# Quantisation Scale-Spaces

arXiv: https://arxiv.org/abs/2103.10491 · HTML: https://mlsanity.com/paper/2103.10491/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Mar 2021.

## Built on by (most cited first, 2 of 2)

- [Generalised Diffusion Probabilistic Scale-Spaces](https://mlsanity.com/paper/2309.08511/) (2023)
- [Skeleton Sparsification and Densification Scale-Spaces](https://mlsanity.com/paper/2509.21398/) (2025)

## Abstract (arXiv)

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.