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

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arXiv:2608.15090v1 Announce Type: cross Abstract: Studies of industrial visual inspection commonly report the area under the receiver operating characteristic curve (AUROC) and the overlap between anomaly maps and defect masks. Neither measure specifies the false-alarm rate at a selected threshold, while recurrent defect locations and mask geometry can inflate overlap. We combine a distribution-free upper tolerance threshold with a paired-minus-crossed spatial test. This test compares each detector's score-contributing locations with the matched defect mask and with masks from other images; the difference in rates defines spatial-evidence lift relative to the empirical chance-overlap rate. We evaluate three detectors on 120 point-defect images from three ISP-AD modalities and three fixed data splits. Of 378 alarms, 230 overlap the matched mask. Paired and crossed rates are nevertheless similar in eight of nine detector--modality cells; only DINOv2--ASM has a positive 95\% bootstrap lower bound (lift 0.259, 95\% interval 0.159--0.347). On the independent Magnetic Tile Defect dataset, the same analysis gives lifts of 0.203 (0.169--0.236) for Wide ResNet-50 (WRN50) patch memory and 0.231 (0.202--0.262) for Vision Transformer B/16 (ViT-B/16) patch memory, with one-sided permutation $p=10^{-5}$ for both. When crossed masks are restricted to the same defect class, the lifts remain 0.185 and 0.210. Exact sample planning shows that, with 150 calibration normals, a 95\%-confidence distribution-free claim is supported only for target false-positive rates of 1.98\% or higher; a 1\% …

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