Multiscale Surface Equilibrium Responses for Unified 3D Anomaly Detection

Two geometric deviations of the same magnitude can carry different evidence of a defect: a narrow bump is often anomalous where a broad variation is not. Reliable 3D anomaly detection therefore requires interpreting not only the size of a deviation but its spatial pattern, relative to the variation observed in normal shapes. We propose a unified framework that uses a nominal surface as the analysis domain and represents each query through four multiscale equilibrium responses. Signed query-to-surface discrepancies are lifted into a scalar field, and screened- Poisson equilibria reveal how this field responds to increasing spatial coupling. This four-channel decomposition is exactly additive: it preserves the input discrepancy while exposing its structure across spatial scales. A single geometry- conditioned Gaussian potential, shared across categories and trained only on nor mal scans, evaluates the joint responses against the variation expected at each surface location. Anomaly scores measure the energy gap from the expected nor mal response, assigning high cost to departures along directions with little normal variation. Despite using one shared model per dataset, our method surpasses not only unified baselines but also the strongest category-specific methods: it achieves point-level AUROC of 92.7% and 97.2% on Real3D-AD and Anomaly-ShapeNet, exceeding the previous best by 4.9 and 3.6 points, respectively, while also attaining the best mean object-level among unified methods on both benchmarks.