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“Slant Transform Image Coding”
by Wen-Hsiung Chen
May 1973
During the past few years the Fourier and Hadamard transforms have been applied quite successfully to obtain a bandwidth reduction and tolerance to channel errors for digital images. Both of these transforms provide a high energy compaction of an image and possess a fast computational algorithm. Neither, however, has been expressly tailored to the characteristic of a typical image. In this dissertation a slant transform matrix consisting of basis vectors which resemble typical lines of an image has been developed. The key feature of the transformation is a set of discrete sawtooth waveforms for the representation of linear spatial brightness changes within an image. A fast transform algorithm based on the matrix decomposition has also been presented. The transform has been proven to be superior, from the standpoint of image quality, to other transforms possessing fast computational algorithms.
The statistical properties of the slant transform have been analyzed by introducing probability density and covariance models for the transform samples. The bandwidth reduction capability of the slant transform has been investigated by several test images. Two methods of achieving bandwidth reduction have been presented, namely, threshold and zonal coding. Studies have indicated that the average coding of a monochrome image can be reduced from 8 bits/pixel to 1 bit/pixel or 1.5 bits/pixel for the threshold and zonal coding, respectively, without seriously degrading the image quality. Studies immunity, and can be practically implemented.
Spatial redundancy of color images and the limitations of human color vision have also been exploited by slant transform coding to achieve a bandwidth reduction for natural color images. It has been found by computer simulation that the average coding of a color image can be reduced from 24 bits/pixel to about 2 bits/pixel while preserving good quality reconstruction.