U-Flow: A U-shaped Normalizing Flow for Anomaly Detection with Unsupervised Threshold

In this work we propose a non-contrastive method for anomaly detection and segmentation in images, that benefits both from a modern machine learning approach and a more classic statistical detection theory. The method consists of three phases. First, features are extracted using a multi-scale image Transformer architecture. Then, these features are fed into a U-shaped Normalizing Flow that lays the theoretical foundations for the last phase, which computes a pixel-level anomaly map, and performs a segmentation based on the a contrario framework. This multiple-hypothesis testing strategy permits to derive robust automatic detection thresholds, which are crucial in many real-world applications, where an operational point is needed. The segmentation results are evaluated using the Intersection over Union (IoU) metric; and for assessing the generated anomaly maps we report the area under the Receiver Operating Characteristic curve (AUROC), and the area under the per-region-overlap curve (AUPRO). Extensive experimentation in various datasets shows that the proposed approach produces state-of-the-art results for all metrics and all datasets, ranking first in most MvTec-AD categories, with a mean pixel-level AUROC of 98.74%. Code and trained models are available at https:// github.com/mtailanian/uflow.