Efficient Energy Minimization for Enforcing Statistics
This addresses the challenge of enforcing statistics in energy minimization for computer vision tasks like image segmentation, offering a more efficient solution for researchers and practitioners in the field.
The paper tackles the problem of constrained energy minimization in computer vision, where the goal is to find the most probable solution consistent with known statistics, and proposes a novel method that finds the discrete optimal solution by maximizing the Lagrangian dual, resulting in less error and over 20 times faster performance than state-of-the-art LP relaxation approaches.
Energy minimization algorithms, such as graph cuts, enable the computation of the MAP solution under certain probabilistic models such as Markov random fields. However, for many computer vision problems, the MAP solution under the model is not the ground truth solution. In many problem scenarios, the system has access to certain statistics of the ground truth. For instance, in image segmentation, the area and boundary length of the object may be known. In these cases, we want to estimate the most probable solution that is consistent with such statistics, i.e., satisfies certain equality or inequality constraints. The above constrained energy minimization problem is NP-hard in general, and is usually solved using Linear Programming formulations, which relax the integrality constraints. This paper proposes a novel method that finds the discrete optimal solution of such problems by maximizing the corresponding Lagrangian dual. This method can be applied to any constrained energy minimization problem whose unconstrained version is polynomial time solvable, and can handle multiple, equality or inequality, and linear or non-linear constraints. We demonstrate the efficacy of our method on the foreground/background image segmentation problem, and show that it produces impressive segmentation results with less error, and runs more than 20 times faster than the state-of-the-art LP relaxation based approaches.