International Journal of Computer Vision

, Volume 89, Issue 2–3, pp 287–308 | Cite as

Hierarchical Shape Segmentation and Registration via Topological Features of Laplace-Beltrami Eigenfunctions

Article

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.

Keywords

Laplace-Beltrami operator Hierarchical mesh segmentation Eigenfunctions Persistence Morse-Smale complex 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringMassachusetts Institute of TechnologyCambridgeUSA

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