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Eigenmodes of Surface Energies for Shape Analysis

  • In this work, we study the spectra and eigenmodes of the Hessian of various discrete surface energies and discuss applications to shape analysis. In particular, we consider a physical model that describes the vibration modes and frequencies of a surface through the eigenfunctions and eigenvalues of the Hessian of a deformation energy, and we derive a closed form representation for the Hessian (at the rest state of the energy) for a general class of deformation energies. Furthermore, we design a quadratic energy, such that the eigenmodes of the Hessian of this energy are sensitive to the extrinsic curvature of the surface. Based on these spectra and eigenmodes, we derive two shape signatures. One that measures the similarity of points on a surface, and another that can be used to identify features of the surface. In addition, we discuss a spectral quadrangulation scheme for surfaces.

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Author:Klaus Hildebrandt, Christian Schulz, Christoph von Tycowicz, Konrad Polthier
Editor:Bernard Mourrain, Scott Schaefer, Guoliang Xu
Document Type:In Collection
Parent Title (English):Advances in Geometric Modeling and Processing (Proceedings of Geometric Modeling and Processing 2010)
First Page:296
Last Page:314
Series:Lecture Notes in Computer Science
Publisher:Springer Berlin / Heidelberg
Fulltext Url:https://nbn-resolving.org/urn:nbn:de:0296-matheon-7325
Year of first publication:2010
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