Title: | Generalized heat kernel signatures |
Authors: | Zobel, Valentin Reininghaus, Jan Hotz, Ingrid |
Citation: | Journal of WSCG. 2011, vol. 19, no. 1-3, p. 93-100. |
Issue Date: | 2011 |
Publisher: | Václav Skala - UNION Agency |
Document type: | článek article |
URI: | http://wscg.zcu.cz/WSCG2011/!_2011_J_WSCG_1-3.pdf http://hdl.handle.net/11025/1251 |
ISSN: | 1213–6972 (hardcopy) 1213–6980 (CD-ROM) 1213–6964 (on-line) |
Keywords: | tvarová analýza;Hodgeův laplacián;tepelné jádro |
Keywords in different language: | shape analysis;Hodge laplacian;heat kernel |
Abstract: | In this work we propose a generalization of the Heat Kernel Signature (HKS). The HKS is a point signature derived from the heat kernel of the Laplace-Beltrami operator of a surface. In the theory of exterior calculus on a Riemannian manifold, the Laplace-Beltrami operator of a surface is a special case of the Hodge Laplacian which acts on r-forms, i. e. the Hodge Laplacian on 0-forms (functions) is the Laplace-Beltrami operator. We investigate the usefulness of the heat kernel of the Hodge Laplacian on 1-forms (which can be seen as the vector Laplacian) to derive new point signatures which are invariant under isometric mappings. A similar approach used to obtain the HKS yields a symmetric tensor field of second order; for easier comparability we consider several scalar tensor invariants. Computed examples show that these new point signatures are especially interesting for surfaces with boundary. |
Rights: | © Václav Skala - UNION Agency |
Appears in Collections: | Number 1-3 (2011) |
Please use this identifier to cite or link to this item:
http://hdl.handle.net/11025/1251
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.