Context without Commitment: Robust Dense Correspondence under Non-Rigid Deformation

Non-rigid point-cloud registration aims to find the corresponding target point for every point on a deforming source surface. Point-level matching keeps the complete target cloud available, but correspondence can become ambiguous when different regions have similar local geometry. Regional or coarse-to-fine methods provide larger spatial context, but an incorrect regional match can exclude the correct point correspondence before the final dense matching stage. We propose CoCo-Reg, which uses regional patches to enrich dense point features without allowing patch predictions to restrict the final point-level search. CoCo-Reg constructs farthest-point-sampled patches, exchanges geometric information within and between the source and target, supervises patch similarity using identity-corrected point overlap, and projects the resulting regional information back to the dense point features. The final registration stage still scores the complete target cloud before performing its global point-level candidate selection. On 726 held-out ModelNet10 objects across nine deformation levels, two established learning-based non-rigid registration baselines obtain mean correspondence errors of 0.1993 and 0.1921, whereas CoCo-Reg obtains 0.0547. Relative to the point-level baseline on which CoCo-Reg is built, this corresponds to a 72.6\% reduction. CoCo-Reg achieves lower correspondence error on 92.3\% of paired test objects and reduces the mean fraction of points with error above 0.1 from 47.3\% to 17.3\%. Chamfer distance and HD95 decrease in the same direction, and CoCo-Reg remains lower across all tested deformation levels. These results support the use of regional context for dense non-rigid correspondence without imposing a hard patch-level restriction on the final search. Because the evaluation uses one checkpoint per method, the reported gains characterize the complete evaluated systems rather than the isolated causal contribution of an individual component. Code will be made publicly available.