Tangles and the Mona Lisa
Combinatorics
2017-11-09 v3 Information Theory
math.IT
Abstract
We show how an image can, in principle, be described by the tangles of the graph of its pixels. The tangle-tree theorem provides a nested set of separations that efficiently distinguish all the distinguishable tangles in a graph. This translates to a small data set from which the image can be reconstructed. The tangle duality theorem says that a graph either has a certain-order tangle or a tree-structure witnessing that this cannot exist. This tells us the maximum resolution at which the image contains meaningful information.
Keywords
Cite
@article{arxiv.1603.06652,
title = {Tangles and the Mona Lisa},
author = {Reinhard Diestel and Geoff Whittle},
journal= {arXiv preprint arXiv:1603.06652},
year = {2017}
}