  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.
