Optimized Subspaces for Deformation-Based Modeling and Shape Interpolation

Abstract

We propose a novel construction of subspaces for real-time deformation-based modeling and shape interpolation. The scheme constructs a subspace that optimally approximates the manifold of deformations relevant for a specific modeling or interpolation problem. The idea is to automatically sample the deformation manifold and construct the subspace that best-approximates these snapshots. This is realized by writing the shape modeling and interpolation problems as parametrized optimization problems with few parameters. The snapshots are generated by sampling the parameter domain and computing the corresponding minimizers. Finally, the optimized subspaces are constructed using a mass-dependent principle component analysis. The optimality provided by this scheme contrasts it from alternative approaches, which aim at constructing spaces containing low-frequency deformations. The benefit of this construction is that compared to alternative approaches a similar approximation quality is achieved with subspaces of significantly smaller dimension. This is crucial because the run-times and memory requirements of the real-time shape modeling and interpolation schemes mainly depend on the dimensions of the subspaces.