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
URI: http://wscg.zcu.cz/WSCG2011/!_2011_J_WSCG_1-3.pdf
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)

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