Stereo matching by compact windows via minimum ratio cycle

Window size and shape selection is a difficult problem in area based stereo. We propose an algorithm which chooses an appropriate window shape by optimizing over a large class of "compact" windows. We call them compact because their ratio of perimeter to area tends to be small. We believe that this is the first window matching algorithm which can explicitly construct non-rectangular windows. Efficient optimization over the compact window class is achieved via the minimum ratio cycle algorithm. In practice it takes time linear in the size of the largest window in our class. Still the straightforward approach to find the optimal window for each pixel-disparity pair is too slow. We develop pruning heuristics which gave practically the same results while reducing running time from minutes to seconds. Our experiments show that unlike fixed window algorithms, our method avoids blurring disparity boundaries as well as constructs large windows in low textured areas. The algorithm has few parameters which are easy to choose, and the same parameters work well for different image pairs.