David Günther, Jan Reininghaus, Hans-Peter Seidel, Olga Sorkine-Hornung, Tino Weinkauf and I will publish our paper "Fast and Memory-Efficient Topological Denoising of 2D and 3D Scalar Fields" in TVCG and David will present the work at SciVis this year. This paper is a much-needed extension of our earlier SGP paper on optimizing over monotonic functions. This new paper provides two new heuristics: 1) a plaided domain decomposition enables efficient optimization on much larger datasets (notably 3D images, e.g. voxel grids), and 2) iterating on our convexification of the monotonicity constraint. This iteration idea greatly improves the quality of solutions when the gradient direction of the harmonic initial guess is far from matching the optimal solution, particularly important in the case of data smoothing. In some sense, one could view this as a sort of trust-region-ish algorithm, but our problem specific knowledge allows us to make much better progress.
Download the paper.