Continuous Energy Minimization via Repeated Binary Fusion

Abstract

Variational problems, which are commonly used to solve low-level vision tasks, are typically minimized via a local, iterative optimization strategy, e.g. gradient descent. Since every iteration is restricted to a small, local improvement, the overall convergence can be slow and the algorithm may get stuck in an undesirable local minimum. In this paper, we propose to approximate the minimization by solving a series of binary subproblems to facilitate large optimization moves. The proposed method can be interpreted as an extension of discrete graph-cut based methods such as α -expansion or LogCut to a spatially continuous setting. In order to demonstrate the viability of the approach, we evaluated the novel optimization strategy in the context of optical flow estimation, yielding excellent results on the Middlebury optical flow datasets.