Article

Theoretical Analysis of the Relationship Between Maximum Clique and Maximum Consensus in Point Cloud Registration

arXiv:2610.27275 studies the relationship between maximum clique and maximum consensus, two robust registration formulations for point cloud registration. It proves that the alignment error of maximum clique solutions can be arbitrarily large and that the set size can far exceed that of the maximum consensus set, and it derives geometric conditions that bound this error. When rotation is fixed, it gives exact error bounds and a discriminating test for the translation subproblem. The study also determines the minimum group size in group-k consistency that guarantees an error bound independent of point cloud scale: d+1 for rotation and translation in d≥2 dimensions, and d+2 when reflections are allowed. An interactive example and Lean theorem prover verification have been made public.

Part of the event: Study Proves Maximum-Clique Solution Error in Point Cloud Registration Can Be Arbitrarily Large

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