One Point Isometric Matching with the Heat Kernel
Open accessAbstract
A common operation in many geometry processing algorithms consists of finding correspondences between pairs of shapes by finding structure‐preserving maps between them. A particularly useful case of such maps is isometries, which preserve geodesic distances between points on each shape. Although several algorithms have been proposed to find approximately isometric maps between a pair of shapes, the structure of the space of isometries is not well understood. In this paper, we show that under mild genericity conditions, a single correspondence can be used to recover an isometry defined on entire shapes, and thus the space of all isometries can be parameterized by one correspondence between a pair of points. Perhaps surprisingly, this result is general, and does not depend on the dimensionality or the genus, and is valid for compact manifolds in any dimension. Moreover, we show that both the initial correspondence and the isometry can be recovered efficiently in practice. This allows us to devise an algorithm to find intrinsic symmetries of shapes, match shapes undergoing isometric deformations, as well as match partial and incomplete models efficiently.
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[40] suggests that fixing one correspondence, all other correspondences can be inferred for non-rigid shapes.
“[40] suggests that fixing one correspondence, all other correspondences can be inferred for non-rigid shapes.”
From Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid (2013) · cites this paper as [40]
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Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid
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- Authors
- Ovsjanikov, M., Mérigot, Q., Mémoli, F., & Guibas, L.
- Affiliations
- Stanford University (US)
- Institut national de recherche en sciences et technologies du numérique (FR)
- Venue
- Computer Graphics Forum
- Publisher
- Wiley
- Published
- 2010-07
- Volume
- 29
- Issue
- 5
- Pages
- 1555-1564
- ISSN
- 0167-7055 (ISSN-L)
- 1467-8659
- OpenAlex
- W2127025496
- Semantic Scholar
- 645abbf4e0ce72f2b65eae5a6d3d9a9021cf206d
- Cited by
- 301
- References
- 46
- Citations by year
- 2026: 5 · 2025: 3 · 2024: 4 · 2023: 2 · 2022: 10 · 2021: 16 · 2020: 19 · 2019: 16 · 2018: 30 · 2017: 21 · 2016: 43 · 2015: 17 · 2014: 34 · 2013: 34 · 2012: 28
- FWCI
- 25.17
- Type
- journal article
- Language
- en
- Open access
- green
- hal.science
- Licence
- Locations
- Computer Graphics Forum (publishedVersion)
- HAL (submittedVersion, other-oa)
- Adelaide Research & Scholarship (AR&S) (University of Adelaide) (submittedVersion)
- King Abdullah University of Science and Technology Repository (King Abdullah University of Science and Technology) (submittedVersion)
- Topics
- Physical Sciences › Engineering › Computational Mechanics › 3D Shape Modeling and Analysis
- Physical Sciences › Mathematics › Applied Mathematics › Geometric Analysis and Curvature Flows
- Physical Sciences › Computer Science › Computer Graphics and Computer-Aided Design › Computational Geometry and Mesh Generation
- Keywords
- heat kernel, isometries, shape correspondence, shape matching, intrinsic symmetry, isometric deformations, partial model matching, incomplete models, compact manifolds, geodesic distance
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