Efficient Globally Optimal Consensus Maximisation with Tree Search

Abstract

Maximum consensus is one of the most popular criteria for robust estimation in computer vision. Despite its widespread use, optimising the criterion is still customarily done by randomised sample-and-test techniques, which do not guarantee optimality of the result. Several globally optimal algorithms exist, but they are too slow to challenge the dominance of randomised methods. Our work aims to change this state of affairs by proposing an efficient algorithm for global maximisation of consensus. Under the framework of LP-type methods, we show how consensus maximisation for a wide variety of vision tasks can be posed as a tree search problem. This insight leads to a novel algorithm based on A* search. We propose efficient heuristic and support set updating routines that enable A* search to efficiently find globally optimal results. On common estimation problems, our algorithm is much faster than previous exact methods. Our work identifies a promising direction for globally optimal consensus maximisation.

What Correspondences Reveal About Unknown Camera and Motion Models?

“…We choose the threshold ǫ = 1.5 px for our method and equivalently for ransac. We further test a globally optimal method of outlier rejection [8] as global.…”

Unsupervised Learning of Consensus Maximization for 3D Vision Problems

“…We further compare the F1-score and runtime with various variants of RANSAC [35] and a globally optimal method [11] on homography estimation in Fig. 8.…”

A generic interval branch and bound algorithm for parameter estimation

“…Since automatically computed matching pairs (m i L , m i R ) may be outliers for some i, the RANSAC algorithm [12] (see Section 2.1) is traditionally used: five pairs are selected to estimate E, then the number of other pairs, called inliers, compatible with this estimation (up to the threshold q) is counted; the procedure is repeated and the estimation of E with a maximal number of inliers is returned. However, the five-point procedure is complex due to its non-linear constraints (9). Therefore they are often relaxed in favor of the estimation of the fundamental matrix F = (K −1 L ) E K −1 R , where K L and K R map direction vectors m L and m R to the image points x L and x R in homogeneous coordinates [15].…”

“…Another work [9,10] solves different computer vision problems as homography estimation, linearised fundamental matrix, or affine registration, finding the maximum number of inliers. The B & B approach used builds a search tree, branching directly on the inliers set.…”