Unsupervised learning of threshold for geometric verification in visual-based loop-closure

A potential loop-closure image pair passes the geometric verification test if the number of inliers from the computation of the geometric constraint with RANSAC exceed a pre-defined threshold. The choice of the threshold is critical to the success of identifying the correct loop-closure image pairs. However, the value for this threshold often varies for different datasets and is chosen empirically. In this paper, we propose an unsupervised method that learns the threshold for geometric verification directly from the observed inlier counts of all the potential loop-closure image pairs. We model the distributions of the inlier counts from all the potential loop-closure image pairs with a two components Log-Normal mixture model - one component represents the state of non loop-closure and the other represents the state of loop-closure, and learn the parameters with the Expectation-Maximization algorithm. The intersection of the Log-Normal mixture distributions is the optimal threshold for geometric verification, i.e. the threshold that gives the minimum false positive and negative loop-closures. Our algorithm degenerates when there are too few or no loop-closures and we propose the χ² test to detect this degeneracy. We verify our proposed method with several large-scale datasets collected from both the multi-camera setup and stereo camera.