Alignment-Aware 3D Point Cloud Anomaly Detection with Adversarial Normalizing Flows

Abstract

Detecting localized morphological anomalies in three-dimensional point clouds is difficult because geometric deviations are entangled with rigid pose variation, residual registration error, sampling noise, and normal inter-subject variability. This challenge is particularly relevant in translational neuroimaging, where abnormal shape changes may be subtle and abnormal annotations are scarce. We propose an unsupervised framework that formulates 3D anomaly detection as a two-stage factorization problem, termed AdvFlow3D-AD. First, Fast Global Registration, followed by multi-scale Iterative Closest Point refinement, establishes a common geometric reference frame and reduces rigid-body nuisance variation. Second, an adversarially regularized normalizing flow models the residual distribution of aligned normal coordinates, enabling localized anomaly scores based on distance from the learned normal latent support. Percentile calibration on normal data then defines interpretable point-level and object-level operating points without requiring abnormal samples during training. We evaluate AdvFlow3D-AD on the Real3D-AD and Anomaly ShapeNet3D datasets, achieving a point-level area under the receiver operating characteristic curve (AUROC) of 0.747 on Real3D-AD and an object-level AUROC of 0.816 on Anomaly ShapeNet3D. We further present an exploratory neurodevelopmental brain-shape case study involving pediatric perinatal-asphyxia cases. The resulting anomaly maps showed qualitative spatial correspondence with anatomically plausible hippocampal and cerebellar regions under neuroradiological review. These results suggest that separating geometric nuisance variation from residual morphology can support interpretable anomaly localization when abnormal labels are limited.