Minimizing Sparse Higher Order Energy Functions of Discrete Variables

Higher order energy functions have the ability to encode high level structural dependencies between pixels, which have been shown to be extremely powerful for image labeling problems. Their use, however, is severely hampered in practice by the intractable complexity of representing and minimizing such functions. We observed that higher order functions encountered in computer vision are very often “sparse”, i.e. many labelings of a higher order clique are equally unlikely and hence have the same high cost. In this paper, we address the problem of minimizing such sparse higher order energy functions. Our method works by transforming the problem into an equivalent quadratic function minimization problem. The resulting quadratic function can be minimized using popular message passing or graph cut based algorithms for MAP inference. Although this is primarily a theoretical paper, it also shows how higher order functions can be used to obtain impressive results for the b...

• Type: Conference
• Year: 2009
• Where: CVPR
• Authors: Carsten Rother (Microsoft Research Cambridge), Pushmeet Kohli (Microsoft Research Cambridge), Wei Feng (The Chinese University of Hong Kong), Jiaya Jia (The Chinese University of Hong Kong)
• Keywords: Computer Vision, CVPR 2009, Sparse Higher Order Energy Functions