Quantisation Scale-Spaces

TL;DR

This paper introduces quantisation scale-spaces based on hierarchical grey-value sparsification, which are linked to information theory and improve image compression over traditional methods.

Contribution

It presents a novel sparsification algorithm for grey-value domains that outperforms uniform quantisation and classical clustering.

Findings

Quantisation scale-spaces are effective for image inpainting-based compression.

The proposed algorithm surpasses traditional uniform quantisation.

Hierarchical quantisation improves coding efficiency.

Abstract

Recently, sparsification scale-spaces have been obtained as a sequence of inpainted images by gradually removing known image data. Thus, these scale-spaces rely on spatial sparsity. In the present paper, we show that sparsification of the co-domain, the set of admissible grey values, also constitutes scale-spaces with induced hierarchical quantisation techniques. These quantisation scale-spaces are closely tied to information theoretical measures for coding cost, and therefore particularly interesting for inpainting-based compression. Based on this observation, we propose a sparsification algorithm for the grey-value domain that outperforms uniform quantisation as well as classical clustering approaches.