A Homologically Persistent Skeleton is a Fast and Robust Descriptor of Interest Points in 2D Images

  • Vitaliy Kurlin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9256)


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 a Homologically Persistent Skeleton, which is scale-and-rotation invariant and depends only on the cloud without extra parameters. This graph

  1. (1)

    is computable in time \(O(n\log n)\) for any n points in the plane;

  2. (2)

    has the minimum total length among all graphs that span a 2D cloud at any scale and also have most persistent 1-dimensional cycles;

  3. (3)

    is geometrically stable for noisy samples around planar graphs.



Skeleton Delaunay triangulation Persistent homology 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Microsoft Research CambridgeCambridgeUK
  2. 2.Department of Mathematical SciencesDurham UniversityDurhamUK

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