SoftPatch: Unsupervised Anomaly Detection with Noisy Data
Authors: Jiang Xi
Jianlin Liu
Jinbao Wang
Qiang Nie
Kai WU
Yong Liu
Chengjie Wang
Feng Zheng
Venue: NeurIPS 2022 Accept (2022)
Keywords: Anomaly Detection
Noisy Label
Outlier Detection

Abstract: Although mainstream unsupervised anomaly detection (AD) algorithms perform well in academic datasets, their performance is limited in practical application due to the ideal experimental setting of clean training data. Training with noisy data is an inevitable problem in real-world anomaly detection but is seldom discussed. This paper considers label-level noise in image sensory anomaly detection for the first time. To solve this problem, we proposed a memory-based unsupervised AD method, SoftPatch, which efficiently denoises the data at the patch level. Noise discriminators are utilized to generate outlier scores for patch-level noise elimination before coreset construction. The scores are then stored in the memory bank to soften the anomaly detection boundary. Compared with existing methods, SoftPatch maintains a strong modeling ability of normal data and alleviates the overconfidence problem in coreset. Comprehensive experiments in various noise scenes demonstrate that SoftPatch outperforms the state-of-the-art AD methods on the MVTecAD and BTAD benchmarks and is comparable to those methods under the setting without noise.

SoftPatch: Unsupervised Anomaly Detection with Noisy Data
Xi Jiang'
Jianlin Liu? jemiingllu@tennenttcom com
1ia.xx20200mail...mmmmmmmmmm www.:/2200mmal.sstttehh....c sustech. edu. cn
Jinbao Wang**
Qian Nie
Kai Wu²
wangjbosustecchco edu. cn
stephenmie@tencent.co com
1loydru@tencent.com com
Yong Liu? choasliu@tencent.com com
Chengjie Wang" j jasoucjvangdtencent.
Feng Zheng"*
2hengfosustech. edu,
Southern University of Science and Technology. Department of Computer Science and Engineering Tencent,, Youtu Lab
Abstract
Although mainstream unsupervised anomaly detection (AD) algorithms perform well in academic datasets, their performance is limited in practical application due the ideal experimental setting of clean training data. Training with noisy data is inevitable problem in real-world anomaly detection but is seldom discussed. This paper considers label-level noise in image sensory anomaly detection for the first time. To solve this problem, we proposed a memory-based unsupervised AD method, SoftPatch, which efficiently denoises the data at the patch level. Noise discriminators elimination before coreset construction. The scores are then stored the memory bank soften the anomaly detection boundary. Compared with existing methods, SoftPatch maintains a strong modeling ability of normal data and alleviates the overconfidence problem in coreset. Comprehensive experiments in various noise scenes demonstrate that SoftPatch outperforms the state-of-thh-arr AD methods on the MVTecAD and BTAD benchmarks and is comparable those methods under the setting without noise.
utilized to generate outlier scores for patch-level noise
Introduction
Detecting anomalies by only nominal images without annotation is an appealing topic, especially in industrial applications where defects be extremely tiny and hard collect. Unsupervised sensory anomaly detection, also called covariate shift detection [[] 2], is proposed to solve this problem
and has been largely explored. Recent deep learning methods B problem as a one-class learning problem and employ computer visual tricks to improve the perception where clean nominal training set is provided to extract representative features. Most previous unsupervised AD methods have to measure the distance between the test sample and the standard dataset distribution determine whether sample differs from the standard dataset. Even though recent methods have achieved excellent performance, they all rely on the clean training set to extract
5
6 7 usually model the AD
"Corresponding Author
36th Conference on Neural Information Processing Systems (NcurIPS 2022).

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nominal features for later comparison with anomalous features. Putting too much faith in training data can lead to pitfalls. If the standard normal dataset is polluted with noisy data, i.e. the defective samples, the estimated boundary will be unreliable, and the classification for abnormal data will have low accuracy. In general, current unsupervised AD methods are not designed for and are not robust to noisy data.
However, in real-world practice, is inevitable that there are noises that sneak into the standard normal dataset, especially for industrial manufacturing, where a large number of products are produced daily, This noise usually comes from the inherent data shift or human misjudgment. Meanwhile, existing unsupervised AD methods 88 9 I0 are susceptible to noisy data due to their exhaustive strategy to model the training set. As Fig. I noisy samples easily misinform those overconfident AD algorithms, so algorithms misclassify similar anomaly samples in the test set and generate wrong locations. Additionally, AD with noisy data can be developed to a fully unsupervised setting, which discards the implicit supervised signal that the training set is all defect-free, compared with the previous unsupervised setting in AD. This setting helps to expand more industrial quality inspection scenarios, i.e., rapid deployment to new production lines without data filtration.
In this paper, we first point out the significance of studying noisy data problems in AD and especially in unsupervised sensory AD. Our solution is inspired by one of the recent state-of-the-ar methods, PatchCore 88. PatchCore proposed a method to subsample the original CNN features of the standard normal dataset with the nearest searching and establish a smaller coreset as a memory bank. However, the coreset selection and classification process are vulnerable polluted data. In this regard, we propose patch-level selection strategy to wipe off the noisy image patch of noisy samples. Compared to conventional sample-level denoising, the abnormal patches are separated, and the normal patches of a noise sample are exploited in coreset. Specifically, the denoising algorithm assigns an outlier factor to each patch to be selected into coreset. Based on the patch-level denoising, we propose a novel AD algorithm with better noise robustness named SoftPatch. Considering noisy samples are hard to be removed completely, SoftPatch utilizes the outlier factor to re-weight the coreset examples. Patch-level denoising and re-weighting the coreset samples are proved effective in revising misaligned knowledge and alleviating the overconfidence of coreset in inference. Extensive experiments in various noise scenes demonstrate that SoftPatch outperforms the of-te-of-thh-at (SOTA) AD methods on MVTec Anomaly Detection (MVTecAD) [T] benchmark. Mcanwhile, due to the noise in existing datasets, SoftPatch achieves optimal results the original BTAD [12] dataset. The code can be found in bestts://githae cow/Tencent conn//enceenYYuuuueeeaaaaaa YoutuResearch /outulaaaarrrcccoooaaaaeleeeeeee
Our main contributions are summarized as follows:
To the best of our knowledge, we are the first to focus on the image sensory anomaly detection with noisy data, which is a more practical setting but seldom investigated. Existing image sensory AD methods fully trust the training set's cleanliness, leading to their performance degradation in noise interference.
We propose a patch-level denoising strategy for coreset memory bank, which essentially improves the data usage rate compared to conventional sample-level denoising. Based on this strategy, we apply three noise discriminators which strengthen model robustness by combining the re-weighting of coreset.
We set a baseline for unsupervised AD with noisy data, which performs well in the settings with additional noisy data and the general settings without noise, providing a new view for further research.
2 Related Work
2.1 Unsupervised Anomaly Detection
Training with agent tasks. Also known as self-supervised learning, agent tasks is a viable solution when there is no category and shape information of anomalies. Sheynin et al. [13] employ transfor- mations such as horizontal flip, shift, rotation, and gray-scale change after a multi-scale generative model to enhance the representation learning. Li et al. [14] mention that naively applying existing self-supervised tasks sub-optimal for detecting local defects and propose novelty agent task named
CutPaste, which simulates an abnormal sample by clipping a patch of standard image and pasting
2

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Train Set
Feature Extraction
Coresct Construction
Inference
Test
Previons
SoftPPtch (Ours)
soft outlier ro-weighting
Noiey Datt
Re-weighting Factor (douper volor means higher nominal probubility)
Nominal Feature
Hard Anomalous Feature
Easy Anomalous Feature
D> Removed Anomalous Feature
Figure 1: Illustration of SoftPatch. Unlike previous methods that construct coreset without considering the negative effect of noisy data, SoftPatch wipes off easy noisy data to formulate clean training set and alleviates hard noisy data's ss impact by soft-reweighting.
it back at a random location. Similarity, DRAEM 15 synthesizes anomalies through Perlin Noise. Nevertheless, the inevitable discrepancy between the synthetic anomaly and the real anomaly disturbs the criteria of the model and limits the generalization performance. The gap between anomalies is usually larger than that between anomaly and normal. This why AD methods deceived by some noisy samples can still work well when handling other kinds of anomalies.
Agnostic methods. Including knowledge distillation and image reconstruction, agnostic methods based on theory that models that have never seen anomalies will behave differently in inference when inputting both normal and anomaly samples. Knowledge distillation ingeniously used in anomaly detection. Bergmann et al. [16] propose that the representations of unusual patches are different between a pretrained teacher model and student model, which tried its best to simulate teacher output with an anomaly-free training set. Based on this theory, Salehi et al. [17] propose that considering multiple intermediate outputs distillation and using a smaller student network lead to better result. Reverse distillation [18] uses reverse flow that avoids the confusion caused by
the same filters and prevents the propagation of anomaly perturbation to the student model, whose structure is similar to reconstruction networks. Image Reconstruction methods 77 19 20 utilize the assumption that the reconstruction network trained in the normal set can not reconstruct the anomaly part. A high-resolution result can be obtained by comparing the differences between the reconstructed and original images. However, all agnostic methods need long training stages, which limit their usage, ie., the rapid deployment assumption in fully unsupervised learning.
Feature modeling. We specifically refer to the direct modeling of the output features of the extractor, including distribution estimation [21 [22 distribution transformation 23 pre-trained model adap- tion (24 25), and memory storage 26 g PaDiM (2 utilizes multivariate Gaussian distributions to
estimate the patch embedding of nominal data. In the inference stage, the embedding of irregular patches will be out distribution.
a simple but efficient method, but Gaussian distribution is inadequate for more complex data cases. So to enhance the estimation of density, DifferNet (23 and CFLOW [ leverage the reversible normalizing flows based on multi-scale representation. Hou et al.
26 proposed that the granularity of division feature maps is closely related the reconstruction capability of the model for both normal and abnormal samples. So a multi-scale bock-wiss memory bank is embedded into autoencoder network model of past data. PatchCore [8] is more explicit but valuable memory- based method, which stores the sub- sampled patch features in the memory bank and calculates the nearest neighbor distance between the test feature and the coreset as an anomaly score. Although PatchCore is outperformance in the typical setting, it is overconfident in the training set, which leads poor noise robustness.
2.2 Learning with Noisy Data
Noisy label recognition is becoming an emerging topic for supervised learning but has rarely been explored in unsupervised anomaly detection because there is no apparent label. For classification, some research 22 28 propose to filter noisy pseudo-labeled data with high confidence threshold. Li et al.
29 selects labseld data with mixture model and trains in a semi-supervised manner.
3

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rnioo dectiokotioe
Feature Grouping
Pauh fasuurcs
bt Xw"
Prversiaed Beckiooe
Randon Projections
positions
diectmntnater
MXCKHKW
Anorall Score and Anomaly Map
Testing
Coreset Selection
Memory Bank
Denoising
Soft Weights
NKh
sumple
Mearest Neighber Seurch
Sampling
Top 1% removed
Coreset
0
CKHKW
Figure 2: Overview of the proposed method. the training phase, the noises are distinguished at patch level at each position of the feature map by a noise discriminator, The deeper color patch node has, the higher probability that it is noise patch. After achieving outlier scores for all patches, the top 7% patches with the highest outlier score are removed. The coreset is subset of remaining patches after denoising. Different from other methods, our memory bank consists of the samples in coresct and their outlier scores which are stored soft weights. Soft weights will be further utilized to re-weight the anomaly score inference.
Kong et al. relabel harmful training samples. For object detection, multi auttiiatugmnttiioonn [ teacher-student 32, contrastive learning [3] are adopted to alleviate noise with the help of the expert model's knowledge. However, current noisy label recognition methods all rely on labeled data to co-rectify noisy data. In comparison, target improve the model's 's noise robustness in an unsupervised manner without introducing labor annotations.
While there are some model robustness researches on unsupervised AD, their objects and tasks are distinguished from our work since "anomaly detection" an overloaded term. A recent survey [34] explores the model robustness of 30 AD algorithms. Nevertheless, unsupervised methods are excluded from the annotation errors setting. Pang et al. [35 deals with video anomaly without manually labeled data where information in consecutive frames can be exploited. While our work tackle eliminate noisy and corrupted data in semantic anomaly detection. Unlike semantic anomaly detection, we focus on image sensory anomaly detection [I], which has recently raised much concern and contains new task, anomaly localization. Although some existing methods 33
anomaly detection from single image. Other related papers [36] 37
38
41 42] treat covariate shift same way they treat semantic shift and enhance model robustness with universal processes, their basic structures poor compared with rapid-developed sensory AD methods, which leads to the robustness improvement insignificant. Noise in image sensory anomaly detection is more similar to the normal data and brings more challenges.
40
The Proposed Method
3.1 Overview
Patch-based unsupervised anomaly methods, such as PatchCore and CFA main processes: feature extraction, coreset selection with memory bank construction, and anomaly detection. One of the important assumptions that training set only contains nominal images, and the coreset should have full coverage of the entire training data distribution. During the test, an incoming image will directly search in the memory bank for similar features, and the anomaly score is the dissimilarity with the nearest patches. The searching process may collapse if the assumed
25 have three

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clean full coverage memory bank contains noise. Therefore, we propose SoftPatch, which filters noisy data by a noise discriminator before coreset construction and softens the searching process for down-weighting the hard unfiltered noisy samples.
The general denoising methods against the label contamination at the sample level are sub-optimal in image sensory anomaly detection. The abnormalities in image sensory AD, represented by industrial defect detection and medical image analysis, usually occupy only a tiny area of the image. At the sample level, noisy data is hard to distinguish, but the sample's ' inherent deviation may be more remarkable. So we propose a patch-level denoising strategy that works on the feature space to judge the noisy patch better. First, the collected features are grouped according to position to narrow the domain of noise discrimination. Then we insert the patch-level noise discrimination process before the coreset sampling, which generates the noise score according to the feature distribution of each position. Since most areas of the noisy image are usually anomaly-free, we remove those noisy patches and retain the rest to maximize the use of data. At the same time, the rest denoising scores reflecting the behavior of clustering are used to scale the anomaly score in inference. The other parts of the algorithm, such feature extraction, dimension reduction, coreset sampling, and nearest neighbor search, follow the baseline PatchCore(81 Figure shows the framework of SoftPatch.
The target of image-level denoising is to find Xnoise from X, where X' = {a, i E [1,N], E RCx HxW) denotes training images (channels C, height H, width W). Following convention in existing work[8] we use dy E [R xh" xw" as the feature map (channels c*, height h*, width w*) of image vi E X, db, w) Re the patch (h, w) on the aggregated feature map with dimension c.
3.2 Noise Discriminative Coreset Selection
With increasing training images, the features memory can become exceedingly large and infeasible to discriminate noise by overall statistics. Therefore, we group all features by position and count their outlier scores. Then all the scores are aggregated to determine noise patches, after which we just remove the features with top 7 percent scores. We apply three noise reduction methods in total.
3.2.1 Nearest Neighbor
With the assumption that the amount of noisy samples Xnoise is much less than clean samples Xnominal, we set Nearest neighbor distance as our baseline [43] where large distance means an outlier. Given a set of images,
RNNxe x xw"" represents all features. Each patch's 's nearest neighbor distance Win is defined as:
Waa (h, w)
min |1 w) (n,,, w)122 nE(L.M],nst
We first calculate the distances, then take the minimum among batch dimensions (neighbor) as W Previous methods 8 25 have proved that the minimum feature distance from pretrained network can be an indicator to discriminate anomaly. This method can discriminate apparent outliers but suffer from uneven distribution of different clusters, where some clusters can have large inter-distance and lead to being mistakenly threshed as noisy data. To treat all clusters equally, we propose another multi-variate Gaussian method calculate the outlier score without the interference of different clusters' densities.
3.2.2 Variate Gaussian
With Gaussian's ' normalizing effect, all clean images' features can be treated equally. To apply Gaussian distribution on image characteristics dynamically, we calculate the inlier probabilities on the batch dimension for each patch (h, w). similar to 3.2.1 The multi-variate Gaussian distribution Nw ) can be formulated that Ns, the batch mean of di w) and sample covariance Dn,w is:
N Σ ())(h, - (o. w) - (n,w)) + el, n=1
where the regularization term el makes En. full rank and invertible (21) Finally, with the estimated multi-variate Gaussian distribution N (ph,wr En.w)) Notice that we do not exclude the z; when
5

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calculating the .N, so all samples can share joint distribution, which is much less computationally intensive than doing the calculations one by one. Mahalanobis distance calculated as the noisy magnitude Win (h, w) of each patch:
W (h, v (oi(h, w) - ((h, of (0,, w) - P(h,ar))
high Mahalanobis distance means a high outlier score. Even though Gaussian distribution normal- izes and captures the essence of image characteristics, small feature clusters may be overwhelmed by large feature clusters. In the scenario of a prominent feature cluster and small cluster in a batch, the small cluster may be out of 1-, 2- or 3-Σ of calculated N(un,w> En.w w and erroneously classified as outliers. After analyzing the above two methods, we need method that can: 1. treat all image characteristics equally; 2. treat large and small clusters equally: 3. high dimension calculation applicable.
3.2.3 Local Outlier Factor (LOF)
[4 is local-density-
outlier detector used mainly on E-commerce for criminal activity
detection. Inspired by LOF, we can solve above mentioned three questions in 3.2.2 1. Calculating the relative density of each cluster can normalize different density clusters; 2. Using local k-distance
as metric to alleviate the overwhelming effect of large clusters; 3. Modeling distance as normalized
feature distance can be used on high-dimensional patch features. Therefore, the k-distance-based absolute local reachability density Ird,(h, w) is first calculated as:
Ird,(h, w) = 1/( (hena) distr (Ø: w), @s w))
()((,,)))
(4)
(h),
distfeach (0:(h, w), ds,h,, w)) mar(dista (0n w)), d(øs (h, w),, where d(o:(h, w), (h, w)) is L2-norm, dist, (h, w)) is the distance of kth-neighbor, (o. (h, w)) is the set of k-nearest neighbors of (h, w) and (o, w))l is the number of the set which usually equal k when without repeated neighbors. With the local reachability density of each patch, the overwhelming effect of large clusters is largely reduced. To normalize local density to relative density for treating all clusters equally, the relative density WoLOF of image is defined below:
(5)
WLOF (h, w) EveNi(onth.n) Irdo((h, w))
(6)
[Wa(os(h, w))l Ird,(h, w)
WLOF (h, w) is the relative density of the neighbors over patch's 's own, and represents patch's confidence of inlier. Our experiments found that all three noise reduction methods above are helpful in data pre-selection before coreset construction, while LOF provides the best performance. However, after visualization of our cleaned training set, we found that hard noisy samples, which are similar to nominal samples, still hidden in the dataset. To further alleviate the effect of noisy data, propose a soft re-ihighting method that can down-weight noisy samples according to outlier scores.
3.3 Anomaly Detection based on SoftPatch
Besides the construction of the Coreset, outlier factors of all the selected patches are stored as soft weights in the memory bank. With the denoised patch-level memory bank A as shown figure the image-level anomaly score E IR can be calculated for test sample z; E eestt by nearest neighbor searching at patch level. Denoting the collection of patch features of a test sample as P(x;). for cach patch Ph, E Pa, the nearest neighbor searching can be formulated as the following equation:
m
arg min ||p ml|2- MEM
After nearest searching, pairs of test patch and its corresponding nearest neighbor in M can be achieved as (p, m²). ). For each patch pi.j E Pa,, the patch-level anomaly score is calculated by
sh.w
Wm llp,,
m m
(8)
where Wm- is the soft weight calculated by one noise discriminator. The image-level anomaly score is attained by finding the largest soft weights re- weightdt patch-level anomaly score: s max 8h,
(h,w)

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Table I: Anomaly detection performance on MVTecAD with noise. The results are evaluated on MVTecAD-noise-O.. Overlap means the injected anomalous images are included in the test set. PaDiM* uses & as the backbone. PatchCore-randon uses 1 1 random subsampler instead of the default greedy subsampler. Gap row shows the performance gap between a noisy scene and a normal scene.
Noise=U.1
No overlap
Overlap
SoftPatch- neurest
SoftPatch- gaussian
SoftPatch- lof
PatchCorc- random
SoftPatch- lof
Category
CFLOW
PatchCore
PaDiM
PatchCore
bottle
0.994
0
1.000
1.000
0.997
0.937
1,000
0.692
0.998
1.000
cable
0.982
0.952
0.995
0.680
0.756
0.920
capsule
0,920
0.947
0.976
0.916
0.662
0.963
0.796
0.783
0.779
0.955
carpet
0.999
0
0,996
0.995
0.999
0.991
0.890
0.681
0.973
0.993
grid
0.966
0.891
0.971
0.972
0.997
0.968
0.674
0.526
0.793
0.969
bazclout
0.956
1.000
0.998
1,000
1.000
1.000
0.543
0.441
0.998
1.000
leather
1.000
1,000
0.739
metal_nu nut
0.987
0.959
0.999
0.994
0.997
0.999
0.820
0.765
0.969
1,000
pill
0.918
0.929
0.975
0.921
0.873
0.963
0.722
0.770
0.874
0,955
screw
0.838
0,784
0.966
0.862
0.475
0,960
0.567
0.710
0,462
0,923
tile
0.977
0.991
0.985
0.996
0.997
0.993
0.830
0.716
1,000
0.981
toothbrush
0.927
0.906
0.997
1,000
0.997
0.997
0.700
0.800
0.797
0,994
transistor
0,953
0.896
0.953
1,000
0.992
0.990
0.471
0.491
0.943
0.999
wood
0,991
0.984
0.997
0.987
0.579
0,980
zipper
0.852
0,928
0.981
0.976
0.979
0.978
0.679
0.792
0,950
0.974
Average
0.943
0,939
0.984
0.970
0.927
0.986
0.740
0.683
0.896
0,982
Gap
-0.007
-0.03
-0.008
+0.002
-0.001
0.0
-0.151
-0,309
-0.015
-0.004
Different from PatchCore which directly considers patches equally, SoftPatch softens anomaly scores by noise level from noise discriminater. The soft weights, i.c., local outlier factors, have considered the local relationship around the nearest node. Thus, a similar effect can be achieved as PatchCore but with more noise robustness and fewer searches. According to the image-level anomaly score, sample is classified into a normal sample or an abnormal sample.
4 Experiments
4.1 Experimental Details
Our experiments are mainly conducted on the MVTecAD and BTAD benchmarks 11 12 MVTecAD contains 15 categories with 3629 training images and 1725 test images in total, and BTAD has three categories with 1799 images, where different classes of industry production mean comprehensive challenge, such object or texture and whether rotation. Since each category of MVTecAD is divided into nominal-only images and test set with both nominal and anomalous samples, create a noisy training set, we sample anomalous images randomly from the test set and mix them with the existing training images. Notice that the original normal number of samples in the training set remains unchanged compared with the noiseless case. In this setting(No overlap). the injected anomalous samples will not be evaluated, which is more likely the case in the real application. We also construct a different setting Overlap) where the injected anomalous samples are also in the test set to demonstrate the risk that defects with similar appearance will severely exacerbate the performance of an anomaly detector trained with noisy data. Meanwhile, the overlap samples test the outlier detection performance of our algorithm. By controlling the proportion of negative samples being injected into the train set, we obtain several new datasets with different noise ratios dubbed MVTecAD-noise-Tn, where n refers to the ratio of noise. For BTAD, we just use the original fold.
Datasets.
Evaluation Metrics. We report both image-level and pixel-level AUROC for each category in MVTecAD and average them to get the average image/pixel level AUROC. In order to represent noise robustness, the performance gaps between noise-free data and noisy data are also displayed. When not otherwise stated, our method SoftPatch refers to SoftPatch-LOF that uses LOF in Section 3.2.3
Implementation Details. We test three SOTA AD algorithms, PatchCore 8 PaDim 21 and CFLOW 9 in noise scene and follow their main settings. In the absence of specific instructions, the backbone of the feature extractor Wide-ResNet50, and the coreset sampling ratio of PatchCore and SoftPatch is 10%. For MVTecAD images, we only use 256 x 256 resolution and center crops
7

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Table 2: Anomaly localization performance on MVTecAD with noise. The results are evaluated on MVTecAD-noise-O.I.
Noise=0.1
No overlap
Overlop
SoftPatch- nearest
SoftPatch. gaussian
PaftPa lof
ParchCore. random
SoftPatch- lof
Category
PaDiM
CFLOW
PatchCCore
PaDiM
PatchCore
Average
0,972
0.969
0.956
0.971 -0.008
0.977
0.979
0,955
0.654
0.951
0,969
Cup
-0.077
-0,006
-0.025
-0.001
-0.002
-0.013
-0.327
-0,021
-0.012
Table 3: Anomaly detection performance on BTAD without additional noise. The best results are in bold, and the second-best results are underlined. The last column lists the count of anomaly samples in the test set.
Category
SPADE
P-SVDD
PatchCore
PaDiM
SoftPatch(ours)
Anomaly samples
01
0.914
0.957
1.000
1.000
0,999
50
02
0.714
0.721
0,871
0.871
0.934
200
03
0.999
0.821
0.999
0.971
0.997
41
Mean
0.876
0.833
0.957
0.947
0.977
them into 224 x 224 along with a normalization. For BTAD, we use 512 512 resolution. We train a separate model for each class. Notice that unlike many methods setting the hyperparameters according to the noise ratio, which is unknowable in reality, we the threshold in SoftPatch and the LOF-K to constant 0.15 and for all noisy scenarios and classes. The effects of hyperparameters studied in the ablation study. All our experiments are run Nvidia V100 GPU and repeated three times to report the average results.
4.2 Anomaly Detection Performance with Noise
Experiments on MVTecAD. As indicated in Table and Table 2 when 10% of anomalous samples are added corrupt the train set, all existing methods have different extents of performance decrease, although not disastrously in No overlap setting. Compared to other methods, the proposed SoftPatch exhibits much stronger robustness against noisy data both in terms of anomaly detection and localiza- tion, no matter which noise discriminator is used. Among three variants of SoftPatch, SoftPatch-loff achieves the best overall performance with the highest accuracy and strongest robustness. Interest- ingly, [2DiM[1]. CFLOW and SoftPatch-gaus gaussian show significantly less performance drop than PatchCore, which indicates that modeling feature as Gaussian distribution does help denoising. While modeling feature distribution at each spatial location as a single Gaussian distribution can't 't handle misaligned images, such as screw class in MVT which explains the poor performance on these classes(sce screw row). On the other hand, PatchCore's 's prredy-sampling strategy is double-edged sword with higher feature space coverage and higher sensitivity to noise. That's 's why using random sampling in PatchCore is more robust with compromised performance(see PatchCore 1%-Randow column). SoftPatch-neaat
does a slightly better job in the misaligned cases. However, it doesn't t take feature distribution into account, which leads to inferior performance.
Experiments on BTAD. We also compare SoftPatch with other SOTA methods on another dataset, BTAD. Surprisingly, SoftPatch gives out new SOTA result, even in the original setting that contains no additional noise (Table 3). By reviewing all the training samples, we find that there are already many noisy samples (usually small scratches) in the training set of category BTAD-02, which is more consistent with our setting and further demonstrates the necessity of our approach. The noisy images provided in Appendix A.6 (Table 8). Morcover, the BTAD-02 contains more anomaly samples with similar appearance anomalies. In the category of BTAD-02, our method attains significant improvement compared to others. SoftPatch can also maintain the leading performance if the noise is added antificiall((Appenni A.8).
Performance trends. In order to explore how different methods behave with the increasing noise level, experiments are further performed on MVTecAD-nnise--(0 ~ 0.15). The results of the proposed methods are provided in Figure 3 Under the No overlup setting, as the noise ratio increases, PatchCore shows pixel-level AUROC drop up to 3.7%. The performance decreases as the noise ratio rises. On the contrary, although the default performance is slightly poorer than PatchCore(about 0.006
8

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PatchCore
lof
nearest
gaussian
Image
Pixel level
Image lovel
Pixel
0.95
0.98
0.8
0.9
0.8
0.9
0.96
0.9
0.94
0.7
0.7
0.05
0.92
0.5
0
0.02
0.04
0.06
0.1
0.15
0.02 0.04 0.06 0.1 0.15
0.02 0.04 0.06 0.1 0.15
0.02 0.04 0.06 0.1 0.15
a) overlap
b) Overlap
Figure 3: The comparison of anomaly detection performance under noisy training. no overlap means the injected anomalous images are removed from test set while overlap are not.
and decrease in image-level and pixel-level AUROC), the proposed SoftPatch-lof deteriorates much slower, which demonstrates better denoising ability. As for SoftPatch-nearest and SoftPatch-gaussian, they also robust, however, with worse base performance(see Figure 3 at noise ratio=0). The visualization of the coreset in Figure[5Jalse shows that random sampling avoids sampling the outlier but can model normal adequately. Being consistent with the discussion above, under the Overlap setting, PatchCore's 's performance is getting worse and worse catastrophically(up to 40% AUROC drop both image and pixel level) as more noises are added. This is expectable since PatchCore uses greedy strategy for coreset sampling, which favors outliers in feature space. SoftPatch-lot consistently outperforms other methods with no significant performance drop as the noise level goes up. Appendix A.3] (Figure and shows more comparison with others. The experimental results indicate that the risk hidden by the fact that defects MVTecAD have very different appearances. In this case, even if some anomalous features are added mistakenly to the coreset, they are unlikely to be retrieved during test time. However, the risk still exists and will triggered when similar defects show up at test time.
More experiments can be found in appendix, such the comparison of image-level and patch- level denoising(Appent A.44, computational Analysis(Appendix A.5 and an augmented overlap Detting(Appendee (..pp.
Table 4: The ablation study of soft weight. The performance scores MVTecAD.
Image/pixxl- AUROC on
No overlap
Overlap
Noise discriminator
Soft weight
Image level
Pixel level
Image level
Pixel level
None
0.985
0,946
0.685
0.693
Gaussian
0.927
0.977
0,925
0.961
Gaussian
0,922
0.974
0.924
0.965
Nearest
0.970
0.971
0.966
0.944
Nearest
0.972
0.978
0.968
0.958
LOF
0,985
0.984
0,984
0,963
LOF
0.986
0.979
0,982
0.969
4.3 Ablation Study
4.3.1 Effectiveness of the Proposed Modules
We validated the effectiveness of two proposed modules noise discriminator and soft weight by removing them from the pipeline. As shown in Table 4 the noise discriminator significantly improves the noise robustness terms of pixel-level AUROC. Among three decision choices of noise discriminator, LOF achieved the best balance between robustness and capacity, resulting in the most performance boost under all settings. We further analyzed the intermediate results by visualizing the sampled coreset of different methods, which shows that SoftPatch-LOS sampled much fewer anomalous features than the baseline(see Figure Soft weight used alongside the noise discriminator to further improve the final results. We only observed minor improvement for using Soft weight in SoftPatch-Nearest. We suspect that the other two kinds of noise discriminators are already robust against noise data.

---

Table 5: Jmage/pixel--evell AUROC result for different LOF-K on two settings.
Overlap
0.983/0.955
0,982/0.
0.983/0.959
0.982/0.975 0,984/0.922
0.981A0.973
0.982/0. 968
0.980N0.965
No overlup
0.985/0.972
0.985/0.975
0 0.98410.777
0.985/0.908 980
01984/0.988.
0.981/0.982
Smaert ALTEX 100.
0.90
0:965
0.906
0:581
0:981
0.986
0.961
0.90
0.978
0.971
0.981
0.981
0.079
0.96
0.974
0.978
0.082
0,982
0L9813
0.96
0.969
0.969
0.733
0.94
(1945
0.94
6,048
0.92
0.92
0.9
0.9
0.80
Overlap
No overlap
0.88
0.88
Overlap overlap
0.86
0.86
0.01
(U95
11.00)
0.13
0.15
0.17
0.01
0.05
11,09
0L13
0.15
0.17
Threshold
Threshold
Figure 4: Performance trend with the threshold in SoftPatch-LOF. The results are evaluated on MVTecAD-noise-0.1
4.3.2 Parameter Selection
To explore the impact of two parameters (LOFF- and threshold r) the final performance, perform parameters searching on our method. As in Ta our method achieves better performance when LOF-K greater than 5, which suggests that our method not sensitive LOF-k, long as is not too small or too large. If LOF-k is too small, it fails to estimate the local density accurately because too few neighbors are considered. On the contrary, a large LOF-K may lead undesirable cross-clusters connection that can not capture real data distribution.
Threshold refers to the ratio of eliminated patch features when building coreset. Figure Liddicates an increasing trend of AUROC as threshold r increases under Overlap setting, which is expected since higher threshold means more aggressive denoising strategy. In Overlap setting, the mistakenly sampled features are the direct reason for the drastic performance drop. Therefore more aggressive denoising improves the result significantly. However, In No Overlap setting, the effect of the noisy feature is less prominent. Although the best LOF-k and threshold are changed according to the class and noise level, we simply use fixed values, and 0.15, in all situations.
Conclusions
This paper emphasizes the practical value of investigating noisy data problems in unsupervised AD, Introducing novel noisy setting the previous task, we test the performance of existing methods and SoftPatch. For existing methods, despite no adaptation to noisy settings, some them have slight performance decrease some scenes. However, the performance decrease could be more significant and catastrophic for other methods or in other scenes. For the proposed SoftPatch, it shows consistent performance in all noise settings, which outperforms other methods.
Industrial inspection systems are an important computer vision application that requires good ro- bustness. The noise injected into the training set break with the naive assumption that the training samples were normal. Noise also gives the model early exposure to the distribution of anomalies. The unsupervised AD with noisy data needs research in the future.
Acknowledgement
This work is supported by the National Natural Science Foundation of China under Grant No. 61972188, 62 22105335 and 62206122.
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Checklist
1. For all authors...
(a) Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope? [Yes]
(b) Did you describe the limitations of your work? [Yes] In the Experiments and Conclu- sions sections, we state that our method improve robustness at cost of slight performance decrease for some categories.
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13


Reviews:
[{"review_id": "wp0YpEvofBG", "reviewer": "Reviewer_MPDh", "summary": "The authors propose a robust unsupervised anomaly detection model, SoftCore, that explicitly detects outliers in the training data and selects an anomaly-free coreset as a memory bank. \nThis memory bank is used as a reference of normality to detect novel test anomalies. The training noise discriminator that detects training contamination is based on the well-known density-based method: LOF [1]. \nExperiments that are conducted on the MVTec dataset show that SoftCore outperforms some baselines.\n\n\nReferences: \n[1] Markus M Breunig, Hans-Peter Kriegel, Raymond T Ng, and Jörg Sander. Lof: identifying density-based local outliers. In Proceedings of the 2000 ACM SIGMOD international conference on Management of data, pages 93–104, 2000.\n\n[2] Gong, Dong, Lingqiao Liu, Vuong Le, Budhaditya Saha, Moussa Reda Mansour, Svetha Venkatesh and Anton van den Hengel. “Memorizing Normality to Detect Anomaly: Memory-Augmented Deep Autoencoder for Unsupervised Anomaly Detection.” 2019 IEEE/CVF International Conference on Computer Vision (ICCV) (2019): 1705-1714.\n\n[3] Liu, Tongliang and Dacheng Tao. “Classification with Noisy Labels by Importance Reweighting.” IEEE Transactions on Pattern Analysis and Machine Intelligence 38 (2016): 447-461.\n\n[4] Alghushairy, Omar, Raed Alsini, Terence Soule and Xiaogang Ma. “A Review of Local Outlier Factor Algorithms for Outlier Detection in Big Data Streams.” Big Data Cogn. Comput. 5 (2021): 1.\n\n[5] Pang, Guansong, Cheng Yan, Chunhua Shen, Anton van den Hengel and Xiao Bai. “Self-Trained Deep Ordinal Regression for End-to-End Video Anomaly Detection.” 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) (2020): 12170-12179.\n\n[6] Liu, Boyang, Ding Wang, Kaixiang Lin, Pang-Ning Tan and Jiayu Zhou. “RCA: A Deep Collaborative Autoencoder Approach for Anomaly Detection.” IJCAI : proceedings of the conference 2021 (2021): 1505-1511 .\n\n[7] Zhou, Chong and Randy Clinton Paffenroth. “Anomaly Detection with Robust Deep Autoencoders.” Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (2017): n. pag.", "questions": "-", "limitations": "The limitations of this method are not discussed", "rating": 3, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "The paper is not particularly well written, and it contains a relatively large number of grammatical mistakes. The main points, however, are comprehensible.\nThe ideas presented here are not particularly original. The idea of reweighting the training data according to their anomalousness degree has been done before (e.g. some recent references [2,3]). Using LOF for the anomaly detection of noisy data is by no means new (e.g. [4]).\n\nStrengths\n\t• The comparison to other methods shows the advantage of the method when it comes to noisy training data. However, it would be beneficial to see the results on more challenging datasets.\n\nWeaknesses:\n\t• The overall idea is not novel, while the specific of the methods suggested here are. The idea of reweighting the training data according to their anomalousness degree has been done before (e.g.  recent references [2,3,4]). \n\t• To construct the memory bank (i.e., the reference of the normality), the authors propose to reject “the top τ% patches with the highest outlier scores”. Do they implicitly assume that the ratio of the noise in the training data is known in advance? This assumption is strong in a real-world environment where the ratio of the contamination may vary according to the collected training data. \n\t• Experiments on other challenging state-of-the-art datasets are desirable.\n\t• Limitations are not thoroughly discussed (e.g., the complexity).\n\nClarity:\n\t• The paper is not particularly well written. But, the main points are comprehensible.\n\t• The notations of the formulas are sometimes confusing, which makes it difficult to follow. For example, in line 193, “w” denotes the anomaly weight. However, w denotes the batch position at line 140. \n\nRelation to prior work:\nThe authors state that “we are the first one to study the abnormal detection with noisy data”. However, many studies have been proposed in this research field: e.g., [5,6,7]\n\nReproducibility:\n\t• The conducted experiments are well described. \n\t• It would be helpful if the entire code would be made accessible in case the paper is accepted.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "u9MVVmxfjlt", "reviewer": "Reviewer_zKJo", "summary": "This paper addresses a practical setting of Anomaly Detection, namely AD with noisy data. The authors propose a novel AD algorithm named SoftCore to enhance model performance and noise robustness. By using a patch-level selection strategy, the model can reweight the coreset samples and wipe off the noisy image patch of noisy samples.", "questions": "Please refer to the weakness", "limitations": "Yes.", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n+ The paper is well-structured, and easy to follow.\n+ This paper explores the impact of noise data on anomaly detection tasks, which has highly practical significance.\n+ The proposed task setup is reasonable, and the authors have conducted fundamental experiments to explain insights and analyze the impact of noise on AD tasks.\n+ From the experimental results, the effectiveness of the proposed method is verified. \n\nWeaknesses:\n- There are some grammatical errors: Line 156, $W_(i)$ should be $W_{(i)}$; Line 268, LOF achieve -> achieved.\n- The mathematical notation should be improved. For example, the symbol of sample variance $\\sum_{h,w}$ is confusing in Eq(2) and (3).\n- The critical threshold τ should be given more explanations.\n", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "JAUhXK_dVm3", "reviewer": "Reviewer_m85i", "summary": "1. The authors proposed to add noisy data into the training set of unsupervised anomaly detection and created a new task setting.\n2. The authors introduced a denoising mechanism and investigated 3 sampling strategies for distinguishing between noisy and clean (normal) data.\n3. The experimental results are superior in the new setting.\n", "questions": "1.\tExplanations of the weakness mentioned are important.\n2.\tIt is confusing in Fig.2. The explanation of notions: ’N, H, W, C’ is missing. The arrow under ‘outlier factors of all selected patches’ are misleading, which is started from all samples including noisy ones.\n3.\tThe authors mentioned on Page 6 Line 197: ‘The soft weights, i.e., local outlier factors, have considered the local relationship around the nearest node.’ An analysis of the neighbor's influence is needed.\n4.\tThe English statement needed to be modified. On Page3 Line 94. ‘too long a training stage limits its usage.’ is confusing.\n", "limitations": "None", "rating": 4, "confidence": 5, "soundness": 2, "presentation": 2, "contribution": 1, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths：\n1.\tIt is interesting to create a new task that adds noisy data to normal training images for simulating real scenes.\n2.\tThe authors made their motivation and statement clear.\n3.\tThe authors conducted many experiments to verify their proposed methods.\nWeaknesses:\n1.\tThe novelty of the proposed method is weak. It seems to be a modified version of previous work: PatchCore, by adding a denoising process to the memory bank. \n2.\tThe setting of ‘Overlap’ experiment is somewhat confusing and meaningless. It is unfair for methods to train and test on the same (overlap) data. \n3.\tIn the experiments on ‘No overlap’ setting, little performance drops were seen on state-of-the-art methods, and the comparison between the proposed methods (98.6) and PatchCore (98.4) can not show the benefits of the new approach.\n", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "7BUtE-Qroad", "reviewer": "Reviewer_P5sf", "summary": "This paper sets forth a memory-based unsupervised AD method for anomaly detection. The novelty lies in efficiently denoising the data at the patch level. To this end, noise discriminators are utilized to generate outlier scores for patch-level noise elimination before corset construction. Compared to the existing algorithms, the proposed algorithm is relatively well performed.", "questions": "I'd like to authors to respond to the two points in the weakness. ", "limitations": "not mentioned.", "rating": 7, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 4, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n+ A patch-level denoising strategy for coreset memory bank sounds reasonable and intersting\n+ Setup a practical setting for unsupervised anomaly detection\n+ Experimental results adequate\n\nWeakness:\n- No test on real noisy dataset is provided\n- No computational analysis is provided", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}]

Author rebuttal:

Decision: Accept