A New Algorithm for Energy Minimization with Discontinuities

Abstract

Many tasks in computer vision involve assigning a label (such as disparity) to every pixel. These tasks can be formulated as energy minimization problems. In this paper, we consider a natural class of energy functions that permits discontinuities. Computingthe exact minimum is NP-hard. We have developed a new approximation algorithm based on graph cuts. The solution it generates is guaranteed to be within a factor of 2 of the energy function’s global minimum. Our method produces a local minimum with respect to a certain move space. In this move space, a single move is allowed to switch an arbitrary subset of pixels to one common label. If this common label is á then such a move expands the domain of á in the image. At each iteration our algorithm efficiently chooses the expansion move that gives the largest decrease in the energy. We apply our method to the stereo matching problem, and obtain promisingex perimental results. Empirically, the new technique outperforms our previous algorithm [6] both in terms of runningti me and output quality.