FracGM: A Fast Fractional Programming Technique for Geman-McClure Robust Estimator
This addresses outlier rejection in applications like navigation and point-cloud registration, offering incremental improvements over existing methods.
The paper tackled robust estimation in computer vision and robotics by developing FracGM, a fast fractional programming technique for the Geman-McClure estimator, which achieved up to 88% lower error increases with outlier rates up to 80% and improved computation time by 19.43%.
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.