An Improved Riemannian Metric Approximation for Graph Cuts

DANĚK, Ondřej and Pavel MATULA. An Improved Riemannian Metric Approximation for Graph Cuts. In 16th International Conference on Discrete Geometry for Computer Imagery. Berlin, Heidelberg: Springer-Verlag, 2011, p. 71-82. ISBN 978-3-642-19866-3. Available from: https://dx.doi.org/10.1007/978-3-642-19867-0_6.

Basic information

Original name

An Improved Riemannian Metric Approximation for Graph Cuts

Name in Czech

Vylepšená aproximace Riemannovské metriky pomocí grafových řezů

Authors

DANĚK, Ondřej (203 Czech Republic, guarantor, belonging to the institution) and Pavel MATULA (203 Czech Republic, belonging to the institution)

Edition

Berlin, Heidelberg, 16th International Conference on Discrete Geometry for Computer Imagery, p. 71-82, 12 pp. 2011

Publisher

Springer-Verlag

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Other information

Language

English

Type of outcome

Stať ve sborníku

Field of Study

10201 Computer sciences, information science, bioinformatics

Country of publisher

Germany

Confidentiality degree

není předmětem státního či obchodního tajemství

Publication form

printed version "print"

References:

URL

Impact factor

Impact factor: 0.402 in 2005

RIV identification code

RIV/00216224:14330/11:00067211

Organization unit

Faculty of Informatics

ISBN

978-3-642-19866-3

ISSN

DOI

http://dx.doi.org/10.1007/978-3-642-19867-0_6

UT WoS

000297039900006

Keywords in English

graph cuts; metric approximation; Riemannian metrics; image segmentation

Tags

International impact, Reviewed

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Abstract

V originále

Boykov and Kolmogorov showed that it is possible to find globally minimal contours and surfaces via graph cuts by embedding an appropriate metric approximation into the graph edge weights and derived the requisite formulas for Euclidean and Riemannian metrics. In [2] we have proposed an improved Euclidean metric approximation that is invariant under (horizontal and vertical) mirroring, applicable to grids with anisotropic resolution and with a smaller approximation error. In this paper, we extend our method to general Riemannian metrics that are essential for graph cut based image segmentation or stereo matching. It is achieved by the introduction of a transformation reducing the Riemannian case to the Euclidean one and adjusting the formulas from [9] to be able to cope with non-orthogonal grids. We demonstrate that the proposed method yields smaller approximation errors than the previous approaches both in theory and practice.

In Czech

Článek se zabývá aproximací Riemannovské metriky pomocí grafových řezů.

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Links

LC535, research and development project	Name: Dynamika a organizace chromosomů během buněčného cyklu v normě a patologii Investor: Ministry of Education, Youth and Sports of the CR, Dynamika a organizace chromosomů během buněčného cyklu v normě a patologii
MSM0021622419, plan (intention)	Name: Vysoce paralelní a distribuované výpočetní systémy Investor: Ministry of Education, Youth and Sports of the CR, Highly Parallel and Distributed Computing Systems
MUNI/A/0914/2009, interní kód MU	Name: Rozsáhlé výpočetní systémy: modely, aplikace a verifikace (Acronym: SV-FI MAV) Investor: Masaryk University, Category A
2B06052, research and development project	Name: Vytipování markerů, screening a časná diagnostika nádorových onemocnění pomocí vysoce automatizovaného zpracování multidimenzionálních biomedicínských obrazů (Acronym: Biomarker) Investor: Ministry of Education, Youth and Sports of the CR, Determination of markers, screening and early diagnostics of cancer diseases using highly automated processing of multidimensional biomedical images