G2M-Reg: Graph-to-Manifold Verification for Robust Point Cloud Registration

Robust point cloud registration remains challenging under low overlap, where sparse true matches can be overwhelmed by locally consistent outliers that form strong compatibility structures. Consequently, an incorrect pose may receive substantial correspondence support while failing to explain the underlying common surface. This reveals a fundamental limitation of correspondence-space reasoning: evidence that is effective for generating a pose is not necessarily sufficient for verifying its geometric validity. We propose G2M-Reg, a training-free Graph-to-Manifold Verification framework that separates pose proposal from pose verification. A correspondence graph first generates a set of plausible pose hypotheses. Instead of ranking them solely by correspondence-level evidence, G2M-Reg evaluates the cross-cloud surface relation induced by each candidate pose. Bidirectional partial-overlap consensus measures whether the two fragments mutually explain a plausible common region, while structural reliability evaluates whether the supporting geometry is coherent and sufficiently informative to constrain the pose. Graph, surface, and structural evidence is subsequently integrated in rank space to select a surface-valid hypothesis, followed by constrained surface-guided refinement. Experiments across indoor and outdoor benchmarks and diverse hand-crafted and learned correspondence sources demonstrate that G2M-Reg consistently improves robust pose selection, particularly in challenging low-overlap scenarios.