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arXiv · 2204.04857

Why Shape Coding? Asymptotic Analysis of the Entropy Rate for Digital Images

Gangtao Xin·Pingyi Fan·Khaled B. Letaief
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Abstract

This paper focuses on the ultimate limit theory of image compression. It proves that for an image source, there exists a coding method with shapes that can achieve the entropy rate under a certain condition where the shape-pixel ratio in the encoder/decoder is $O({1 \over {\log t}})$. Based on the new finding, an image coding framework with shapes is proposed and proved to be asymptotically optimal for stationary and ergodic processes. Moreover, the condition $O({1 \over {\log t}})$ of shape-pixel ratio in the encoder/decoder has been confirmed in the image database MNIST, which illustrates the soft compression with shape coding is a near-optimal scheme for lossless compression of images.

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Gangtao Xin, Pingyi Fan, Khaled B. Letaief. 2022-12-27. Why Shape Coding? Asymptotic Analysis of the Entropy Rate for Digital Images. https://doi.org/10.3390/e25010048

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