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Linear shift-invariant operators for processing surface meshes
Alexa, M.
Dept. of Comput. Sci., Darmstadt Univ. of Technol., Germany;

This paper appears in: 3D Data Processing, Visualization and Transmission, 2004. 3DPVT 2004. Proceedings. 2nd International Symposium on
Publication Date: 6-9 Sept. 2004
On page(s): 76- 81
ISSN:
ISBN: 0-7695-2223-8
INSPEC Accession Number: 8244529
Digital Object Identifier: 10.1109/TDPVT.2004.1335151
Current Version Published: 2004-09-20

Abstract
Shift-invariant operators for surface meshes are defined using geometric realizations of the mesh. Then, shift-invariance essentially means isotropy w.r.t. a distance metric. The particular case of the so-defined LSI operators with small support is analyzed in detail, showing a connection to mean value coordinates. The topological Laplacian operator turns out to be the LSI operator of the topological realization of the mesh. More generally, assuming different geometric realizations or metrics allows interpreting various mesh processing techniques as LSI operators.

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