GaugeDefect: Detecting Surface Anomalies by Curvature of Feature Transport

Industrial anomaly localization has advanced rapidly with feature-based, reconstruction-based, and distillation-based methods. Most of these methods score a region by asking how unusual its local appearance or feature representation is with respect to normal training images. This is a strong and practical formulation. In this work, we study a complementary geometric cue for cases where an abnormal region may still contain locally plausible visual features. Thin scratches, small dents, and disrupted repeated patterns often do not make every local patch individually abnormal; instead, they disturb how nearby features vary and connect across the surface. We propose GaugeDefect, a geometric method for surface anomaly localization based on the curvature of feature transport. Given a feature lattice, we estimate a local feature frame at each node and compute orthogonal transports between neighboring frames. The accumulated transport around a small closed loop gives a holonomy matrix, whose deviation from identity measures feature-transport curvature. After calibration on normal training images, unusually large curvature indicates a local inconsistency in the feature field. The curvature here is not the physical curvature of the inspected object, but a representation-space measure of neighborhood inconsistency. This makes the method applicable to curved surfaces, textured materials, and non-planar industrial objects. Its main role is to improve localization of subtle surface disruptions, while often producing sharper responses near defect boundaries as a natural consequence of the curvature signal.