Hierarchical Shape Segmentation and Registration via Topological Features of Laplace-Beltrami Eigenfunctions
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Reuter_Hierarchical Shape.pdf
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4.04 MB
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Adobe PDF
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Author(s)
Reuter, Martin
Date Issued
August 2009
Journal
International Journal of Computer Vision
Publisher
Springer Netherlands
Citation
Reuter, Martin. “Hierarchical Shape Segmentation and Registration via Topological Features of Laplace-Beltrami Eigenfunctions.” International Journal of Computer Vision 89.2 (2010) : 287-308.
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Terms of Use
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.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s11263-009-0278-1
