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A popular paradigm for 3D point cloud registration is by extracting 3Dkeypoint correspondences, then estimating the registration function from thecorrespondences using a robust algorithm. However, many existing 3D keypointtechniques tend to produce large proportions of erroneous correspondences oroutliers, which significantly increases the cost of robust estimation. Analternative approach is to directly search for the subset of correspondencesthat are pairwise consistent, without optimising the registration function.This gives rise to the combinatorial problem of matching with pairwiseconstraints. In this paper, we propose a very efficient maximum cliquealgorithm to solve matching with pairwise constraints. Our technique combinestree searching with efficient bounding and pruning based on graph colouring. Wedemonstrate that, despite the theoretical intractability, many real probleminstances can be solved exactly and quickly (seconds to minutes) with ouralgorithm, which makes our approach an excellent alternative to standard robusttechniques for 3D registration.

A Practical Maximum Clique Algorithm for Matching with Pairwise Constraints