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

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Computer Analysis of Images and Patterns (CAIP 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9256))

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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 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.

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Author information

Authors and Affiliations

  1. Microsoft Research Cambridge, 21 Station Road, Cambridge, CB1 2FB, UK

    Vitaliy Kurlin

  2. Department of Mathematical Sciences, Durham University, Durham, DH1 3LE, UK

    Vitaliy Kurlin

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  1. Vitaliy Kurlin
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Correspondence to Vitaliy Kurlin .

Editor information

Editors and Affiliations

  1. University of Malta, Msida, Malta

    George Azzopardi

  2. University of Groningen, Groningen, The Netherlands

    Nicolai Petkov

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Kurlin, V. (2015). A Homologically Persistent Skeleton is a Fast and Robust Descriptor of Interest Points in 2D Images. In: Azzopardi, G., Petkov, N. (eds) Computer Analysis of Images and Patterns. CAIP 2015. Lecture Notes in Computer Science(), vol 9256. Springer, Cham. https://doi.org/10.1007/978-3-319-23192-1_51

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  • DOI: https://doi.org/10.1007/978-3-319-23192-1_51

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23191-4

  • Online ISBN: 978-3-319-23192-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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