Fast quasi-harmonic weights for geometric data interpolation
Abstract
We propose quasi-harmonic weights for interpolating geometric data, which are orders of magnitude faster to compute than state-of-the-art. Currently, interpolation (or, skinning) weights are obtained by solving large-scale constrained optimization problems with explicit constraints to suppress oscillative patterns, yielding smooth weights only after a substantial amount of computation time. As an alternative, our weights are obtained as minima of an unconstrained problem that can be optimized quickly using straightforward numerical techniques. We consider weights that can be obtained as solutions to a parameterized family of second-order elliptic partial differential equations. By leveraging the maximum principle and careful parameterization, we pose weight computation as an inverse problem of recovering optimal anisotropic diffusivity tensors. In addition, we provide a customized ADAM solver that significantly reduces the number of gradient steps; our solver only requires inverting tens of linear systems that share the same sparsity pattern. Overall, our approach achieves orders of magnitude acceleration compared to previous methods, allowing weight computation in near real-time.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jul 19, 2021
- Source ID
- 10.1145/3450626.3459801
Entities
People
- Justin Solomon
- Yu Wang
Organizations
- Air Force Office of Scientific Research
- Army Research Office
- Massachusetts Institute of Technology
- National Science Foundation