PC-Reg: Modeling Spatial Dependencies for Logical Anomaly Detection

In industrial visual inspection, individual components may look normal even when their arrangement or quantity is incorrect. For example, a cable may be plugged into the wrong slot of a connector, although every part in the image is intact. These logical anomalies are difficult for methods such as PatchCore, which score image regions independently, while the vision-language pipelines that can reason about them are slow and costly to deploy on a production line. In this work, we present Positional Contextual Regression (PC-Reg), which is a method that learns from defect-free images how each region relates to its surroundings, without gradient-based training. A frozen vision backbone provides the patch features, and a closed-form ridge regression at each grid position predicts every patch feature from its neighbors; the Mahalanobis distance of the prediction residual, calibrated per position, measures how far a region departs from its expected context. The attention of the backbone weights the neighbors, and a complementary score captures the content of the four image quadrants. With one fixed configuration across 32 categories of MVTec LOCO AD, MVTec AD, and VisA, the combined method, PC-RegDual, reaches 85.7%, 98.8%, and 92.6% AUROC (87.5%, 99.0%, and 93.5% with a larger backbone). On the same features, it outperforms a nearest-neighbor baseline that follows PatchCore on MVTec LOCO AD by 5.3 percentage points overall and by 14.6 percentage points on logical anomalies, and it outperforms PaDiM and a mean-subtraction baseline on all three benchmarks. Diagnostic feature-space tests show that PC-Reg responds to broken spatial relationships that independent patch scoring misses, and an evaluation on production-line images (BTAD) gives results comparable to the best baselines. On a consumer GPU, fitting takes about 5 s per category (72 s on one CPU core) and inference 55 ms per image, with deterministic output and no external services, so new products can be set up in minutes on local hardware.