Three-Class Correspondence Reliability for Deformation-Preserving ICP: Controlled Synthetic Evaluation and a Cross-Domain Stress Test

Multi-epoch point-cloud analysis requires rigid alignment without allowing genuine geometric change to bias the estimated pose. This study presents a reliability-guided iterative closest point (ICP) formulation in which a compact classifier assigns each candidate correspondence to stable, deformation-candidate, or unreliable classes. Stable-class scores softly weight a Cauchy-robust point-to-plane objective on the special Euclidean group SE(3), while deformation candidates are retained for signed-residual mapping. Controlled evaluation comprised 28 factor-level blocks, with 20 independently generated random trials per block and 560 paired trials per method. The three-class method achieved median rotational and translational errors of 0.227 degrees and 4.103 mm and 96.61% registration recall. Its principal benefit was changed-region discrimination: the F1 score (harmonic mean of precision and recall) reached 0.524 for the 5 and 10 mm cases, compared with 0.413 for binary classifier-guided ICP. However, the binary method produced slightly better rigid-registration accuracy, and the three-class stable-region false-positive rate was 6.71%. An external stress test on a Stanford Bunny scan pair used 60 controlled initialisations. Point-to-point ICP achieved 100% success, whereas the unretrained three-class method achieved 0% and assigned 39.3% of rigid-object correspondences to the deformation class. The results support three-way correspondence modelling as a controlled proof of concept but demonstrate that balanced synthetic training does not yield calibration-free transfer. Real-domain calibration, stronger geometric baselines, and validation with independent displacement ground truth are required before deployment.