A cascadic geometric filtering approach to subdivision
Computer Aided Geometric Design
Evolutionary partial differential equations for biomedical image processing
Journal of Biomedical Informatics
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A new multiscale method in surface processing is presented herewhich combines the image processing methodology based on nonlineardiffusion equations and the theory of geometric evolutionproblems. Its aim is to smooth discretized surfaces while simultaneouslyenhancing geometric features such as edges and corners.This is obtained by an anisotropic curvature evolution, where timeis the multiscale parameter. Here, the diffusion tensor depends onthe shape operator of the evolving surface.A spatial finite element discretization on arbitrary unstructuredtriangular meshes and a semi-implicit finite difference discretizationin time are the building blocks of the easy to code algorithmpresented here. The systems of linear equations in each timestepare solved by appropriate, preconditioned iterative solvers. Differentapplications underline the efficiency and flexibility of the presentedtype of surface processing tool.