatively small number of them may be used to transmit relevant information about an image. Furthermore, contours organise the image data into pixel classes that are characterised by smooth connecting lines. It is reasonable to assume that these contour lines can be represented by very low rank models. The distribution of the approximating parameters in the model is then used to derive a coding scheme. In this way first and second order information is used to compress the image data. The first order information, the data itself, is low rank approximated. The second order information, typically represented by the correlation structure of the image, is used to derive the probabilistic structure of the approximation parameters so that probable para-meters may be coded into short words and improbable ones into long words. As contours tend to be shaped very much like adjacent contours, as in the contouring of a peak or valley on a topographic map, it is reasonable to assume that the correlation between contours can be exploited to reduce further the number of bits required to represent a scene.