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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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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 .

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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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