Certified Abstention for Provably-Unidentifiable Index-Phase Recovery in Image Registration

Dinh Tuan Nguyen, Trong Nhan Nguyen, Vu Nguyen Minh Hung, Tien Minh Khoi Nguyen, Jaeyeop Choi +3

Image registration underpins measurement across scanning, camera, and microscopy imaging, yet a fundamental question is rarely posed: when is the sample-to-position map recoverable at all, and when does any estimator that reports a position necessarily fabricate one? We show that in reference-perturbed sampled imaging, where samples are localized through a perturbed reference, position fidelity (where samples land) and phase fidelity (which reference index becomes each block's origin) are logically independent: no policy acting on position information alone can guarantee phase fidelity. We derive a tight resolution threshold separating recoverable from provably-unidentifiable registration, and a recovery framework that certifies identifiable regions--recovering them exactly--while abstaining on provably-unidentifiable regions rather than hallucinating structure. On a deployed scanning system we measure a direction-bimodal registration offset consistent with the theory. Against classical and learned restoration baselines, certificate-free offset estimators fabricate structure on the unidentifiable regime, whereas the certified method abstains rather than fabricating. Finally, the…