Simplifying Energy Optimization using Partial Enumeration

TL;DR

This paper introduces a partial enumeration method for simplifying the optimization of high-order, non-submodular energies in vision tasks, enabling efficient near-global solutions by reducing complex problems to pairwise CSPs.

Contribution

The paper presents a novel partial enumeration technique that transforms high-order energies into pairwise CSPs, improving efficiency and solution quality in large-scale vision problems.

Findings

Outperforms existing algorithms on challenging problems like curvature regularization and stereo.

Achieves near-global minimum solutions with better speed.

Enables direct evaluation of curvature in segmentation using integral geometry.

Abstract

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.