Fast approximate energy minimization via graph cuts

In this paper we address the problem of minimizing a large class of energy functions that occur in early vision. The major restriction is that the energy function´s smoothness term must only involve pairs of pixels. We propose two algorithms that use graph cuts to compute a local minimum even when very large moves are allowed. The first move we consider is an α-β-swap: for a pair of labels α,β, this move exchanges the labels between an arbitrary set of pixels labeled a and another arbitrary set labeled β. Our first algorithm generates a labeling such that there is no swap move that decreases the energy. The second move we consider is an α-expansion: for a label a, this move assigns an arbitrary set of pixels the label α. Our second algorithm, which requires the smoothness term to be a metric, generates a labeling such that there is no expansion move that decreases the energy. Moreover, this solution is within a known factor of the global minimum. We experimentally demonstrate the effectiveness of our approach on image restoration, stereo and motion