Change search
ReferencesLink to record
Permanent link

Direct link
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, 13-21 p.Article in journal (Refereed) PublishedText
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, 13-21 p.
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 Science
Identifiers
URN: urn:nbn:se:kth:diva-181226DOI: 10.1111/cgf.12514ISI: 000362978000002ScopusID: 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: 2016-02-05Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Search in DiVA

By author/editor
Vejdemo-Johansson, Mikael
By organisation
Computer Vision and Active Perception, CVAP
In the same journal
Computer graphics forum (Print)
Computer Science

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 55 hits
ReferencesLink to record
Permanent link

Direct link