Dipartimento di Matematica ''F. Casorati''

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Laplacian Spectral Basis for Numerical Geometry Processing and 3D Shape Analysis

Dr. Giuseppe Patanč, IMATI-CNR, Genova

Sala conferenze IMATI-CNR, Pavia - Tuesday, March 27, 2018 h.15:00

Abstract. Representing a signal as a linear combination of a set of basis functions is central in a wide range of applications, such as approximation, de-noising, and compression. In this context, this talk addresses the main aspects of signal approximation, such as the definition, computation, and comparison of basis functions, on arbitrary 3D shapes. Focusing on the class of basis functions induced by the Laplace-Beltrami operator and its spectrum, we introduce the diffusion and Laplacian spectral basis functions, which are then compared with the harmonic and Laplacian eigenfunctions. As main properties of these basis functions, which are commonly used for numerical geometry processing and 3D shape analysis, we discuss the partition of the unity and non-negativity; intrinsic definition and invariance with respect to shape transformations; locality, smoothness, and orthogonality; numerical stability with respect to the domain discretization; computational cost and storage overhead. As main applications, we focus on the definition of Laplacian spectral kernels and distances, as a function that resembles the usual distance properties, but exhibits features that make them useful to processing and analyzing geometric data. We also present functional approaches for the computation of shape correspondence and 2D/3D shape deformation.

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Dipartimento di Matematica ''F. Casorati''

Università degli Studi di Pavia - Via Ferrata, 5 - 27100 Pavia
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