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A Gromov-Hausdorff Framework with Diffusion Geometry for Topologically-Robust Non-rigid Shape Matching
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“In cases with large topological changes, the isometry assumption may fail [38]; handling such issues is a challenging task.”
From Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid (2013) · cites this paper as [38]
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“Recent intrinsic techniques [36], [38], [39] use low dimensional embedding to by-pass the high-dimensionality problem by assuming a strong inelastic isometry constraint.”
From Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid (2013) · cites this paper as [38]
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Cited by
Sorted by citations
A Concise and Provably Informative Multi‐Scale Signature Based on Heat Diffusion
Sun, J. Z., Ovsjanikov, M., & Guibas, L. J. (2009) · Computer Graphics Forum · doi:10.1111/j.1467-8659.2009.01515.x · Cited by 1,466
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“Finally, another promising direction is the use of multimodal hashing [Bronstein et al. 2010e] to cope with the problem of cross-representation retrieval and different versions of vocabularies.”
BackgroundMethodInfluentialSelf-citationThe wave kernel signature: A quantum mechanical approach to shape analysis
Aubry, M., Schlickewei, U., & Cremers, D. (2011) · IEEE International Conference on Computer Vision Workshops · doi:10.1109/iccvw.2011.6130444 · Cited by 747
“The heat kernel is intimately related to the diffusion distance between points which has been used intensively for shape analysis recently (cf. e.g. [6]).”
BackgroundScale-invariant heat kernel signatures for non-rigid shape recognition
Bronstein, M. M., & Kokkinos, I. (2010) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2010.5539838 · Cited by 690
“In [5], shapes were analyzed as metric spaces equipped with diffusion metrics.”
MethodSelf-citation
Metadata
- Authors
- Bronstein, A. M., Bronstein, M. M., Kimmel, R., Mahmoudi, M., & Sapiro, G.
- Affiliations
- Technion – Israel Institute of Technology (IL)
- University of Minnesota (US)
- Corresponding author
- Sapiro, Guillermo
- Venue
- International Journal of Computer Vision
- Published
- 2009-10-08
- Volume
- 89
- Issue
- 2-3
- Pages
- 266-286
- ISSN
- 0920-5691 (ISSN-L)
- 1573-1405
- OpenAlex
- W1982465050
- Cited by
- 267
- References
- 78
- Citations by year
- 2026: 1 · 2025: 5 · 2024: 6 · 2023: 4 · 2022: 5 · 2021: 10 · 2020: 12 · 2019: 16 · 2018: 19 · 2017: 22 · 2016: 17 · 2015: 18 · 2014: 27 · 2013: 30 · 2012: 31
- FWCI
- 25.28
- Type
- journal article
- Language
- en
- Open access
- green
- hdl.handle.net
- Licence
- www.springer.com/tdm (tdm)
- Locations
- International Journal of Computer Vision (publishedVersion)
- University of Minnesota Digital Conservancy (University of Minnesota) (submittedVersion)
- Funders
- National Institutes of Health
- Defense Advanced Research Projects Agency
- Topics
- Physical Sciences › Computer Science › Computer Graphics and Computer-Aided Design › 3D Shape Modeling and Analysis
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Topological and Geometric Data Analysis
- Physical Sciences › Mathematics › Applied Mathematics › Geometric Analysis and Curvature Flows
- Keywords
- non-rigid shape matching, shape recognition, diffusion distance, Gromov-Hausdorff distance, metric geometry, topological robustness, geodesic distance, non-rigid deformation, missing data
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