Computing Minimum Area Homologies

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dc.contributor.authorChambers, Erin Wolfen_US
dc.contributor.authorVejdemo‐Johansson, Mikaelen_US
dc.contributor.editorDeussen, Oliver and Zhang, Hao (Richard)en_US
dc.date.accessioned2015-10-12T13:32:45Z
dc.date.available2015-10-12T13:32:45Z
dc.date.issued2015en_US
dc.description.abstractCalculating 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.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.en_US
dc.description.number6en_US
dc.description.sectionheadersArticlesen_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume34en_US
dc.identifier.doi10.1111/cgf.12514en_US
dc.identifier.urihttps://doi.org/10.1111/cgf.12514en_US
dc.publisherCopyright © 2015 The Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectcurves and surfacesen_US
dc.subjectcomputational geometryen_US
dc.subjectweird mathen_US
dc.subjectI.3.5 [Computer Graphics]: Computational Geometry and Object Modelling–Geometric algorithmsen_US
dc.subjectlanguages and systems; I.5.3 [Pattern Recognition]: Clustering–Similarity measuresen_US
dc.titleComputing Minimum Area Homologiesen_US
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