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Study Proves Maximum-Clique Solution Error in Point Cloud Registration Can Be Arbitrarily Large
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In arXiv:2610.27275, Abolfazl Babanazari and Kaveh Fathian theoretically analyze the relationship between the maximum clique and maximum consensus formulations of robust registration for point clouds, proving that the alignment error of the maximum-clique solution can be arbitrarily large and that its set size can also far exceed that of the maximum consensus set under any fixed positive tolerance, and they derive geometric conditions that bound this error. For the case of fixed rotation, the authors give exact error bounds and a discrimination test for the translation subproblem, which can exactly characterize maximum consensus. The study also determines the minimum group size in group-k consensus that guarantees an error bound independent of point cloud scale: for dimension d≥2, it is d+1 for rotation and translation, and d+2 when reflections are allowed. Related interactive examples and Lean theorem prover verification have been made public.
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- 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.
arXiv cs.RO ·