A discrete total variation of the surface normal, equal to the discrete total mean curvature, is proposed as a shape prior that lets reconstruction recover polyhedral shapes instead of rounding them.
Automated shape differentiation in the Unified Form Language
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abstract
We discuss automating the calculation of weak shape derivatives in the Unified Form Language (Aln{\ae}s et al., ACM Trans. Math. Softw., 2014) by introducing an appropriate additional step in the pullback from physical to reference space that computes G\^ateaux derivatives with respect to the coordinate field. We illustrate the ease of use with several examples.
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Discrete Total Variation of the Normal Vector Field as Shape Prior with Applications in Geometric Inverse Problems
A discrete total variation of the surface normal, equal to the discrete total mean curvature, is proposed as a shape prior that lets reconstruction recover polyhedral shapes instead of rounding them.