Efficient Algorithms for Maximum Consensus Robust Fitting

Maximum consensus robust fitting is a fundamental problem in many computer vision applications, such as vision-based robotic navigation and mapping. While exact search algorithms are computationally demanding, randomized algorithms are cheap but the solution quality is not guaranteed. Deterministic algorithms fill the gap between these two kinds of algorithms, which have better solution quality than randomized algorithms while being much faster than exact algorithms. In this article, we develop two highly efficient deterministic algorithms based on the alternating direction method of multipliers (ADMM) and proximal block coordinate descent (BCD) frameworks. Particularly, the proposed BCD algorithm is guaranteed convergent. Furthermore, on the slack variable in the BCD algorithm, which indicates the inliers and outliers, we establish some meaningful properties, such as support convergence within finite iterations and convergence to restricted strictly local minimizer. Compared with state-of-the-art algorithms, the new algorithms with initialization from a randomized or convex relaxed algorithm can achieve improved solution quality while being much more efficient (e.g., more than an order of magnitude faster). An application of the new ADMM algorithm in simultaneous localization and mapping (SLAM) has also been provided to demonstrate its effectiveness. Code for reproducing the results is available online.
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