Unsupervised Learning of Consensus Maximization for 3D Vision Problems

Consensus maximization is a key strategy in 3D vision for robust geometric model estimation from measurements with outliers. Generic methods for consensus maximization, such as Random Sampling and Consensus (RANSAC), have played a tremendous role in the success of 3D vision, in spite of the ubiquity of outliers. However, replicating the same generic behaviour in a deeply learned architecture, using supervised approaches, has proven to be difficult. In that context, unsupervised methods have a huge potential to adapt to any unseen data distribution, and therefore are highly desirable. In this paper, we propose for the first time an unsupervised learning framework for consensus maximization, in the context of solving 3D vision problems. For that purpose, we establish a relationship between inlier measurements, represented by an ideal of inlier set, and the subspace of polynomials representing the space of target transformations. Using this relationship, we derive a constraint that must be satisfied by the sought inlier set. This constraint can be tested without knowing the transformation parameters, therefore allows us to efficiently define the geometric model fitting cost. This model fitting cost is used as a supervisory signal for learning consensus maximization, where the learning process seeks for the largest measurement set that minimizes the proposed model fitting cost. Using our method, we solve a diverse set of 3D vision problems, including 3D-3D matching, non-rigid 3D shape matching with piece-wise rigidity and image-to-image matching. Despite being unsupervised, our method outperforms RANSAC in all three tasks for several datasets.