Hyperspectral Inverse Skinning

In example‐based inverse linear blend skinning (LBS), a collection of poses (e.g. animation frames) are given, and the goal is finding skinning weights and transformation matrices that closely reproduce the input. These poses may come from physical simulation, direct mesh editing, motion capture or another deformation rig. We provide a re‐formulation of inverse skinning as a problem in high‐dimensional Euclidean space. The transformation matrices applied to a vertex across all poses can be thought of as a point in high dimensions. We cast the inverse LBS problem as one of finding a tight‐fitting simplex around these points (a well‐studied problem in hyperspectral imaging). Although we do not observe transformation matrices directly, the 3D position of a vertex across all of its poses defines an affine subspace, or flat. We solve a ‘closest flat’ optimization problem to find points on these flats, and then compute a minimum‐volume enclosing simplex whose vertices are the transformation matrices and whose barycentric coordinates are the skinning weights. We are able to create LBS rigs with state‐of‐the‐art reconstruction error and state‐of‐the‐art compression ratios for mesh animation sequences. Our solution does not consider weight sparsity or the rigidity of recovered transformations. We include observations and insights into the closest flat problem. Its ideal solution and optimal LBS reconstruction error remain an open problem. In example‐based inverse linear blend skinning (LBS), a collection of poses (e.g. animation frames) are given, and the goal is finding skinning weights and transformation matrices that closely reproduce the input. These poses may come from physical simulation, direct mesh editing, motion capture or another deformation rig. We provide a re‐formulation of inverse skinning as a problem in high‐dimensional Euclidean space. The transformation matrices applied to a vertex across all poses can be thought of as a point in high dimensions. We cast the inverse LBS problem as one of finding a tight‐fitting simplex around these points (a well‐studied problem in hyperspectral imaging). Although we do not observe transformation matrices directly, the 3D position of a vertex across all of its poses defines an affine subspace, or flat. We solve a ‘closest flat’ optimization problem to find points on these flats, and then compute a minimum‐volume enclosing simplex whose vertices are the transformation matrices and whose barycentric coordinates are