Efficient Large Scale Inlier Voting for Geometric Vision Problems

Outlier rejection and equivalently inlier set optimization is a key ingredient in numerous applications in computer vision such as filtering point-matches in camera pose estimation or plane and normal estimation in point clouds. Several approaches exist, yet at large scale we face a combinatorial explosion of possible solutions and state-of-the-art methods like RANSAC, Hough transform or Branch\&Bound require a minimum inlier ratio or prior knowledge to remain practical. In fact, for problems such as camera posing in very large scenes these approaches become useless as they have exponential runtime growth if these conditions aren't met. To approach the problem we present a efficient and general algorithm for outlier rejection based on "intersecting" $k$-dimensional surfaces in $R^d$. We provide a recipe for casting a variety of geometric problems as finding a point in $R^d$ which maximizes the number of nearby surfaces (and thus inliers). The resulting algorithm has linear worst-case complexity with a better runtime dependency in the approximation factor than competing algorithms while not requiring domain specific bounds. This is achieved by introducing a space decomposition scheme that bounds the number of computations by successively rounding and grouping samples. Our recipe (and open-source code) enables anybody to derive such fast approaches to new problems across a wide range of domains. We demonstrate the versatility of the approach on several camera posing problems with a high number of matches at low inlier ratio achieving state-of-the-art results at significantly lower processing times.