Learning Canonical Representations for Rotation-Invariant and Unified 3D Anomaly Detection

3D anomaly detection is critical in industrial manufacturing because defects are defined by surface geometry that 2D inspection often misses. In practice, a single inspection pipeline covers many object categories, and the objects arrive in arbitrary poses. Recent unified methods train a single model for many categories, but they assume a fixed input pose and build on backbones pre-trained on external shape data. Methods that address rotation align each test sample to a reference, which is costly and does not carry over to the unified setting. Our key idea is to canonicalize before scoring, so that local geometry no longer carries the object pose. The canonicalizer must therefore keep the canonical frame unchanged when a defect is present and consistent across samples of the same category. We present a framework that learns Canonical representations for Rotation-invariant and Unified 3D anomaly detection (CRU3D-AD), which meets both conditions with an SO(3)-equivariant canonicalizer trained under a pairing loss and a prototype loss. The canonicalizer is then frozen while a feature extractor, a geometry-aware local attention module, and a point-wise scorer are trained on synthetically generated defects, using no external pre-training and no memory bank. Experiments on Real3D-AD and Anomaly-ShapeNet show the best point-level localization among unified methods on both datasets, with competitive object-level detection. The code will be made available upon acceptance.