CliReg: Clique-Based Robust Point Cloud Registration

We propose a branch-and-bound algorithm for robust rigid registration of two point clouds in the presence of a large number of outlier correspondences. For this purpose, we consider a maximum consensus formulation of the registration problem and reformulate it as a (large) maximal clique search in a correspondence graph, where a clique represents a complete rigid transformation. Specifically, we use a maximum clique algorithm to enumerate large maximal cliques and a fitness procedure that evaluates each clique by solving a least-squares optimization problem. The main advantages of our approach are 1) it is possible to exploit the cutting-edge optimization techniques employed by current exact maximum clique algorithms, such as partial maximum satisfiability-based bounds, branching by partitioning or the use of bitstrings, etc.; 2) the correspondence graphs are expected to be sparse in real problems (confirmed empirically in our tests), and, consequently, the maximum clique problem is expected to be easy; 3) it is possible to have a good control of suboptimality with a k-nearest neighbor analysis that determines the size of the correspondence graph as a function of $k$. The new algorithm is called CliReg and has been implemented in C++. To evaluate CliReg, we have carried out extensive tests both on synthetic and real public datasets. The results show that CliReg clearly dominates the state of the art (e.g., RANSAC, FGR, and TEASER++) in terms of robustness, with a running time comparable to TEASER++ and RANSAC. In addition, we have implemented a fast variant called CliRegMutual that performs similarly to the fastest heuristic FGR.