Discrete quadratic curvature energies
Computer Aided Geometric Design
Distance-aware smoothing of surface meshes for surgical planning
Proceedings of the First International Workshop on Digital Engineering
Technical Section: Context-aware mesh smoothing for biomedical applications
Computers and Graphics
Staircase-aware smoothing of medical surface meshes
EG VCBM'10 Proceedings of the 2nd Eurographics conference on Visual Computing for Biology and Medicine
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Abstract: In triangulated surface meshes, there are often very noticeable size variances (the vertices are distributed unevenly). The presented noise of such surface meshes is therefore composite of vast frequencies. In this paper, we solve a diffusion partial differential equation numerically for noise removal of arbitrary triangular manifolds using an adaptive time discretization. The proposed approach is simple and is easy to incorporate into any uniform timestep diffusion implementation with significant improvements over evolution results with the uniform timesteps. As an additional alternative to the adaptive discretization in the time direction, we also provide an approach for the choice of an adaptive diffusion tensor in the diffusion equation.