A fully implicit alternating direction method of multipliers for the minimization of convex problems with an application to motion segmentation

Motivated by a variational formulation of the motion segmentation problem, we propose a fully implicit variant of the (linearized) alternating direction method of multipliers for the minimization of convex functionals over a convex set. The new scheme does not require a step size restriction for stability and thus approaches the minimum using considerably fewer iterates. In numerical experiments on standard image sequences, the scheme often significantly outperforms other state of the art methods.