GaugeDefect: Detecting Surface Anomalies by Curvature of Feature Transport

Yefan Wang

cs.CVSep 8, 2026

GaugeDefect: Detecting Surface Anomalies by Curvature of Feature Transport

Authors: Yefan Wang

Organizations: University of Shanghai for Science and Technology, Shanghai, China

Abstract

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.

Figures & tables

Figure 1: Overview of GaugeDefect. The method extracts a feature lattice, builds local feature frames, estimates orthogonal transport, computes loop holonomy and curvature, calibrates curvature with normal data, and produces a dense anomaly map.

Figure 2: Principle of GaugeDefect. In a normal region, local feature transport around a loop is consistent, so the holonomy is close to the identity and the curvature is small. In a defective region, the local feature field is disturbed, the same loop becomes inconsistent, and the curvature increases. Loop scores are then aggregated into node scores and finally into an anomaly map.

Method	I-AUROC $\uparrow$	I-AP $\uparrow$	P-AUROC $\uparrow$	P-AP $\uparrow$	AUPRO $\uparrow$
PatchCore [ 13 ]	99.1	99.2	98.1	55.3	93.2
SimpleNet [ 8 ]	99.4	99.3	98.0	58.2	89.9
EfficientAD [ 2 ]	99.1	99.3	97.8	60.2	93.0
RealNet [ 19 ]	99.2	99.2	98.9	62.8	92.8
GLASS [ 5 ]	99.0	99.2	98.2	63.7	93.5
GeneralAD [ 16 ]	99.4	99.5	98.1	65.1	94.0

Table 1: Main results on MVTec AD.

Method	MVTec AD	VisA	Real-IAD
PatchCore [ 13 ]	93.2	91.2	91.0
EfficientAD [ 2 ]	93.0	92.2	89.2
SimpleNet [ 8 ]	89.9	90.1	84.1
RealNet [ 19 ]	92.8	92.6	90.8
Dinomaly [ 6 ]	94.3	93.7	93.3
GaugeDefect	96.5	95.1	94.4

Table 2: Cross-dataset AUPRO summary.

Figure 3: Qualitative comparison of anomaly localization results. GaugeDefect tends to provide more precise responses on subtle surface disruptions such as thin scratches, small dents, and broken local patterns.

Node construction	P-AUROC $\uparrow$	P-AP $\uparrow$	AUPRO $\uparrow$
DINOv2 patch-token lattice	98.8	76.4	96.5
ResNet50 convolutional lattice	97.2	59.6	91.8
Early feature layer	97.9	64.8	93.4
Middle feature layer	98.8	76.4	96.5
Late feature layer	98.3	70.6	94.7
Dense nodes $(\rho=1)$	98.8	76.4	96.5

Table 3: Ablation on feature-lattice node construction. Except for the ResNet50 row, all variants are based on the default DINOv2 configuration

Figure 4: Sensitivity analysis on spatial support.

Variant	P-AUROC $\uparrow$	P-AP $\uparrow$	AUPRO $\uparrow$
Full GaugeDefect	98.8	76.4	96.5
Feature distance only	98.2	67.2	94.6
Frame discrepancy only	98.0	65.8	94.0
Raw curvature without calibration	98.1	68.9	94.3
Fixed transport $R_{ij}=I_{r}$	97.6	62.7	92.8
Rank $r=2$	98.1	68.4	94.3

Table 4: Ablation on feature-transport curvature. All variants are evaluated under the default DINOv2 configuration.

Figure 5: Metric profile on MVTec AD with per-axis best-score normalization.

Image-level detection
Entry	I-AUROC $\uparrow$	I-AP $\uparrow$	ms $\downarrow$	FPS $\uparrow$	GPU/CPU GB $\downarrow$
VisA	98.8	99.1	–	–	–
Real-IAD	97.6	98.2	–	–	–
MVTec AD runtime
Dinomaly (DINOv2-B/14)	–	–	36.8	27.2	3.6/4.0
INP-Former (DINOv2-B/14)	–	–	52.4	19.1	5.0/4.8

Table 5: Image-level results and runtime.

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