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Computing Minimum Area Homologies
KTH, School of Computer Science and Communication (CSC), Computer Vision and Active Perception, CVAP. University of Minnesota, United States; Jozef Stefan Institute, Slovenia.ORCID iD: 0000-0001-6322-7542
2015 (English)In: Computer graphics forum (Print), ISSN 0167-7055, E-ISSN 1467-8659, Vol. 34, no 6, p. 13-21Article in journal (Refereed) Published
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Abstract [en]

Calculating and categorizing the similarity of curves is a fundamental problem which has generated much recent interest. However, to date there are no implementations of these algorithms for curves on surfaces with provable guarantees on the quality of the measure. In this paper, we present a similarity measure for any two cycles that are homologous, where we calculate the minimum area of any homology (or connected bounding chain) between the two cycles. The minimum area homology exists for broader classes of cycles than previous measures which are based on homotopy. It is also much easier to compute than previously defined measures, yielding an efficient implementation that is based on linear algebra tools. We demonstrate our algorithm on a range of inputs, showing examples which highlight the feasibility of this similarity measure.

Place, publisher, year, edition, pages
Blackwell Publishing, 2015. Vol. 34, no 6, p. 13-21
Keyword [en]
computational geometry, curves and surfaces, I.3.5 [Computer Graphics]: Computational Geometry and Object Modelling-Geometric algorithms, languages and systems; I.5.3 [Pattern Recognition]: Clustering-Similarity measures, weird math, Computer graphics, Geometry, Linear algebra, Pattern recognition, Pattern recognition systems, Efficient implementation, Homotopies, Linear algebra tools, Object modelling, Similarity measure, Clustering algorithms
National Category
Computer Sciences
Identifiers
URN: urn:nbn:se:kth:diva-181226DOI: 10.1111/cgf.12514ISI: 000362978000002Scopus ID: 2-s2.0-84942370228OAI: oai:DiVA.org:kth-181226DiVA: diva2:900941
Note

QC 20160205

Available from: 2016-02-05 Created: 2016-01-29 Last updated: 2018-01-10Bibliographically approved

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Vejdemo-Johansson, Mikael

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