TY - GEN A1 - Hildebrandt, Klaus A1 - Schulz, Christian A1 - Tycowicz, Christoph von A1 - Polthier, Konrad A2 - Mourrain, Bernard A2 - Schaefer, Scott A2 - Xu, Guoliang T1 - Eigenmodes of Surface Energies for Shape Analysis T2 - Advances in Geometric Modeling and Processing (Proceedings of Geometric Modeling and Processing 2010) N2 - 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. Y1 - 2010 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/5483 VL - 6130 SP - 296 EP - 314 PB - Springer Berlin / Heidelberg ER -