Deterministic Approximate Methods for Maximum Consensus Robust Fitting

Maximum consensus estimation plays a critically important role in several robust fitting problems computer vision. Currently, the most prevalent algorithms for maximization draw from class of randomized hypothesize-and-verify algorithms, which are cheap but can usually deliver only rough approximate solutions. On other extreme, there exact exhaustive search nature and be costly practical-sized inputs. This paper fills gap between two extremes by proposing deterministic to approximately optimize maximum criterion. Our work begins reformulating with linear complementarity constraints. Then, we develop novel algorithms: one based on non-smooth penalty method Frank-Wolfe style optimization scheme, Alternating Direction Method Multipliers (ADMM). Both solve convex subproblems efficiently perform optimization. We demonstrate capability our greatly improve initial estimate, such as those obtained using least squares or algorithm. Compared approach is much more practical realistic input sizes. Further, naturally applicable geometric residuals. Matlab code demo program methods downloaded https://goo.gl/FQcxpi.