Distribution-free false-alarm calibration and chance-corrected spatial evaluation for industrial anomaly detection

Vision-based industrial anomaly detectors are calibrated on one distribution but may be deployed on another that differs in illumination, fixture placement, or sensor characteristics, sharply degrading an otherwise accurate detector. Adapting to the incoming lot is a natural response, but labeled anomalies are scarce. We therefore consider calibration using only a handful of verified-normal images available before scoring the rest of the lot. Existing fixes require backpropagation, detector-specific tuning, or choices about feature directions that few calibration samples cannot justify. We present SPARC, a few-shot calibration method that intercepts patch features between encoder and detector and removes a closed-form, spatially indexed estimate of deployment-time nuisance through per-cell subspace projection. It needs only $k \le 8$ verified-normal images and uses the algebraic saturation rank $r{=}k{-}1$ on the encoder's native patch grid. The correction requires no gradient or weight updates and works with memory-bank, density, prototype, and mutual detectors. On the shift-prone benchmarks, SPARC improves pooled Image AUROC and AU-PRO$_{0.3}$ for all seven detectors whose image scores depend on corrected patch features by $+13.8$ and $+3.5$ percentage points (pp), respectively; on benchmarks without engineered shift, the changes are small and mixed. Controls that give competing corrections the same calibration images attribute these gains to the per-cell subspace structure rather than the images alone. Further ablations support the saturation-rank choice and characterize sensitivity to backbone and calibration conditions.

Recent advances in anomaly detection (AD) for industrial inspection have pushed performance on standard benchmarks toward saturation. However, strong benchmark performance does not necessarily translate to real-world deployment, as these benchmarks are primarily collected under controlled acquisition conditions. Changes in illumination, background, viewpoint, and other environmental factors can shift normal samples away from the learned normal distribution and cause false anomaly responses. We address AD under such distribution shifts by explicitly modeling nuisance variation from changing imaging conditions in feature space. Without anomaly labels or target-domain data, our Nuisance-Filtered Anomaly Detection (NFAD) framework estimates a nuisance subspace from matched feature displacements induced by content-preserving perturbations and suppresses its contribution to anomaly residuals at inference. The same subspace supports two complementary branches: full projection for image-level detection and selective suppression for pixel-level localization, preserving evidence of localized defects. On AeBAD-S, a benchmark specifically designed for AD under acquisition shifts, NFAD achieves 91.0% image-level AUROC, establishing a new state of the art. Notably, this robustness does not come at the expense of conventional AD performance: NFAD remains competitive on standard benchmarks that do not explicitly evaluate distribution shift, including VisA, Real-IAD, and MVTec AD. These results show that explicitly suppressing such nuisance variation improves AD under distribution shift while preserving strong performance in standard settings.

Few-shot anomaly detectors are judged by ranking metrics, yet deployment requires an alarm threshold with a controlled false-alarm rate (FAR). We ask how much normal evidence, in images or category units, is needed to certify such a threshold for an unseen category. Using a frozen DINOv2 principal component analysis (PCA) residual ranker on 15 MVTec and 12 VisA categories under four corruption types, we show that target-only leave-one-image-out (LOIO) calibration is resolution-limited and shift-fragile: rank values cannot fall below $1/(k+1)$, and at the attainable level $α=0.20$, empirical FAR reaches 0.341 on Gaussian-corrupted MVTec at $k=4$, 1.7 times the nominal level. A category-count feasibility calculus is then derived: even with all-zero category losses and no multiplicity charged, any deterministic, uniformly valid, distribution-free 95% upper confidence bound (UCB) requires at least 14, 29, and 59 independent and identically distributed (iid) category draws at $α=0.20$, $0.10$, and $0.05$; these counts are necessary but not sufficient. The Cross-category Reliability Estimation with Source Support (CRESS) protocol splits source categories into disjoint reference, proposal, and certification roles. With only three or four certification categories, all 960 frozen configurations return the fail-closed threshold $τ^\star=0$, and the smallest category-level UCB is 0.950. Image-unit analyses of the same archive select positive thresholds in 36.7% to 60.3% of target cells; these bounds hold for the selected source mixture, not for the marginal risk of a new-category draw. The contribution is a quantitative feasibility boundary and an estimand-aware protocol specifying when source evidence can, and cannot, support a transferable reliability claim.