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Tangles and the Mona Lisa
Reinhard Diestel, Geoff Whittle · 2016-03-22 · via cs.IT updates on arXiv.org

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.

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