Title: A homologically persistent skeleton in computer vision
Dr Vitaliy Kurlin (Department of Mathematical Sciences, Durham University &
Microsoft Research Cambridge, UK) http://kurlin.org/

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Abstract: 2D images often contain irregular salient features and interest points with non integer coordinates.
Our skeletonization problem for such a noisy sparse cloud is to summarize the topology of a given
2D cloud across all scales in the form of a graph, which can be used for combining local features
into a more powerful object-wide descriptor. We extend a classical Minimum Spanning Tree of a cloud
to the new fundamental concept of a homologically persistent skeleton, which is scale-and-rotation
invariant and depends only on the given cloud without extra parameters. This graph 
(1) is computable in time O(n log n) for any n points in the plane;
(2) has the minimum length over all graphs that span a 2D cloud and have most persistent 1-dimensional cycles;
(3) gives a close geometric and correct topological approximation to a good graph given only by a noisy sample. 
The paper is available at http://kurlin.org/projects/homologically-persistent-skeleton-dim2.pdf (15 pages, 2.8M).