International Conference on Computer Analysis of Images and Patterns

CAIP 2015: Computer Analysis of Images and Patterns pp 606-617 | Cite as

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

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

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 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.

     

Keywords

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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