Stable Topological Signatures for Points on 3D Shapes

Comparing points on 3D shapes is among the fundamental operations in shape analysis. To facilitate this task, a great number of local point signatures or descriptors have been proposed in the past decades. However, the vast majority of these descriptors concentrate on the local geometry of the shape...

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Vydané v:Computer graphics forum Ročník 34; číslo 5; s. 1 - 12
Hlavní autori: Carrière, Mathieu, Oudot, Steve Y., Ovsjanikov, Maks
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Oxford Blackwell Publishing Ltd 01.08.2015
Predmet:
3-D graphics
Analysis
and systems
Categories and Subject Descriptors (according to ACM CCS)
I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Geometric algorithms
I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Geometric algorithms, languages, and systems
languages
Learning
Mathematical analysis
Signatures
Studies
Tasks
Three dimensional
Topological manifolds
Topology
Training
Vectors (mathematics)
ISSN:0167-7055, 1467-8659
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Popis
Shrnutí:Comparing points on 3D shapes is among the fundamental operations in shape analysis. To facilitate this task, a great number of local point signatures or descriptors have been proposed in the past decades. However, the vast majority of these descriptors concentrate on the local geometry of the shape around the point, and thus are insensitive to its connectivity structure. By contrast, several global signatures have been proposed that successfully capture the overall topology of the shape and thus characterize the shape as a whole. In this paper, we propose the first point descriptor that captures the topology structure of the shape as ‘seen’ from a single point, in a multiscale and provably stable way. We also demonstrate how a large class of topological signatures, including ours, can be mapped to vectors, opening the door to many classical analysis and learning methods. We illustrate the performance of this approach on the problems of supervised shape labeling and shape matching. We show that our signatures provide complementary information to existing ones and allow to achieve better performance with less training data in both applications.
Bibliografia:istex:9B33B9A7CFA585013C133852FCF229E5A9034A9F
ArticleID:CGF12692
ark:/67375/WNG-4CV55959-L
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.12692