research-article

Separatrix persistence: extraction of salient edges on surfaces using topological methods

Authors:

D. GüntherAuthors Info & Claims

SGP '09: Proceedings of the Symposium on Geometry Processing

Pages 1519 - 1528

Published: 15 July 2009 Publication History

Abstract

Salient edges are perceptually prominent features of a surface. Most previous extraction schemes utilize the notion of ridges and valleys for their detection, thereby requiring curvature derivatives which are rather sensitive to noise. We introduce a novel method for salient edge extraction which does not depend on curvature derivatives. It is based on a topological analysis of the principal curvatures and salient edges of the surface are identified as parts of separatrices of the topological skeleton. Previous topological approaches obtain results including non-salient edges due to inherent properties of the underlying algorithms. We extend the profound theory by introducing the novel concept of separatrix persistence, which is a smooth measure along a separatrix and allows to keep its most salient parts only. We compare our results with other methods for salient edge extraction.

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Gehre ALim IKobbelt LGomes APurgathofer WJorge JLin M(2016)Adapting feature curve networks to a prescribed scaleProceedings of the 37th Annual Conference of the European Association for Computer Graphics10.5555/3058909.3058951(319-330)Online publication date: 9-May-2016
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Campen MIbing MEbke HZorin DKobbelt LKobbelt LOvsjanikov MPanozzo D(2016)Scale-invariant directional alignment of surface parametrizationsProceedings of the Symposium on Geometry Processing10.1111/cgf.12958(1-10)Online publication date: 20-Jun-2016
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Separatrix persistence: extraction of salient edges on surfaces using topological methods

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Published In

cover image Guide Proceedings

SGP '09: Proceedings of the Symposium on Geometry Processing

July 2009

278 pages

Conference Chair:
Konrad Polthier
Freie Universität Berlin
,
Program Chairs:
Marc Alexa
Technische Universität Berlin
,
Michael Kazhdan
Johns Hopkins University

Publisher

Eurographics Association

Goslar, Germany

Publication History

Published: 15 July 2009

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Cited By

Gehre ALim IKobbelt LGomes APurgathofer WJorge JLin M(2016)Adapting feature curve networks to a prescribed scaleProceedings of the 37th Annual Conference of the European Association for Computer Graphics10.5555/3058909.3058951(319-330)Online publication date: 9-May-2016
https://dl.acm.org/doi/10.5555/3058909.3058951
Biasotti SCerri APittaluga SSobrero DSpagnuolo MBiasotti SPintore GStanco F(2016)Tracking the evolution of rainfall precipitation fields using persistent maximaProceedings of the Conference on Smart Tools and Applications in Computer Graphics10.5555/3056860.3056865(29-37)Online publication date: 3-Oct-2016
https://dl.acm.org/doi/10.5555/3056860.3056865
Campen MIbing MEbke HZorin DKobbelt LKobbelt LOvsjanikov MPanozzo D(2016)Scale-invariant directional alignment of surface parametrizationsProceedings of the Symposium on Geometry Processing10.1111/cgf.12958(1-10)Online publication date: 20-Jun-2016
https://dl.acm.org/doi/10.1111/cgf.12958
De Floriani LFugacci UIuricich FMagillo P(2015)Morse complexes for shape segmentation and homological analysisComputer Graphics Forum10.1111/cgf.1259634:2(761-785)Online publication date: 1-May-2015
https://dl.acm.org/doi/10.1111/cgf.12596
Weber CHahmann SHagen HBonneau G(2012)Sharp feature preserving MLS surface reconstruction based on local feature line approximationsGraphical Models10.1016/j.gmod.2012.04.01274:6(335-345)Online publication date: 1-Nov-2012
https://dl.acm.org/doi/10.1016/j.gmod.2012.04.012
Wekel THellwich O(2012)Voronoi-Based extraction of a feature skeleton from noisy triangulated surfacesProceedings of the 11th Asian conference on Computer Vision - Volume Part II10.1007/978-3-642-37444-9_9(108-119)Online publication date: 5-Nov-2012
https://dl.acm.org/doi/10.1007/978-3-642-37444-9_9
Reininghaus JGünther DHotz IProhaska SHege H(2010)TADDProceedings of the Third international congress conference on Mathematical software10.5555/1888390.1888436(198-208)Online publication date: 13-Sep-2010
https://dl.acm.org/doi/10.5555/1888390.1888436
Myles APietroni NKovacs DZorin DDeRose T(2010)Feature-aligned T-meshesACM SIGGRAPH 2010 papers10.1145/1833349.1778854(1-11)Online publication date: 26-Jul-2010
https://dl.acm.org/doi/10.1145/1833349.1778854
Myles APietroni NKovacs DZorin D(2010)Feature-aligned T-meshesACM Transactions on Graphics10.1145/1778765.177885429:4(1-11)Online publication date: 26-Jul-2010
https://dl.acm.org/doi/10.1145/1778765.1778854
Weinkauf TGingold YSorkine O(2010)Topology-based smoothing of 2D scalar fields with C1-continuityProceedings of the 12th Eurographics / IEEE - VGTC conference on Visualization10.1111/j.1467-8659.2009.01702.x(1221-1230)Online publication date: 9-Jun-2010
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