Training-Free Logical and Structural Anomaly Detection via Calibrated Fusion

Changyi Li; Miao Yu; Kai Dong; Yu Xiao

cs.CVSep 4, 2026

Training-Free Logical and Structural Anomaly Detection via Calibrated Fusion

Authors: Changyi Li, Miao Yu, Kai Dong, Yu Xiao

Organizations: Aalto University, 02150 Espoo, Finland · Harbin Engineering University, 150001 Harbin, China

Abstract

Industrial anomaly detection must handle two distinct defect families: structural anomalies, which manifest as local texture corruptions, and logical anomalies, which violate global rules on object count, composition, or arrangement. Existing detectors typically favor one family at the expense of the other. In particular, training-free methods effectively exploit frozen representations but lack an explicit notion of object count, while methods that reason about counts usually rely on category-specific component modeling. We show that counting ability can be introduced into training-free anomaly detection without additional training or part-level supervision. Our key idea is a normal-set calibration that aligns heterogeneous anomaly cues using statistics from normal images, enabling their direct fusion within a unified training-free framework. Built upon this calibration, our detector combines complementary frozen cues to address both logical and structural anomalies. On MVTec-LOCO, our method achieves image-level AUROCs of 89.0 and 95.9 on logical and structural anomalies, respectively, yielding a 92.5 average---the best among training-free detectors in our comparison. It remains competitive with methods requiring network training or part annotations, while its structural variant matches PatchCore on MVTec-AD (99.1 image-AUROC), suggesting that the proposed calibration generalizes beyond logical anomaly detection.

Figures & tables

Figure 1: Logical and structural anomalies on the same product (left: normal reference). A logical anomaly (middle) preserves local appearance but violates global rules on count or composition, whereas a structural anomaly (right) preserves global composition but disrupts local appearance. Handling both requires complementary global and local reasoning, yet existing detectors often excel at one at the expense of the other.

Figure 2: Overview of the proposed calibrated fusion framework. Frozen branches extract complementary anomaly cues spanning appearance, texture, and open-vocabulary counting. Our key idea, normal-set calibration, rescales these heterogeneous scores onto a common scale using only normal-image statistics, enabling their fusion through a $p$ -norm soft-OR into the final anomaly score $S$ . The calibrated scores also yield interpretable evidence attribution for logical and structural decisions.

Figure 3: Normal-set calibration renders heterogeneous branch scores directly comparable. On the screw_bag category, calibrated appearance ( deep ) and counting ( sam ) scores place normal images near the shared threshold (

\hat{s}=1

, dashed), while anomalies extend beyond it in both branches. This branch-independent scale makes heterogeneous cues directly fusible.

	Method	Logical	Structural	Average
labels	PSAD † [ 7 ]	98.1	91.6	94.9
trained	GCAD [ 2 ]	86.0	80.7	83.4
	EfficientAD-M [ 1 ]	86.8	94.7	90.7
	SLSG [ 15 ]	89.6	91.4	90.3
	PUAD [ 14 ]	92.0	94.1	93.1
	CSAD [ 5 ]	96.7	94.0	95.3

Table 1: Comparison with prior work on MVTec-LOCO (image-level AUROC, %). Methods are grouped by the supervision they require. Best overall results are shown in bold , and the best training-free results are underlined . PatchCore results are from [ 5 ] ; all others are taken from the cited papers.

Category	GCAD	SINBAD	PSAD †	Ours
breakfast_box	87.0	97.7	100.0	99.4
juice_bottle	100.0	97.1	99.1	92.7
pushpins	97.5	88.9	100.0	89.2
screw_bag	56.0	81.1	99.3	77.2
splicing_connectors	89.7	91.5	91.9	86.5
Average	86.0	91.2	98.1	89.0

Table 2: Per-category breakdown of logical anomaly detection on MVTec-LOCO (AUROC, %). Best results in each category are shown in bold . † denotes part supervision. Results are taken from the cited papers.

Figure 6: Sensitivity to the shared hyperparameters on MVTec-LOCO (average image-AUROC, %). Dashed lines indicate the values used in all experiments. Performance remains stable across broad ranges of the fusion exponent

p

, reliability scale

v_{0}

, and standard-deviation floor

\tau

Variant	Logical	Structural	Average	Fusion rule	Average
Ours (full)	89.0	95.9	92.5	$p$ -norm ( $p\!=\!6$ )	92.5
$-$ counting	85.6	96.7	91.1	plain sum	90.6
$-$ textural	88.7	94.3	91.5	rank-max	89.0
$-$ semantic	89.9	91.7	90.8	top-2 pool	89.7

Table 3: Ablations (MVTec-LOCO average image-AUROC). Left: leave-one-branch-out from the full model. Right: fusion rule at fixed branches. Best average in bold .

	breakfast	juice	pushpins	screw_bag	splicing	Average
Axis-attr. acc.	81.5	78.0	52.9	81.3	75.1	73.8

Table 4: Explainability: accuracy of the logical/structural axis attribution per category (% of anomalies whose predicted axis matches the ground-truth type).

Figure 7: Self-explaining outputs for logical and structural anomalies. Logical anomalies are explained through detected concept instances and their count rationales, whereas structural anomalies are localised by the patch-memory heatmap. Cyan circles mark the labelled anomalous regions for reference (dashed when the object is missing). All explanations reuse the calibrated scores used for detection and axis attribution, requiring no additional explanation model.

Average $99.1$ (DINOv2 memory only: $98.6$ ; full five-branch fusion: $78.4$ )
Category	AUROC	Category	AUROC	Category	AUROC
bottle	100.0	hazelnut	100.0	tile	100.0
cable	95.3	leather	100.0	toothbrush	96.9
capsule	99.2	metal_nut	100.0	transistor	100.0
carpet	99.9	pill	98.6	wood	99.8
grid	100.0	screw	96.5	zipper	100.0

Table 5: Structural generalisation to MVTec-AD (per-category image-AUROC, %). Because MVTec-AD contains only structural anomalies, we evaluate the structural configuration of our framework while disabling the logical branches.

Figure 8: Failure case: unstable counting on screw_bag . Two normal images with identical parts receive different ”nut” counts from the frozen segmenter, reflecting its difficulty in separating small, visually similar components. The resulting variability broadens the normal count distribution and limits logical discrimination on this category.

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LogiCo: A Unified Framework for Logical and Structural Anomaly Detection

Ximiao Zhang, Min Xu, Xiuzhuang Zhou

School of Intelligent Engineering and Automation, Beijing University of Posts and Telecommunications, Beijing, China · College of Information and Engineering, Capital Normal University, Beijing, China

Industrial Anomaly Detection Reconstruction-Based Anomaly Detection Anomaly Detection

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Current anomaly detection methods primarily focus on structural anomalies, while paying insufficient attention to anomalies that violate logical constraints. Conversely, top-performing logical anomaly detection approaches address this by modeling global semantic consistency, but perform poorly on subtle structural anomalies due to inadequate detection granularity. In this paper, we propose LogiCo, a unified framework for Logical and structural anomaly detection via Component-level feature reconstruction. Unlike existing methods that rely on explicit global semantic modeling, LogiCo employs a novel component-level feature reconstruction technique to capture inter-component logical constraints. Specifically, LogiCo maps pre-trained image features into a discrete component-level feature space and performs collaborative feature reconstruction at both component and patch levels, enabling it to effectively detect both logical and structural anomalies. Furthermore, to address the specific challenge of count-related logical anomalies, we integrate a segmentation-map discriminator that extends the model's capability to identify quantitative inconsistencies. LogiCo achieves state-of-the-art performance on both logical and structural anomaly detection across four benchmarks, including MVTec-LOCO, MVTec-AD, VisA, and Real-IAD, demonstrating its superiority and practical feasibility. The code is available at https://github.com/cnulab/LogiCo.

Abstract

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