Learning local and global prototypes with optimal transport for unsupervised anomaly detection and localization

Carole Lartizien; Robin Trombetta

REVIEW 4 major objections 5 minor 49 references

Learning local and global prototypes with optimal transport for unsupervised anomaly detection and localization

T0 review · 4 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The paper proposes an unsupervised anomaly detection method, PRADOT, whose structural cost in optimal transport improves detection of logical image incoherencies.

desk verdict PRADOT is a competent prototype-based UAD method with a genuinely new feature-spatial OT cost, but its advertised claim about spatial structure during prototype learning driving the gain is not established by the reported ablation. read the letter →

arxiv 2508.12927 v2 pith:Y7MVZCSI submitted 2025-08-18 eess.IV cs.AI

Robin Trombetta , Carole Lartizien This is my paper · ORCID

classification eess.IVcs.AI

keywords unsupervisedanomalydetectionprototypelearningoptimaltransportlocalizationlogicalanomaliesstructuralconstraintmulti-scalefeaturesentropicregularisation

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper proposes PRADOT, an unsupervised anomaly detection method that learns local and global prototypes from pre-trained image features using optimal transport. Its central claim is that adding a spatial cost to the feature-comparison cost during prototype learning and assignment captures the structural organisation of normal images, and that this improves detection of logical incoherencies such as misplaced objects. The method is evaluated on two industrial benchmark datasets, where it reports performance on par with compared baselines and ranks second on MVTec AD LOCO, with the structural cost shown to drive gains on logical anomalies. A sympathetic reader should care because it offers a single knob, the spatial-cost weight, that trades between detecting shape-level defects and detecting violations of expected layout, and it makes those failures visible through embedding-to-prototype assignment maps.

What carries the argument

The central object is the cost function $C(f,P) = (1-\alpha)(1 - \frac{\langle z,p\rangle}{\|z\|\|p\|}) + \alpha \|c-\rho\|^2$, which combines a cosine feature distance with an L2 spatial distance and is embedded in an entropic optimal transport problem between batch embeddings and prototypes. The named mechanism is the spatial or structural cost controlled by $\alpha$: because prototypes occupy fixed grid coordinates and the transport problem couples features to those coordinates, increasing $\alpha$ forces assignments to respect image layout. Prototype vectors are updated as weighted barycentres of assigned embeddings via an exponential moving average, after solving the entropically regularised optimal transport problem. The final anomaly map averages scores from global ($\alpha = 0$) and local ($\alpha > 0$) prototypes at two encoder scales.

What would settle it

Take a normal-image training set with a dominant background and rare foreground positions, train PRADOT twice, once with uniform marginals and once with marginals proportional to observed location frequency, and compare localisation of anomalies placed at rare positions: if the uniform-marginal model localises them markedly worse, the uniform assumption is the cause.

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Extended reading notes

Core claim

PRADOT builds a set of prototypes placed on the same spatial grid as encoder features, with several prototypes per grid cell. During training, an entropic optimal transport plan assigns each embedding to prototypes under uniform marginal distributions, and prototype vectors are updated by exponential moving average, so a prototype becomes a barycentre of the features assigned to it. The cost between an embedding and a prototype is $C(f,P) = (1-\alpha)(1 - \frac{\langle z,p\rangle}{\|z\|\|p\|}) + \alpha \|c-\rho\|^2$, where the second term penalises spatial displacement. With $\alpha = 0$ the prototypes are purely feature-based or global; with $\alpha > 0$ they become local, so an embedding whose feature matches a prototype far away pays a spatial penalty. At inference the minimum cost to any prototype is the anomaly score, and local and global maps at multiple scales are averaged. The claimed effect is that higher $\alpha$ specifically improves detection and localisation of logical anomalies on MVTec AD LOCO, while a lower $\alpha$ remains preferable for structural defects.

Load-bearing premise

The load-bearing premise is that every spatial location and every prototype should receive equal mass in the transport problem, which can misrepresent normal data with a dominant background or strongly non-uniform object placement.

Editorial extensions

If this is right

Tuning $\alpha$ lets one pipeline interpolate between detecting structural defects and detecting logical incoherencies, so a user can choose the operating point for the anomaly type that matters.
Because the assignment penalises spatial displacement, a patch that is normal in itself but appears in the wrong location receives a high anomaly score.
Averaging global and local prototype maps, and combining two feature scales, improves both image-level and pixel-level results over either alone.
The reconstructed-prototype visualisation provides a native explanation: abnormal regions are replaced by semantically coherent patches, which could also serve as an image-restoration side output.
The embedding-to-prototype assignment arrows give a per-image account of why a region was scored anomalous.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

One testable extension is to replace the uniform embedding marginal with an empirical location-frequency marginal; if a dataset has dominant background regions, this should change which prototypes form and where localisation errors concentrate.
The $\alpha$ trade-off suggests a per-category or adaptive $\alpha$ selected on validation could keep the structural-defect performance on MVTec AD while preserving the logical-anomaly gains on LOCO.
The same spatial-assignment mechanism transfers naturally to medical imaging, where normal anatomy has strong layout regularity and the anomalies of interest are misplaced or duplicated structures; the uniform-marginal assumption would need revisiting there.
The assignment vectors from embedding to prototype can themselves be read as a saliency map for why a region is flagged.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

I read PRADOT. The first thing to know: it's a competent prototype-based UAD method with a genuinely new cost function, but the paper's main causal claim—that spatial regularization during prototype learning improves logical anomaly detection—is not supported by the reported ablation.

What is new: the combination of optimal-transport prototype learning with a fused feature-and-spatial cost is not in the cited baselines like PatchCore or the few-shot OT methods. The authors show sensible ablations linking the spatial cost parameter α to logical versus structural anomalies, and they ship code. Performance is on par with strong baselines on MVTec AD and second on LOCO, which is a reasonable empirical result.

Soft spots, in order of importance. First, the ablation in Section 4.3 varies α jointly in training and inference. The text in the abstract and conclusion says the structural constraint is enforced "when learning the prototypes," but Fig. 3b and Fig. 4 show only the assignment cost at test time. The paper itself describes the effect as "imposing a structural constraint on the embedding-to-prototype assignment" (Section 4.3), which is an inference-side statement. To claim prototype learning benefits from α, you need at least one cell where training uses α=0 and inference uses α>0, or vice versa. As reported, the gain could come entirely from the test-time spatial penalty. That is a load-bearing gap, not a minor nit.

Second, Eq. (5) is inconsistent with the pseudocode in Appendix B. The main text shows pi ← -η pi + (1-η)... while the pseudocode and standard EMA use +η pi. One of them is wrong; this matters for reproducibility.

Third, hyperparameters (α, n, η, ε) are set without any described validation procedure, and results are reported without error bars across seeds. This is common in the field but still a weakness for a paper making a quantitative claim about LOCO performance.

The uniform-marginal concern in Eq. (2) is real but minor. A dominant background could bias prototypes toward rare spatial locations, but this is a modeling assumption, not a fatal flaw.

Overall, the method is plausible and the empirical work is honest, but the central attribution is unproven. The paper deserves a serious referee, mainly because the issue is fixable with a clean controlled ablation and the method itself is likely useful to the industrial UAD community. My recommendation: send to peer review, but ask the authors to separate training and inference α, fix Eq. (5), and report seeds.

Referee Report

4 major / 5 minor

Summary. The manuscript proposes PRADOT, an unsupervised anomaly detection and localization method that learns feature-space prototypes from a pre-trained encoder under a fused feature/spatial cost inspired by the fused Gromov-Wasserstein distance. Embeddings and prototypes carry spatial coordinates on a fixed grid; during training, Sinkhorn optimal transport assigns batch embeddings to local and global prototypes and prototypes are updated by an exponential moving average; at inference, each embedding is scored by the minimum fused cost to any prototype. The method is evaluated on MVTec AD and MVTec AD LOCO, reporting competitive or second-best average performance on LOCO and strong results on MVTec AD, with ablations on the spatial cost weight, number of prototypes, and batch size.

Significance. If the central claim is fully supported, the paper makes a useful contribution: it connects prototype-based anomaly detection to balanced optimal transport and introduces a simple structural cost that appears to help detect logical incoherencies. The code is released, the ablation study is informative, and the reported numbers are competitive with recent baselines. The main strength is that the central claim is falsifiable: the contribution of the structural constraint can, in principle, be separated into a learning-side and an inference-side effect. At present that separation is not performed, so the significance is conditional on the results of the additional experiment requested below.

major comments (4)

[3.1, Eq. (5) vs Appendix B Algorithm 1] The prototype update is written in Eq. (5) as p_i <- -η p_i + (1-η) Np/(B*H*W) Σ_k T*(k,i) z_k, but Algorithm 1 in Appendix B gives p_i <- η p_i + (1-η)(n*H_l*W_l)/(B*H_l*W_l) Σ_k T*(k,i) z_k. The sign of the first term differs. If Eq. (5) is taken literally, the update is not an exponential moving average and can drive prototypes away from the data; if the pseudocode is the intended update, Eq. (5) must be corrected. Because this is a central formula, the inconsistency must be resolved.
[4.3, Fig. 3b and Table 2] The ablation varies alpha jointly in training (Eqs. (1), (3), and (5)) and in inference (Eq. (6)), so the reported improvement for logical anomalies does not identify whether the gain comes from learning spatially organized prototypes or merely from applying the spatial penalty at test time. The abstract and Section 5 claim a benefit 'when learning the prototypes,' but this is not established by the current experiments. Please add a two-way experiment, for example training with alpha = 0 and scoring with alpha in {0, 0.3, 0.5} versus training with alpha = 0.3 and scoring with the same inference values; this directly tests whether local prototype learning contributes beyond the inference-side structural cost.
[Table 1 vs Appendix A Table 3] There is a numerical inconsistency in the reported baselines: MVTec AD LOCO localization for PaDiM is 42.6 in Table 1 but the category-wise mean in Appendix A Table 3 is 52.1. The value 42.6 appears to be copied from the DRAEM row. Since Table 1 is used to support the 'second rank' claim, this error must be corrected and all affected averages recomputed.
[4.1, hyperparameters] The values of the main hyperparameters (alpha = 0.3, n = 16, eta = 0.95, epsilon = 0.01, 50 epochs, batch size 64) are stated without a validation procedure. Since Fig. 3b shows that alpha strongly affects the trade-off between logical and structural anomaly detection, the reader cannot rule out that the headline numbers were obtained by selecting alpha on the test set. Please specify how each hyperparameter was chosen, for example via a fixed schedule, a held-out set of normal images, or a reported sensitivity range, and ideally report standard deviations over multiple runs.

minor comments (5)

[3.1, Eq. (2)] The marginal constraint 'tT 1_{NHW} = nu' should read T^T 1_{NHW} = nu; as typeset, the transposition is confusing.
[3.1, Eqs. (1) and (3)] Eq. (1) defines the cost without the max-normalization that appears in Eq. (3); it would help to state explicitly that Eq. (1) is the conceptual cost and Eq. (3) is the normalized implementation.
[3.1, paragraph after Eq. (2)] The uniform-marginal assumption is asserted without discussion. Given that normal industrial images often contain a dominant background, a sentence acknowledging this limitation, or a sensitivity check using reweighted marginals, would be useful.
[4.1 and Table 1] No error bars or multiple-seed results are reported. Given the small margins in Table 1 (for example PRADOT versus PaDiM/SPADE on LOCO localization), seed-averaged results with standard deviations would strengthen the ranking claims.
[Appendix B] The pseudocode contains rendering artifacts, including garbled symbols in the input and initialization lines; these should be cleaned before publication.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the method's derived quantities are independent of its empirical claims.

full rationale

The paper introduces a new prototype-learning method based on an explicit optimal transport formulation. The central claim that enforcing a structural constraint improves detection of incoherencies is an empirical result supported by ablations and benchmark comparisons, not a quantity derived from the model's own definitions. The cost function in Eq. (1), the OT problem in Eq. (2), the prototype update in Eq. (5), and the inference score in Eq. (6) are all stated explicitly and do not presuppose the experimental conclusion. No parameter is fitted to the target metric and then reported as a prediction; alpha is a hyperparameter whose effect is studied, and its joint influence on training and inference is a possible experimental confound, not a circular reduction. The paper also does not rely on load-bearing self-citations or imported uniqueness theorems; its references are to external benchmarks and standard OT literature. Thus, the derivation chain is self-contained and the empirical claims are separable from the model construction.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The method introduces no new entities, but relies on several modeling choices: uniform OT marginals, a handcrafted feature-spatial cost, and a frozen pre-trained encoder. These are reasonable but none is derived from first principles.

free parameters (4)

alpha (structural cost weight) = 0.3 (local prototypes)
Balances feature and spatial costs in Eq. (1); ablation in Fig. 3b shows detection of logical vs structural anomalies trades off with alpha.
n (prototypes per grid cell) = 16
Number of prototypes per spatial grid position; ablation in Fig. 3a shows performance improves from n=4 to n=16.
eta (EMA rate) = 0.95
Update rate for prototype features; standard choice, no sensitivity analysis reported.
epsilon (entropic regularization) = 0.01
OT regularization; standard small value, no sensitivity analysis.

assumptions (4)

domain assumption Uniform marginal distributions for embeddings and prototypes in the OT problem
Eq. (2) sets both mu and nu to uniform, assuming equal mass per embedding and per prototype; this may misrepresent non-uniform data.
domain assumption Pre-trained ResNet50 features are discriminative for normal vs abnormal patterns
The method relies entirely on a frozen ImageNet-pretrained encoder; no fine-tuning or adaptation is done.
ad hoc to paper Squared Euclidean distance on normalized grid coordinates is a valid structural cost
The spatial cost in Eq. (1) is chosen ad hoc; no justification beyond intuition.
ad hoc to paper Prototypes are fixed to the same grid as embeddings
The paper restricts prototype coordinates to the H x W grid to simplify modelling, which limits representation power.

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Cite this review

Pith. "Pith review of Learning local and global prototypes with optimal transport for unsupervised anomaly detection and localization." pith.science (2026). https://pith.science/paper/Y7MVZCSI

@misc{pith2026250812927,
  author       = {Pith},
  title        = {Pith review of: Learning local and global prototypes with optimal transport for unsupervised anomaly detection and localization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Y7MVZCSI}},
  note         = {Machine review of arXiv:2508.12927}
}

read the original abstract

Unsupervised anomaly detection aims to detect defective parts of a sample by having access, during training, to a set of normal, i.e. defect-free, data. It has many applications in fields, such as industrial inspection or medical imaging, where acquiring labels is costly or when we want to avoid introducing biases in the type of anomalies that can be spotted. In this work, we propose a novel UAD method based on prototype learning and introduce a metric to compare a structured set of embeddings that balances a feature-based cost and a spatial-based cost. We leverage this metric to learn local and global prototypes with optimal transport from latent representations extracted with a pre-trained image encoder. We demonstrate that our approach can enforce a structural constraint when learning the prototypes, allowing to capture the underlying organization of the normal samples, thus improving the detection of incoherencies in images. Our model achieves performance that is on par with strong baselines on two reference benchmarks for anomaly detection on industrial images.

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Works this paper leans on

49 extracted references · 25 canonical work pages

[1]

International Journal of Computer Vision130(4), 947–969 (2022)

Bergmann,P.,Batzner,K.,Fauser,M.,Sattlegger,D.,Steger,C.:Beyonddentsand scratches: Logical constraints in unsupervised anomaly detection and localization. International Journal of Computer Vision130(4), 947–969 (2022)

2022
[2]

In: 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

Bergmann, P., Fauser, M., Sattlegger, D., Steger, C.: Mvtec ad — a comprehen- sive real-world dataset for unsupervised anomaly detection. In: 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). pp. 9584–9592 (2019)

work page 2019
[3]

International Conference on Learning Repre- sentations (2019)

Brendel, W., Bethge, M.: Approximating cnns with bag-of-local-features models works surprisingly well on imagenet. International Conference on Learning Repre- sentations (2019)

work page 2019
[4]

Advances in neural information processing systems 35, 39090–39102 (2022) Prototype-based anomaly detection with optimal transport 15

Cao, Z., Xu, Q., Yang, Z., He, Y., Cao, X., Huang, Q.: Otkge: Multi-modal knowl- edge graph embeddings via optimal transport. Advances in neural information processing systems 35, 39090–39102 (2022) Prototype-based anomaly detection with optimal transport 15

work page 2022
[5]

Advances in neural information processing systems33, 9912–9924 (2020)

Caron, M., Misra, I., Mairal, J., Goyal, P., Bojanowski, P., Joulin, A.: Unsupervised learning of visual features by contrasting cluster assignments. Advances in neural information processing systems33, 9912–9924 (2020)

2020
[6]

arXiv preprint arXiv:2005.02357 (2020)

Cohen, N., Hoshen, Y.: Sub-image anomaly detection with deep pyramid corre- spondences. arXiv preprint arXiv:2005.02357 (2020)

arXiv 2020
[7]

Courty, N., Flamary, R., Tuia, D., Rakotomamonjy, A.: Optimal transport for domainadaptation.IEEEtransactionsonpatternanalysisandmachineintelligence 39(9), 1853–1865 (2016)

2016
[8]

In: Advances in Neural Information Processing Systems

Cuturi, M.: Sinkhorn distances: Lightspeed computation of optimal transport. In: Advances in Neural Information Processing Systems. vol. 26 (2013)

work page 2013

Show all 49 references

[9]

In: Proceedings of the European conference on computer vision (ECCV)

Damodaran, B.B., Kellenberger, B., Flamary, R., Tuia, D., Courty, N.: Deepjdot: Deep joint distribution optimal transport for unsupervised domain adaptation. In: Proceedings of the European conference on computer vision (ECCV). pp. 447–463 (2018)

2018
[10]

In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

Deng, H., Li, X.: Anomaly detection via reverse distillation from one-class em- bedding. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). pp. 9737–9746 (June 2022)

2022
[11]

In: Proceedings of the IEEE/CVF interna- tional conference on computer vision

Gong, D., Liu, L., Le, V., Saha, B., Mansour, M.R., Venkatesh, S., Hengel, A.v.d.: Memorizing normality to detect anomaly: Memory-augmented deep autoencoder for unsupervised anomaly detection. In: Proceedings of the IEEE/CVF interna- tional conference on computer vision. pp. 1...

2019
[12]

Communications of the ACM 63(11), 139–144 (2020)

Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., Bengio, Y.: Generative adversarial networks. Communications of the ACM 63(11), 139–144 (2020)

2020
[13]

In: Pro- ceedings of the IEEE/CVF International Conference on Computer Vision

Guo, H., Ren, L., Fu, J., Wang, Y., Zhang, Z., Lan, C., Wang, H., Hou, X.: Template-guided hierarchical feature restoration for anomaly detection. In: Pro- ceedings of the IEEE/CVF International Conference on Computer Vision. pp. 6447–6458 (2023)

2023
[14]

He,K.,Zhang,X.,Ren,S.,Sun,J.:Deepresiduallearningforimagerecognition.In: Proceedings of the IEEE conference on computer vision and pattern recognition. pp. 770–778 (2016)

2016
[15]

Advances in neural information processing systems33, 6840–6851 (2020)

Ho, J., Jain, A., Abbeel, P.: Denoising diffusion probabilistic models. Advances in neural information processing systems33, 6840–6851 (2020)

2020
[16]

In: Proceedings of the ieee/cvf conference on computer vision and pattern recognition

Izquierdo, S., Civera, J.: Optimal transport aggregation for visual place recogni- tion. In: Proceedings of the ieee/cvf conference on computer vision and pattern recognition. pp. 17658–17668 (2024)

2024
[17]

In: Proceedings of the IEEE/CVF conference on computer vision and pattern recognition

Kim, J., Oh, T.H., Lee, S., Pan, F., Kweon, I.S.: Variational prototyping-encoder: One-shot learning with prototypical images. In: Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. pp. 9462–9470 (2019)

2019
[18]

arXiv preprint arXiv:2301.12171 (2023)

Kim, K., Oh, Y., Ye, J.C.: Zegot: Zero-shot segmentation through optimal trans- port of text prompts. arXiv preprint arXiv:2301.12171 (2023)

2023 arXiv
[19]

In: Proceedings of the IEEE/CVF conference on computer vision and pattern recognition

Li, C.L., Sohn, K., Yoon, J., Pfister, T.: Cutpaste: Self-supervised learning for anomaly detection and localization. In: Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. pp. 9664–9674 (2021)

2021
[20]

arXiv preprint arXiv:2402.02653 (2024)

Lu, H., Gong, D., Wang, S., Xue, J., Yao, L., Moore, K.: Learning with mixture of prototypes for out-of-distribution detection. arXiv preprint arXiv:2402.02653 (2024)

2024 arXiv
[21]

Advances in Neural Information Processing Systems36, 17602–17622 (2023) 16 R

Lu, Y., Qin, Y., Zhai, R., Shen, A., Chen, K., Wang, Z., Kolouri, S., Stepputtis, S., Campbell, J., Sycara, K.: Characterizing out-of-distribution error via optimal transport. Advances in Neural Information Processing Systems36, 17602–17622 (2023) 16 R. Trombetta et al

2023
[22]

ArXiv e-prints (2018)

McInnes, L., Healy, J., Melville, J.: UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction. ArXiv e-prints (2018)

2018
[23]

In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition

Park, H., Noh, J., Ham, B.: Learning memory-guided normality for anomaly de- tection. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. pp. 14372–14381 (2020)

2020
[24]

In: International conference on machine learning

Peyré, G., Cuturi, M., Solomon, J.: Gromov-wasserstein averaging of kernel and distance matrices. In: International conference on machine learning. pp. 2664–2672. PMLR (2016)

2016
[25]

In: Proceedings of the IEEE/CVF conference on computer vision and pattern recognition

Roth, K., Pemula, L., Zepeda, J., Schölkopf, B., Brox, T., Gehler, P.: Towards total recall in industrial anomaly detection. In: Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. pp. 14318–14328 (2022)

2022
[26]

In: Proceedings of the 35th International Conference on Machine Learning

Ruff, L., Vandermeulen, R.A., Görnitz, N., Deecke, L., Siddiqui, S.A., Binder, A., Müller, E., Kloft, M.: Deep one-class classification. In: Proceedings of the 35th International Conference on Machine Learning. vol. 80, pp. 4393–4402 (2018)

2018
[27]

Schlegl,T.,Seeböck,P.,Waldstein,S.M.,Langs,G.,Schmidt-Erfurth,U.:f-anogan: Fastunsupervisedanomalydetectionwithgenerativeadversarialnetworks.Medical image analysis 54, 30–44 (2019)

2019
[28]

In: European Conference on Com- puter Vision

Schlüter, H.M., Tan, J., Hou, B., Kainz, B.: Natural synthetic anomalies for self- supervised anomaly detection and localization. In: European Conference on Com- puter Vision. pp. 474–489. Springer (2022)

2022
[29]

IEEE Transactions on Industrial Informatics 19(7), 8072–8082 (2023)

Shan, D., Zhang, Y., Coleman, S., Kerr, D., Liu, S., Hu, Z.: Unseen-material few-shot defect segmentation with optimal bilateral feature transport network. IEEE Transactions on Industrial Informatics 19(7), 8072–8082 (2023). https: //doi.org/10.1109/TII.2022.3216900

2023
[30]

Ad- vances in neural information processing systems30 (2017)

Snell, J., Swersky, K., Zemel, R.: Prototypical networks for few-shot learning. Ad- vances in neural information processing systems30 (2017)

2017
[31]

Machine learning 54, 45–66 (2004)

Tax, D.M., Duin, R.P.: Support vector data description. Machine learning 54, 45–66 (2004)

2004
[32]

Advances in neural information processing systems35, 21792–21804 (2022)

Thual, A., Tran, Q.H., Zemskova, T., Courty, N., Flamary, R., Dehaene, S., Thirion, B.: Aligning individual brains with fused unbalanced gromov wasserstein. Advances in neural information processing systems35, 21792–21804 (2022)

2022
[33]

Tian, L., Li, Y., Dai, Y., Chen, W., Liu, X., Chen, B.: Fastref:fast prototype refinement for few-shot industrial anomaly detection (2025),https://arxiv.org/ abs/2506.21398

2025 arXiv
[34]

Advances in neural information processing systems30 (2017)

Van Den Oord, A., Vinyals, O., et al.: Neural discrete representation learning. Advances in neural information processing systems30 (2017)

2017
[35]

In: Proceedings of the 36th International Conference on Machine Learning

Vayer, T., Courty, N., Tavenard, R., Laetitia, C., Flamary, R.: Optimal trans- port for structured data with application on graphs. In: Proceedings of the 36th International Conference on Machine Learning. vol. 97, pp. 6275–6284 (2019)

2019
[36]

Advances in Neural Infor- mation Processing Systems35, 11800–11814 (2022)

Vincent-Cuaz, C., Flamary, R., Corneli, M., Vayer, T., Courty, N.: Template based graph neural network with optimal transport distances. Advances in Neural Infor- mation Processing Systems35, 11800–11814 (2022)

2022
[37]

arXiv preprint arXiv:2103.04257 (2021)

Wang, G., Han, S., Ding, E., Huang, D.: Student-teacher feature pyramid matching for anomaly detection. arXiv preprint arXiv:2103.04257 (2021)

2021 arXiv
[38]

IEEE Transac- tions on Cybernetics54(5), 2720–2733 (2024)

Xie, G., Wang, J., Liu, J., Lyu, J., Liu, Y., Wang, C., Zheng, F., Jin, Y.: Im-iad: Industrial image anomaly detection benchmark in manufacturing. IEEE Transac- tions on Cybernetics54(5), 2720–2733 (2024)

2024
[39]

In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition

Xu, M., Gould, S.: Temporally consistent unbalanced optimal transport for un- supervised action segmentation. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. pp. 14618–14627 (2024) Prototype-based anomaly detection with optimal transport 17

2024
[40]

In: Proceedings of the IEEE/CVF international conference on computer vision

Xu, Y., Chen, H.: Multimodal optimal transport-based co-attention transformer with global structure consistency for survival prediction. In: Proceedings of the IEEE/CVF international conference on computer vision. pp. 21241–21251 (2023)

2023
[41]

In: Proceedings of the AAAI conference on artificial intelligence

Yan, X., Zhang, H., Xu, X., Hu, X., Heng, P.A.: Learning semantic context from normal samples for unsupervised anomaly detection. In: Proceedings of the AAAI conference on artificial intelligence. vol. 35, pp. 3110–3118 (2021)

2021
[42]

In: European Conference on Computer Vision

Yao, H., Liu, M., Yin, Z., Yan, Z., Hong, X., Zuo, W.: Glad: towards better recon- struction with global and local adaptive diffusion models for unsupervised anomaly detection. In: European Conference on Computer Vision. pp. 1–17. Springer (2024)

2024
[43]

In: Proceedings of the Asian conference on computer vision (2020)

Yi, J., Yoon, S.: Patch svdd: Patch-level svdd for anomaly detection and segmen- tation. In: Proceedings of the Asian conference on computer vision (2020)

2020
[44]

arXiv preprint arXiv:2111.07677 (2021)

Yu, J., Zheng, Y., Wang, X., Li, W., Wu, Y., Zhao, R., Wu, L.: Fastflow: Unsuper- vised anomaly detection and localization via 2d normalizing flows. arXiv preprint arXiv:2111.07677 (2021)

2021 arXiv
[45]

In: Proceedings of the IEEE/CVF international conference on computer vision

Zavrtanik, V., Kristan, M., Skočaj, D.: Draem-a discriminatively trained re- construction embedding for surface anomaly detection. In: Proceedings of the IEEE/CVF international conference on computer vision. pp. 8330–8339 (2021)

2021
[46]

Pattern Recognition112, 107706 (2021)

Zavrtanik, V., Kristan, M., Skočaj, D.: Reconstruction by inpainting for visual anomaly detection. Pattern Recognition112, 107706 (2021)

2021
[47]

In: Proceedings of the IEEE/CVF Winter Conference on Ap- plications of Computer Vision

Zhang, J., Suganuma, M., Okatani, T.: Contextual affinity distillation for image anomaly detection. In: Proceedings of the IEEE/CVF Winter Conference on Ap- plications of Computer Vision. pp. 149–158 (2024)

2024
[48]

In: Proceedings of the IEEE/CVF conference on computer vision and pattern recognition

Zhou, T., Wang, W., Konukoglu, E., Van Gool, L.: Rethinking semantic segmenta- tion: A prototype view. In: Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. pp. 2582–2593 (2022)

2022
[49]

IEEE Transactions on Neural Net- works and Learning Systems (2024) 18 R

Zhou, Y., Xu, X., Song, J., Shen, F., Shen, H.T.: Msflow: Multiscale flow-based framework for unsupervised anomaly detection. IEEE Transactions on Neural Net- works and Learning Systems (2024) 18 R. Trombetta et al. A Additional results T able 3. Results of our method compared...

2024

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [1]

International Journal of Computer Vision130(4), 947–969 (2022)

Bergmann,P.,Batzner,K.,Fauser,M.,Sattlegger,D.,Steger,C.:Beyonddentsand scratches: Logical constraints in unsupervised anomaly detection and localization. International Journal of Computer Vision130(4), 947–969 (2022)

2022

[2] [2]

In: 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

Bergmann, P., Fauser, M., Sattlegger, D., Steger, C.: Mvtec ad — a comprehen- sive real-world dataset for unsupervised anomaly detection. In: 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). pp. 9584–9592 (2019)

work page 2019

[3] [3]

International Conference on Learning Repre- sentations (2019)

Brendel, W., Bethge, M.: Approximating cnns with bag-of-local-features models works surprisingly well on imagenet. International Conference on Learning Repre- sentations (2019)

work page 2019

[4] [4]

Advances in neural information processing systems 35, 39090–39102 (2022) Prototype-based anomaly detection with optimal transport 15

Cao, Z., Xu, Q., Yang, Z., He, Y., Cao, X., Huang, Q.: Otkge: Multi-modal knowl- edge graph embeddings via optimal transport. Advances in neural information processing systems 35, 39090–39102 (2022) Prototype-based anomaly detection with optimal transport 15

work page 2022

[5] [5]

Advances in neural information processing systems33, 9912–9924 (2020)

Caron, M., Misra, I., Mairal, J., Goyal, P., Bojanowski, P., Joulin, A.: Unsupervised learning of visual features by contrasting cluster assignments. Advances in neural information processing systems33, 9912–9924 (2020)

2020

[6] [6]

arXiv preprint arXiv:2005.02357 (2020)

Cohen, N., Hoshen, Y.: Sub-image anomaly detection with deep pyramid corre- spondences. arXiv preprint arXiv:2005.02357 (2020)

arXiv 2020

[7] [7]

Courty, N., Flamary, R., Tuia, D., Rakotomamonjy, A.: Optimal transport for domainadaptation.IEEEtransactionsonpatternanalysisandmachineintelligence 39(9), 1853–1865 (2016)

2016

[8] [8]

In: Advances in Neural Information Processing Systems

Cuturi, M.: Sinkhorn distances: Lightspeed computation of optimal transport. In: Advances in Neural Information Processing Systems. vol. 26 (2013)

work page 2013