FracGM: A Fast Fractional Programming Technique for Geman-McClure Robust Estimator

TL;DR

FracGM introduces a fast, convex dual reformulation for Geman-McClure robust estimation, significantly improving outlier rejection and computational efficiency in computer vision tasks.

Contribution

It proposes a novel fractional programming-based algorithm that guarantees global optimality and outperforms existing methods in robustness and speed.

Findings

Achieves 53% and 88% lower errors in rotation and translation with high outlier rates.

Outperforms state-of-the-art algorithms in 13 out of 18 real-world scenarios.

Reduces computation time by approximately 19.43%.

Abstract

Robust estimation is essential in computer vision, robotics, and navigation, aiming to minimize the impact of outlier measurements for improved accuracy. We present a fast algorithm for Geman-McClure robust estimation, FracGM, leveraging fractional programming techniques. This solver reformulates the original non-convex fractional problem to a convex dual problem and a linear equation system, iteratively solving them in an alternating optimization pattern. Compared to graduated non-convexity approaches, this strategy exhibits a faster convergence rate and better outlier rejection capability. In addition, the global optimality of the proposed solver can be guaranteed under given conditions. We demonstrate the proposed FracGM solver with Wahba's rotation problem and 3-D point-cloud registration along with relaxation pre-processing and projection post-processing. Compared to state-of-the-art algorithms, when the outlier rates increase from 20% to 80%, FracGM shows 53% and 88% lower rotation and translation increases. In real-world scenarios, FracGM achieves better results in 13 out of 18 outcomes, while having a 19.43% improvement in the computation time.