2016/03/22 by Reinhard Diestel, Diestel, Reinhard, Geoff Whittle +1 · 2 citations
Computer Science · #05C83 #65D18 #68P #68U10 #94A08 #Advanced Graph Theory Research #Combinatorics (math.CO) #Digital Image Processing Techniques #FOS: Computer and information sciences #FOS: Mathematics #H.2.8 #Information Theory (cs.IT) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1603.06652
openalex publication_date 2016/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.