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CG
2004
Springer

Surface processing methods for point sets using finite elements

9 years 2 months ago
Surface processing methods for point sets using finite elements
We present a framework for processing point-based surfaces via partial differential equations (PDEs). Our framework efficiently and effectively brings well-known PDE-based processing techniques to the field of point-based surfaces. At the core of our method is a finite element discretization of PDEs on point surfaces. This discretization is based on the local assembly of PDE-specific mass and stiffness matrices, using a local point coupling computation. Point couplings are computed using a local tangent plane construction and a local Delaunay triangulation of point neighborhoods. The definition of tangent planes relies on moment-based computation with proven scaling and stability properties. Once local stiffness matrices are obtained, we are able to easily assemble global matrices and efficiently solve the corresponding linear systems by standard iterative solvers. We demonstrate our framework by several types of PDE-based surface processing applications, such as segmentation, texture...
Ulrich Clarenz, Martin Rumpf, Alexandru Telea
Added 16 Dec 2010
Updated 16 Dec 2010
Type Journal
Year 2004
Where CG
Authors Ulrich Clarenz, Martin Rumpf, Alexandru Telea
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