An efficient algorithm for Co-segmentation

This paper is focused on the Co-segmentation problem [1] - where the objective is to segment a similar object from a pair of images. The background in the two images may be arbitrary; therefore, simultaneous segmentation of both images must be performed with a requirement that the appearance of the two sets of foreground pixels in the respective images are consistent. Existing approaches [1, 2] cast this problem as a Markov Random Field (MRF) based segmentation of the image pair with a regularized difference of the two histograms - assuming a Gaussian prior on the foreground appearance [1] or by calculating the sum of squared differences [2]. Both are interesting formulations but lead to difficult optimization problems, due to the presence of the second (histogram difference) term. The model proposed here bypasses measurement of the histogram differences in a direct fashion; we show that this enables obtaining efficient solutions to the underlying optimization model. Our new algorithm is similar to the existing methods in spirit, but differs substantially in that it can be solved to optimality in polynomial time using a maximum flow procedure on an appropriately constructed graph. We discuss our ideas and present promising experimental results.