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International Workshop on Graph-Based Representations in Pattern Recognition

GbRPR 2013: Graph-Based Representations in Pattern Recognition pp 184–193Cite as

Towards Minimal Barcodes

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 7877))

Abstract

In the setting of persistent homology computation, a useful tool is the persistence barcode representation in which pairs of birth and death times of homology classes are encoded in the form of intervals. Starting from a polyhedral complex K (an object subdivided into cells which are polytopes) and an initial order of the set of vertices, we are concerned with the general problem of searching for filters (an order of the rest of the cells) that provide a minimal barcode representation in the sense of having minimal number of “k-significant” intervals, which correspond to homology classes with life-times longer than a fixed number k. As a first step, in this paper we provide an algorithm for computing such a filter for k = 1 on the Hasse diagram of the poset of faces of K.

Partially supported under grant MTM2012-32706. Authors listed alphabetically.

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Author information

Authors and Affiliations

  1. Applied Math Dept., School of Computer Engineering, U. Seville, Spain

    Rocío González-Díaz & María-José Jiménez

  2. ECE Dept., NCSU, Raleigh, NC, USA

    Hamid Krim

Authors
  1. Rocío González-Díaz
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  2. María-José Jiménez
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  3. Hamid Krim
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Editor information

Editors and Affiliations

  1. Dept. of Pattern Recognition and Image Processing, Vienna University of Technology, Favoritenstr. 9-11, 186-3, 1040, Vienna, Austria

    Walter G. Kropatsch , Nicole M. Artner  & Yll Haxhimusa ,  & 

  2. Department of Computer Science, University of Münster, Einsteinstr. 62, 48149, Münster, Germany

    Xiaoyi Jiang

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González-Díaz, R., Jiménez, MJ., Krim, H. (2013). Towards Minimal Barcodes. In: Kropatsch, W.G., Artner, N.M., Haxhimusa, Y., Jiang, X. (eds) Graph-Based Representations in Pattern Recognition. GbRPR 2013. Lecture Notes in Computer Science, vol 7877. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38221-5_20

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  • DOI: https://doi.org/10.1007/978-3-642-38221-5_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38220-8

  • Online ISBN: 978-3-642-38221-5

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