Bi-harmonic diffusion to smooth weight maps over meshes.


 C++ code ] for the experiment.

Goal: diffuse weight maps by using one or several steps of Jacobi iterations to solve the Biharmonic equation. For now I could solve using the bilaplacian L*M^-1*L operator with a sparse LU solver (note: Biharmonic functions minimize Laplacian energy). Trying to use Jacobi iterations doesn't really produce the results I was expecting. Mainly I have 3 problems:

Future work

Maybe the non negativity constraints in Alec's papers (bounding biharmonic weights) can help ?
There is also this paper: Multiscale Biharmonic kernels (Eurographics Raif M. Rustamov) to explore.

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