An Efficient Maximum Entropy Approach with Consensus Constraints for Robust Geometric Fitting

Robust geometric fitting is one of the crucial and fundamental problems in computer vision and pattern recognition. While random sampling and consensus maximization have been popular strategies for robust fitting, finding a balance between optimization quality and computational efficiency remains a persistent obstacle. In this paper, we adopt an optimization perspective and introduce a novel maximum consensus robust fitting algorithm that incorporates the maximum entropy framework into the consensus maximization problem. Specifically, we incorporate the probability distribution of inliers calculated using maximum entropy with consensus constraints. Furthermore, we introduce an improved relaxed and accelerated alternating direction method of multipliers (R-A-ADMMs) strategy tailored to our framework, facilitating an efficient solution to the optimization problem. Our proposed algorithm demonstrates superior performance compared to state-of-the-art methods on both synthetic and contaminated real datasets, particularly when dealing with contaminated datasets containing a high proportion of outliers.