NDLI: Multi-scale Feature Spaces for Shape Processing and Analysis

Content Provider	IEEE Xplore Digital Library
Author	Patanè, G. Falcidieno, B.
Copyright Year	2010
Abstract	In digital geometry processing and shape modeling, the Laplace-Beltrami and the heat diffusion operator, together with the corresponding Laplacian eigenmaps, harmonic and geometry-aware functions, have been used in several applications, which range from surface parameterization, deformation, and compression to segmentation, clustering, and comparison. Using the linear FEM approximation of the Laplace-Beltrami operator, we derive a discrete heat kernel that is linear, stable to an irregular sampling density of the input surface, and scale covariant. With respect to previous work, this last property makes the kernel particularly suitable for shape analysis and comparison; in fact, local and global changes of the surface correspond to a re-scaling of the time parameter without affecting its spectral component. Finally, we study the scale spaces that are induced by the proposed heat kernel and exploited to provide a multi-scale approximation of scalar functions defined on 3D shapes.
Starting Page	113
Ending Page	123
File Size	4181549
Page Count	11
File Format	PDF
ISBN	9781424472598
e-ISBN	9781424472604
DOI	10.1109/SMI.2010.27
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-06-21
Publisher Place	France
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Shape Kernel Space heating Geometry Solid modeling Deformable models Laplace equations Linear approximation Sampling methods Multiresolution analysis shape analysis Scale-space methods heat kernel Laplacian matrix spectral analysis signal and function smoothing critical points
Content Type	Text
Resource Type	Article

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