Hierarchical Shape Segmentation and Registration via Topological Features of Laplace-Beltrami Eigenfunctions
This work introduces a method to hierarchically segment articulated shapes into meaningful parts and to register these parts across populations of near-isometric shapes (e.g. head, arms, legs and fingers of humans in different body postures). The method exploits the isometry invariance of eigenfunct...
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| Format: | Article |
| Language: | en_US |
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Springer Netherlands
2011
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| Online Access: | http://hdl.handle.net/1721.1/65160 |
| _version_ | 1811092522083024896 |
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| author | Reuter, Martin |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Reuter, Martin |
| author_sort | Reuter, Martin |
| collection | MIT |
| description | This work introduces a method to hierarchically segment articulated shapes into meaningful parts and to register these parts across populations of near-isometric shapes (e.g. head, arms, legs and fingers of humans in different body postures). The method exploits the isometry invariance of eigenfunctions of the Laplace-Beltrami operator and uses topological features (level sets at important saddles) for the segmentation. Concepts from persistent homology are employed for a hierarchical representation, for the elimination of topological noise and for the comparison of eigenfunctions. The obtained parts can be registered via their spectral embedding across a population of near isometric shapes. This work also presents the highly accurate computation of eigenfunctions and eigenvalues with cubic finite elements on triangle meshes and discusses the construction of persistence diagrams from the Morse-Smale complex as well as the relation to size functions. |
| first_indexed | 2024-09-23T15:19:32Z |
| format | Article |
| id | mit-1721.1/65160 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:19:32Z |
| publishDate | 2011 |
| publisher | Springer Netherlands |
| record_format | dspace |
| spelling | mit-1721.1/651602022-09-29T14:12:43Z Hierarchical Shape Segmentation and Registration via Topological Features of Laplace-Beltrami Eigenfunctions Reuter, Martin Massachusetts Institute of Technology. Department of Mechanical Engineering Reuter, Martin Reuter, Martin This work introduces a method to hierarchically segment articulated shapes into meaningful parts and to register these parts across populations of near-isometric shapes (e.g. head, arms, legs and fingers of humans in different body postures). The method exploits the isometry invariance of eigenfunctions of the Laplace-Beltrami operator and uses topological features (level sets at important saddles) for the segmentation. Concepts from persistent homology are employed for a hierarchical representation, for the elimination of topological noise and for the comparison of eigenfunctions. The obtained parts can be registered via their spectral embedding across a population of near isometric shapes. This work also presents the highly accurate computation of eigenfunctions and eigenvalues with cubic finite elements on triangle meshes and discusses the construction of persistence diagrams from the Morse-Smale complex as well as the relation to size functions. Alexander von Humboldt Foundation 2011-08-16T13:06:42Z 2011-08-16T13:06:42Z 2009-08 2009-07 Article http://purl.org/eprint/type/JournalArticle 0920-5691 1573-1405 http://hdl.handle.net/1721.1/65160 Reuter, Martin. “Hierarchical Shape Segmentation and Registration via Topological Features of Laplace-Beltrami Eigenfunctions.” International Journal of Computer Vision 89.2 (2010) : 287-308. en_US http://dx.doi.org/10.1007/s11263-009-0278-1 International Journal of Computer Vision Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Springer Netherlands Reuter |
| spellingShingle | Reuter, Martin Hierarchical Shape Segmentation and Registration via Topological Features of Laplace-Beltrami Eigenfunctions |
| title | Hierarchical Shape Segmentation and Registration via Topological Features of Laplace-Beltrami Eigenfunctions |
| title_full | Hierarchical Shape Segmentation and Registration via Topological Features of Laplace-Beltrami Eigenfunctions |
| title_fullStr | Hierarchical Shape Segmentation and Registration via Topological Features of Laplace-Beltrami Eigenfunctions |
| title_full_unstemmed | Hierarchical Shape Segmentation and Registration via Topological Features of Laplace-Beltrami Eigenfunctions |
| title_short | Hierarchical Shape Segmentation and Registration via Topological Features of Laplace-Beltrami Eigenfunctions |
| title_sort | hierarchical shape segmentation and registration via topological features of laplace beltrami eigenfunctions |
| url | http://hdl.handle.net/1721.1/65160 |
| work_keys_str_mv | AT reutermartin hierarchicalshapesegmentationandregistrationviatopologicalfeaturesoflaplacebeltramieigenfunctions |