Simplifying Energy Optimization using Partial Enumeration
This addresses the computational bottleneck in vision tasks requiring complex energy formulations, though it appears incremental as an improvement over existing optimization methods.
The paper tackles the NP-hard optimization problem of high-order non-submodular energies in vision by proposing a partial enumeration technique that reduces these to pairwise Constraint Satisfaction Problems, achieving near global minimum and better speed while outperforming state-of-the-art algorithms on problems like curvature regularization, stereo, and deconvolution.
Energies with high-order non-submodular interactions have been shown to be very useful in vision due to their high modeling power. Optimization of such energies, however, is generally NP-hard. A naive approach that works for small problem instances is exhaustive search, that is, enumeration of all possible labelings of the underlying graph. We propose a general minimization approach for large graphs based on enumeration of labelings of certain small patches. This partial enumeration technique reduces complex high-order energy formulations to pairwise Constraint Satisfaction Problems with unary costs (uCSP), which can be efficiently solved using standard methods like TRW-S. Our approach outperforms a number of existing state-of-the-art algorithms on well known difficult problems (e.g. curvature regularization, stereo, deconvolution); it gives near global minimum and better speed. Our main application of interest is curvature regularization. In the context of segmentation, our partial enumeration technique allows to evaluate curvature directly on small patches using a novel integral geometry approach.