A polynomial-time bound for matching and registration with outliers

Abstract

We present a framework for computing optimal transformations, aligning one point set to another, in the presence of outliers. Example applications include shape matching and registration (using, for example, similarity, affine or projective transformations) as well as multiview reconstruction problems (triangulation, camera pose etc.).While standard methods like RANSAC essentially use heuristics to cope with outliers, we seek to find the largest possible subset of consistent correspondences and the globally optimal transformation aligning the point sets. Based on theory from computational geometry, we show that this is indeed possible to accomplish in polynomial-time. We develop several algorithms which make efficient use of convex programming. The scheme has been tested and evaluated on both synthetic and real data for several applications. 1

Robust Fitting for Multiple View Geometry

“…The most similar works to ours include [9][10][11][12][13] where the aim is to develop algorithms which provably maximizes the number of inliers. In [9,10], branchand-bound techniques are developed which have exponential worst-time complexity.…”

“…In [12], a triangulation method is presented, but it is only practical for a few outliers due to its high computational complexity. For quasiconvex residual functions, an O(n d+2 ) algorithm is given in [13], where n is the number of points and d the dimension of the model. We improve on this result by showing it is possible to solve the same problem in O(n d+1 ).…”

Deterministically maximizing feasible subsystem for robust model fitting with unit norm constraint

“…For problems with pseudoconvexity, Olsson et al [17] presented a hit-or-miss strategy with a polynomial-time bound. When the problem can be described by a linear system, the robust fitting problem becomes the MaxFS.…”

Consensus set maximization with guaranteed global optimality for robust geometry estimation

“…The only exception we are aware of is [15] where an interesting post-validation idea is proposed to verify whether or not a solution is the optimal one. But, such a hit-or-miss type procedure gives no upper bound on the number of trials needed.…”