Computing Skinning Weights via Convex Duality

Abstract

We study the problem of optimising for skinning weights through the lens of convex duality. In particular, we show that the popular bounded biharmonic weight (BBW) model for skinning is dual to a non-negative least-squares problem, which is amenable to efficient solution via iterative algorithms; the final weights are then recoverable via a closed-form expression. Our formulation maintains convexity and is provably equivalent to the original problem. We also provide theoretical discussion giving intuition for the dual problem in the smooth case. Our final algorithm, which can be implemented in a few lines of code, achieves efficient convergence times relative to generic quadratic programming tools applied to the primal problem, without nonconvex formulations, relaxations or specialised optimisation techniques.