Revisiting Deep Feature Reconstruction for Logical and Structural Industrial Anomaly Detection
Authors: Sukanya Patra
Souhaib Ben Taieb
Venue: Accepted by TMLR ()

Abstract: Industrial anomaly detection is crucial for quality control and predictive maintenance, but it presents challenges due to limited training data, diverse anomaly types, and external factors that alter object appearances. Existing methods commonly detect structural anomalies, such as dents and scratches, by leveraging multi-scale features from image patches extracted through deep pre-trained networks. However, significant memory and computational demands often limit their practical application. Additionally, detecting logical anomalies—such as images with missing or excess elements—requires an understanding of spatial relationships that traditional patch-based methods fail to capture. In this work, we address these limitations by focusing on Deep Feature Reconstruction (DFR), a memory- and compute-efficient approach for detecting structural anomalies. We further enhance DFR into a unified framework, called ULSAD, which is capable of detecting both structural and logical anomalies. Specifically, we refine the DFR training objective to improve performance in structural anomaly detection, while introducing an attention-based loss mechanism using a global autoencoder-like network to handle logical anomaly detection. Our empirical evaluation across five benchmark datasets demonstrates the performance of ULSAD in detecting and localizing both structural and logical anomalies, outperforming eight state-of-the-art methods. An extensive ablation study further highlights the contribution of each component to the overall performance improvement. Our code is available at https://github.com/sukanyapatra1997/ULSAD-2024.git.

Published in Transactions on Machine Learning Research (09/2024)
Revisiting Deep Feature Reconstruction for Logical and Struc- tural Industrial Anomaly Detection
Sukanya Patra University of Mons
sukanyo.patra Sakkangg.parrr@ummss..ccc.o aumons.a.mm..c.b
Souhaib Ben Taieb
nouhasb.bentaich souhasb.. bentaieb www.erbbbbaaaaaaaaama
Mohamed bin Zayed Universiby of Artificial Intelligence
University of Mons
Reviewed on OpenReview: https: openreveew. net/ form?? id- kd=kdTC4ktHPD
Abstract
Industrial anomaly detection crucial for quality control and predictive maintenance, but presents challenges due to limited training data, diverse anomaly types, and external factors that alter object appearances. Existing methods commonly detect structural anomalies, such as dents and scratches, by leveraging multi-scale features from image patches extracted through deep pre-trained networks. However, significant memory and computational demands often limit their practical application. Additionally, detecting logical anomalies such as im- ages with missing or excess elements requires an understanding of spatial relationships that traditional patch-based methods fail capture. In this work, we address these limitations by focusing on Deep Feature Reconstruction (DFR), memory- and compute-effiiiet approach for detecting structural anomalies. We further enhance DFR into unified framework, called ULSAD, which is capable of detecting both structural and logical anomalies. Specifically, refine the DFR training objective to improve performance in structural anomaly detection, while introducing an alfenttion-bssed loss mechanism using a global autoencoder-like nerw to handle logical anomaly detection. Our empirical evaluation across five benchmark datasets demonstrates the performance ULSAD detecting and localizing both structural and logical anomalies, outperforming eight state-of-tt taate-of-the-arr methods. An extensive ablation study further highlights the contribution of each component. to the overall performance improvement. Our code is available at https:/ http///gthhtt //ggtggt..coooo cww.tb..om/ssaaeee wwt../o/suuuaaaaaaaaaaaaaa.. 011.999777AAAA222411
1 Introduction
Anomaly detection (AD) widely studied problem in many fields that is used to identify rare events or unusual patterns (Salehi et al., 2022). It enables the detection of abnormalities, potential threats, or critical system failures across diverse applications such predictive maintenance (PdM) (Tang et al., 2020; Choi et al., 2022), fraud detection (Ahmed et al., 2016; Hilal et al., 2022), and medicine (Tibshirani & Hastie, 2007; Fernando et al., 2021). Despite its importance and widespread applicability, it remains a challenging task as characterising anomalous behaviours is difficult and the anomalous samples are not known a priori (Ruff et al., 2021). Therefore, AD is often defined as an unsupervised representation learning problem (Pang et al., 2020; Roiss et al., 2022) where the training data contains predominantly normal samples. The aim is to learn the normal behaviour using the samples in the training set and identify anomalies as deviations from this normal behaviour. This setting is also known one-class classification (Ruff et al., 2018).
Our study focuses on Industrial Anomaly Detection (IAD) (Bergmann et al., 2019), with an emphasis on the detection of anomalies in images from industrial manufacturing processes. Image-based IAD methods assign an anomaly score to each image. Further, this study looks into anomaly localization where each pixel of an image is assigned an anomaly score. enables fino-grained localization of the anomalous regions in the image. Over the years, has attracted attention from both industry and academia as AD can be used for various tasks like quality control predictive maintenance, which are of primal interest to industries. Despite the

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Normal
Structural Anomalies
Logical Anomalies
2
2
+
+
+
Figure 1: Types of anomalies for the categories "breakfast box" and "pushpin" in MVTecLOCO dataset. Two normal samples (Left) along with structural (Middle) and logical anomalics (Right) where the anomalous regions are highlighted in blue and red, respectively.
necessity, addressing IAD is challenging because: (i) evolving processes result in different manilestations of anomaly (Gao et al., 2023), and (ii) object appearances vary due to external factors such background, lighting conditions and orientation (Jezek et al., 2021). Furthermore, the anomalies in IAD can be broadly categorized into: (i) structural anomalies where subtle localized structural defects can be observed in the images (Bergmann et al., 2019), and (ii) logical anomalies where violat of logical constraints result. in anomalies (Bergmann et al., 2022). Figure shows examples of both structural and logical anomalies in industrial images.
To detect structural anomalies, state-of-the-art methods divides the image into smaller patches and leverage multi-scale features of the image patches obtained using deep convolutional neural networks (Salehi et al., 2021). PatchCore (Roth et al., 2022) and CFA(Lee et al., 2022) achieved state-of-the-art (SOTA) performance by storing the extracted features in a memory bank during the training phase and comparing the features of the image with their closest neighbour from the memory bank during inference. However, such approaches require considerable storage to accumulate the extracted features, which can be challenging for scage datasets. The first alternative is knowledge distillation- based approaches (Bergmann et al., 2020; 2022), where a student network is trained to mimic the teacher for normal samples. During inference, anomalies identified based the discrepancy between the student and teacher output. A key requirement of these distillation--bsedd approaches is that the student net must be less expressive than the teacher to prevent it from mimicking the teacher on anomalous samples. Thus, regularization methods, such as penalty based on an external dataset or hard-mining loss (Batzner et al., 2024) are applicd, that slows down the training and increases the requirement of computing resources. Moreover, excessive regularization can prevent learning representations for normal images. The second alternative to model the features of normal images using a multivariate Gaussian distribution (Defard et al., 2021) or learn to reconstruct the features using a deep feature reconstruction (DFR) network (Yang et al., 2020). Besides structural anomalies, logical anomalies occur when elements in the images are missing, misplaced, in surplus or violate geometrical constraints (Bergmann et al., 2022). Methods relying on multi-scale features of image patches would fail as they would still be considered normal. It is the combination of objects in the image that makes the image anomalous. Thus, to detect such logical anomalies, it necessary to look beyond image patches and develop a global understanding of the spatial relationships within normal images. Distillation-based methods, which are predominantly used for the detection of logical anomalies, rely on an additional network to learn the spatial relationships between items in the normal image (Batzner et al., 2024).
In this paper, we focus on DFR, the benefits of which are four-fold. First, it does not need large memory for storing the features, unlike PatchCore (Roth et al., 2022). Second, unlike PaDiM (Defard el al., 2021), it does not make any assumption about the distribution of features. Third, learning to reconstruct features in the latent space of pro-trained network is less impacted by the curse of dimensionality than lcarning reconstruct images which are high-dimensional. Fourth, deep networks trained to reconstruct normal images using the per-pixel distance suffer from the loss of sharp edges of the objects textures in the background.
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As consequence, AD performance deteriorates due to increase in false positives, i.c., the number of normal samples falsely labelled anomalies. On the contrary, computing the distance features maps and their corresponding reconstructions during training is less likely to result in such errors (Assran et al., 2023).
We revisit DFR to develop a unified framework for the detection of both structural and logical anomalies. First, we modify the training objective by considering a combination of & and cosine distances between each feature and the corresponding reconstruction. The incorporation of the cosine distance addresses the curse of dimensionality, where high-dimensional features become orthogonal to each other in Euclidean space and the notion of distance disappears (Aggarwal et al., 2001). Second, to simultaneously allow for the detection of logical anomalies, we introduce an attention-baset loss using global autocncoder-like network. We empirically demonstrate that with our proposed changes, not only do the detection and localization capabilities of DFR. improve for structural anomalies, but also it delivers competitive results on the detection of logical anomalies. Our contributions can be summarized as:
Building on DFR, we propose Unified framework for Logical and Structural Anomaly Detection
referred as ULSAD, a framework for detection and localization of both structural and logical anomalies.
To detect structural anomalies, consider both magnitude and angular differences between the extracted and reconstructed feature vectors.
To detect logical anomalies, we propose a novel attention-based loss for learning the logical constraints.
We demonstrate the effectiveness of ULSAD by comparing it with 8 SOTA methods across 5 widely adopted IAD benchmark datasots.
Through extensive ablation study, we show the effect of each component of ULSAD on the overall performance of the end-to-end architecture.
2 Related Work
Several methods have been proposed over the years for addressing Industrial AD (Bergmann et al., 2019; 2022; Jezek et al., 2021). They can be broadly categorized into feature-embeddding based and reconstruction-bet based methods. We briefly highlight some relevant works in each of the category. For an extended discussion on the prior works we refer the readers to the survey by Liu et al. (2024).
Feature Embedddng-bascd methods. There are mainly three different types of LAD methods which utilize feature embeddings from a pre-trained deep neural network: memory bank (Defard et al., 2021; Roth et al., 2022; Lee et al., 2022), student-teacher (Zhang et al., 2023; Batzner et al., 2024), and density- based (Gudovskiy et al., 2021; Yu et al., 2021). The main idca of memory bank methods is to extract features of normal images and store them in a memory bank during the training phase. During the testing phase, the feature of test. image is used as a query to match the stored normal features. There are two main constraints in these methods: how learn useful features and how to reduce the size of the memory bank. While PatchCore (Roth et al., 2022) introduces coresct selection algorithm, CFA (Lee et al., 2022) clusters the features in the memory bank to reduce the size of the memory bank. Nonetheless, the performance of the memory bank methods heavily depends on the completeness of the memory bank, which requires a large number of normal images. Moreover, the memory size is often related to the number of training images, which makes these methods not suitable for large datasets or very high-dimensional images. In the thudent-teacher approach, the student network learns to extract features of the normal images, similar to the teacher model. For anomalous images, the features extracted by the student network are different from the teacher network. Batzner et al. (2024) propose to use an antoencoder model in addition to the student network to identify logical anomalies. For leveraging the multiscale feature from the teacher network to detect anomalics at various scales, Deng & Li (2022) propose Reverse Distillation. Zhang et al. (2023) exlended it by proposing lo utilize two student networks to deal with struct ural and logical anomalies. Yang et al. (2020) propose to learn a deep neural network for learning to reconstruct the features of the normal images extracted using the pre-trained backbone. For density-basen based mothods, first, a model trained to learn the distribution of the features obtained from normal samples. Then, during inference, anomalies are detected based on the likelihood of features extracted from the test images. PaDiM (Defard et al., 2021) uses
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sg
No
U
N
Local branch
Forward Pass
Consistency Loss
Distance Loss
X
No
Global branch
Figure 2: Overview of the end-to-end architecture of ULSAD.
multivariate Gaussian to estimate the density of the features corresponding to the samples from the normal class while FastFlow (Yu et al., 2021) and CFLOW (Gudovskiy et al., 2021) utilize normalizing flows.
Reconstrrucion--aseed methods. Reconstruction--aast methods assume that encoder-decoder models trained on normal samples will exhibit poor performance for anomalous samples. However, relying solely on the reconstruction objective can result in the model collapsing to an identity mapping. To address this, structural assumptions are made regarding the data generation process. One such assumption is the Manifold Assumplion, which posits that the observed data resides in lower-dimenssonall manifold within the data space. Methods leveraging this assumption impose bottleneck by restricting the encoded space to lower dimensionality than the actual data space. Common deep reconstruction models used include AE or VAE-based approaches. Advanced strategies encompass techniques like reconstruction by memorised normality (Gong et al., 2019), model architecture adaptation (Tai et al., 2019) and nartial/conditional reconstruction (Yan et al., 2021; Nguyen et al., 2019). Generative models like GANs are also widely employed for anomaly detection, as the discriminator inherently calculates the reconstruction loss for samples (Zenati et al., 2018). Variants of GANs, such as denoising GANs (Sabokrou al., 2018) and class-conditional GANs (Perera et al., 2019), improve anomaly detection performance by increasing the challenge of reconstruction. Some methods utilize the reconst data from GANs in downstream tasks to enhance the amplification of reconstruction errors for anomaly detection (Zhou et al., 2020). Lastly, DREM (Zavrtanik et al., 2021) trains an additional discriminative network alongside a reconstruction network to improve the AD performance.
In this paper, we focus on feature embedding- methods motivated by their effectiveness in the current. SOTA methods. Specifically, we build on DFR (Yang et al., 2020), which has several benefits. First, is mffory-efficient it does not rely on a memory bank of extracted features, unlike PatchCore (Roth et al., 2022). Second, unlike PaDim (Defard et al., 2021), it does not make any assumption about the distribution of the extracted features. Third, it is computationally efficient and less impacted by the curse of dimensionality as it operates in the lower-dimensions latent space of a deep neural network. Last, by avoiding the use of per-pixel distance in its reconstruction objective, it is less prone to false positives (Assran et al., 2023).
3 The ULSAD Framework for Anomaly Detection
We propose ULSAD, framework for simultancously detection and localization of anomalies in images shown in Figure 2. Firstly, we utilize a feature extractor network for extracting low-dimensional features from high-dimensional images, which we discuss in Section 3.1. Then, for the detection of both structural and logical anomalics, we rely on dual-branch architecture. The local branch detects structural anomalics with the help of a feature reconstruction network applied to the features corresponding to patches in the image. We elaborate this in Section 3.2. Conversely, the global branch, discussed in Section 3.3, detects logical
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anomalies using autoencoder-like network, which takes as imput the image. Lastly, we provide overview of the ULSAD algorithm in Section 3.4 followed by a discussion on the inference process in Section 3.5.
We consider a dataset D = 9i) with n samples where X, E X is an image and yi E 10 is the corresponding label. We refer to the normal class with the label and the anomalous class with the label 1. The samples belonging to the anomalous class can contain eir logical or structural anomalies. We denote the train, validation and test partitions of D as Dirain Dvalid and Prest respectively. The training and validation sets contains only normal samples, i.e., y= O. For the sake of simplicity, we refer to the training set D
X (X.0) D.sin]. The test set Diest includes both normal and anomalous samples.
3.1 Feature Extractor
High--dimensional images pose a significant challenge for AD (Reiss et al., 2022). Recent studies have shown that deep convolutional neural networks (CNNs) trained on ImageNet (Russakovsky et al., 2015) capture discriminative features for several downstream tasks. Typically, AD methods (Salehi et al., 2021; Defard et al., 2021; Yoon et al., 2023) leverage such pre-trained networks to extract features maps corresponding to partially overlapping regions or patches in the images. Learning to detect anomalies using the features is beneficial as it results in reduced computational complexity. A key factor determining the efficiency of such methods is the size of the image patches being used, as anomalies can occur al any scale. To overcome this challenge, feature maps are extracted from multiple layers of the CNNs and fused together (Salehi et al., 2021; Roth et al., 2022; Yang al., 2020). Each clement in feature map obtained from different layers of a convolutional network corresponds to patch of different size in the image depending its receptive field. Thus, combining feature maps from multiple layers results in multi-scale representation of the image patches, which we refer to as patch features.
Similar to DFR, we extract low-dimensional feature maps by combining features from multiple layers of a feature extractor which a pre-trained CNN No parameterized by 6. In this paper, we consider ResNet-like architectures for Ng. With the increasing number of layers, the computation becomes increasingly expensive as the resulting tensor becomes high-dimensional. In order to overcome this, we consider two intermediate mid-level features. Our choice is guided by the understanding that the initial layers of such deep networks capture generic image features, while the latter layers are often biased towards the pre-training classification task (Roth et al., 2022). We denote the features ures extracted at a layer j for an image X as (X). Following this convention, we express the feature map E 4 Re xh" x== produced by the Feature Aggregator (FA) as a concatenation of N (X) and N/+1 (X) obtained from layers j and j + of Ng. Furthermore, to facilitate the concatenation of features extracted from multiple layers of the extractor Ne, the features at the lower resolution layer j 1 are linearly rescaled by FA to match the dimension of the features at layer j. We define invertible transformation f: IR= xh" x=" + Re xk* where k* = ht X w" to convert tensor to matrix and vice versa using f-1 The function f can be computed in practice by reshaping the tensor to obtain a 2D matrix. Now, using f, we compute Z = fUU). We denote each patch feature within the feature map Z by 2/ [ k] = Ul: | h, w). where l = (h - 1) x w' + +w, h E (1,2,.... hh),, w E (1.2...., w.)
3.2 Detecting Structural Anomalies
Having defined Z in the previous section, we elaborate on the local branch of ULSAD for the detection of subtle localized defects in the images, iee. structural anomalies. Specifically, our goal is to learn the reconstruction of the patch features using the dataset DN composed of only normal images. Therefore, we can identify the structural anomalies when the network fails to reconstruct a patch feature during inference.
Feature Reconstruction Network (FRN). As shown in Figure3 3, ULSAD utilizes a convolutional encoder-decoder architecture with a lower-dimensional bottleneck for learn- ing to reconstruct the feature map U using the training dataset Dv. First, the encoder nelwork No. compresses the feature to a lower dimensional space, which in- duces the information bottleneck. It acts as an implicit regularizer, preventing generalization features corre- sponding to anomalous images. The encoded represen-
N
N
U
X
Local branch
Figure 3: Feature Reconstruction Network
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tation is then mapped back to the latent space using decoder network No.- The output of FRN is U (U) E R xh* xw" xh"x"" where Ny = No. Now Besides using the FRN to learn the reconstruction of the patch features for the detection of structural anomalies, we also utilize to reduce errors during the detection of logical anomalies, discussed in Section 3.3. To minimizing computation costs and avoid the use of two separate FRNs, adopt a shared FRN. This is achieved by doubling the number of output channels in the decoder to simultaneously produce two feature maps and U for the detection of structural and logical anomalies, respectively, with both having dimension c* x x w".
mll
Although the feature maps U have significantly lower dimensionality compared the imput images X, they still be considered high-dimensional tensors. In high-dimensional spaces, the & distance is not effective at distinguishing between the nearest and furthest points (Aggarwal et al., 2001), making it an inadequate measure for computing the difference between feature maps during training. Therefore, similar to Salchi et al. (2021), we propose combining & and cosine distances to account for differences in both the magnitude and direction of the patch features as:
R = k- Σ 26), 2k) + + (a
(1)
where ž' = -Ū) Z = f(Z) and A 2 0 controls the effect of La- Furthermore, L,(%), zx) and La(% zx) measure the differences in magnitude and direction between the patch features 2Y and 2/z respectively, as
4. xk) 1 2x112. and 2x(%,
(2)
12 Zk 1
3.3 Detecting Logical Anomalies
Although the feature reconstruction task discussed in Section 3.2 allows to detect structural anomalies, it is not suited for identifying logical anomalies that violate the logical constraints of normal images. Recall that such violations appear in the form of misplaced, misaligned, or surplus objects found in normal images. If we consider the example of misaligned objects, the previously discussed approach will fail as focuses on the individual image patches, which would be normal. It the overall spatial arrangement of objects in the image which is anomalous. Thus, identify such anomalies, our goal is to learn the spatial relationships among the objects present in the normal images of the training dataset DN. We achieve this with the global branch of ULSAD, shown in Figure 4, which leverages the entire image and not just its individual patches.
In order to achieve our goal, we start by analyz- ing the feature maps extracted using the pre- trained network No. Pre-trained CNNs tend to have similar activation patterns for semantically similar objects (Tung & Mori, 2019; Zagoruyko & Komodakis, 2017). In Figure 5, visual- ine four self-attention maps computed from the features of a pre-trained work. It can be seen that in the first map, all the items for the semantic class "fruits" receive high aeteiion score. The remaining attention maps focus on individual semantic concepts like "oranges", "cereal" and "plate", respectively. Based on this observation and inspired by the tttention-transferr concept for knowledge distil- lation (Zagoruyko& & Komodakis, 2017; Tung &
9g
FA
net-
Global branch
Figure 4: Global Branch ULSAD
Mori, 2019), we propose to learn the spatial relationships (Dosovitskly et al., 2021) among the patch features in U obtained from normal images. Recall that each patch feature corresponds to patch in the image. Therefore, learning the spatial relationships among the patch features would allow us to learn the spatial relationships among the patches in the image. This forces ULSAD to learn the relative positions of objects in

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Figure 5: (First) Example image belonging to the category "breakfast box" in the MVTecLOCO dataset. (Rest) Visualization of attention maps computed using the intermediate features from a pre-trained model.
the normal images, thereby enabling to capture the logical constraints. Starting from Z f(U), we first compute the self-attention weight matrix W E RR
T 2g/ VC') expl2Ø
WlP.9
(3)
Σ exp(2% Zn /V/V)*)
Then, the attention map E R=** convolutional autocncoder-like network =N o No. where Ng. is the encoder and No. is the decoder. Similar to standard autoencoder, No. compresses the inpul image X to lower dimensional space. However, No. maps the encoded representation to the feature space U, which has a lower dimension than the input space X. We denote the output of No as Ü = (x)
xk" computed as A ZW. For learning the spatial relations using A
target,
A direct approach would be to compute the self-attention map for Ô and minimize its distance from A. However, makes the optimization problem computationally challenging as each vector in Ô is coupled with every other vector by the network weights No (Zhang et al., 2023). To overcome this, we compute the = =ūū), we first compute W as:
cross- atsentioonn map Å R xk* between U and Ú. Given -=
exp(2 / VV²)
(4)
Σ exp(2% / Ve*)
Then, the attention map À can be computed as À ZW. Given, the self-attention map A and the cross-attention map Å, we define consistency loss Lpg as:
Cps( (A, A)
Σ (ā,, a&) + Ag la(ās, ax),
(5)
where a; = A[; ā Al. k] and X₂ 2 0 controls the effect of la. A limitation of this approach is that autoencoders usually struggle with generating fine-grained patterns as also observed by prior works (Dosovitskiy & Brox, 2016; Assran et al., 2023). As a result, the global branch is prone to false positives in the presence of sharp edges or heavily textured surfaces due to the loss of high-frequency details. To address this limitation, we utilize the FRN No in the local branch to learn the output U. Recall that the output of FRN Ü E x2e""x""xx"" xA"x"" xw" has 2c number of channels to simultaneously generate two feature maps Ú and -if
ü", both having dimension c* x h² x w". Out of which, Ú' is used for learning the patch features. Here, we define the loss Cig to relate the local feature map Ú" with the global feature map Ü as:
Cig( 2
W. + Ag 2x)
(6)
where f("). Therefore, during inference, a difference between the Ú and Ô indicates the presence of logical anomalies. The benefits of such a framework are two-fold: (1) it allows for learning the spatial relationships in the normal images while reducing the chance of having false positives, and (2) doubling the channels in the decoder allows sharing the encoder architecture, reducing the computational costs.
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Algorithm 1: Unified Logical and Structural AD (ULSAD) // Local branch
Global branch
Require:
Training dataset DN, Feature extractor Ng, Feature reconstruction network No.
Global autoencoder No: Number of epochs e, Learning rale 7) Pre-trained feature statictics μ4, a for (epoch E 1,....,, and (X Dx) do Extract normalized features maps using the pre-trained network:
U - (X)
U < (U (U-N)/o
Z - f(U)
Reconstruct the features maps using the local branch:
*+NN(U
Compute local loss (Eq. 1):
4 4 (2)
10
Obtain the output of the global autoencoder:
Ô < (X)
2 - n())
13
14
Compute consistency loss (Eq. 5):
1g & Lpg (2, 2)
15
16
Compute local-global loss (Eq. 6):
li f Lig( i2 Z")
17
Compute overall loss:
( 4 + bg + hix.
20
Update model parameters:
21
1 + レ V/ ml
22
① x Φ v
23 end
Return: No. No
3.4
ULSAD Algorithm Overview
An overview of ULSAD outlined in Algorithm 1, which can simultancously detoct structural and logical anomalies. Firstly, we pass a normal image from the training dataset Dv through the feature extractor N₂ to obtain feature maps U. We normalize the features (line 4, Algorithm 1) with the channel-wise mean μa and standard deviation computed over all the images in DN. We do not include this step in Algorithm 1 the calculation is trivial. Instead, we consider the values f and a to be given as input parameters for the sake of simplicity. Secondly, we obtain Ü by passing U through the feature reconstruction network No (line 7, Algorithm 1). Recall that, Ú has dimension 2ct x ht w² which can be decomposed into two feature maps Ú' and Ú cach with dimension c* x h" w". The feature reconstruction loss Lpt is then computed between Z and Z', where Z f(U) and Ž' = f(Ü). Thirdly, we obtain the features Ú by passing the input sample X through the autoencoder Ng. Then for learning the spatial relationships from the normal images, compute Lpg between the self-attention map of Z and the cross-attention map between Z and Ž f(Ü (line 15, Algorithm 1). In the fourth step, we compute the loss Lig between 2 and z" = =f(ü", Finally, the model parameters & and & are updated based on the gradient of the total loss (line 21 - 22, Algorithm 1). The end-to-end pipeline illustrated in Figure 2.
"
3.5 Anomaly Detection and Localization
After discussing how ULSAD is trained detect structural and logical anomalies, we now focus on the inference process. The first step is to compute anomaly map M for given test image X, which assigns a per-pixel
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anomaly score. We begin by calculating the local anomaly map M' R "a"" based on the difference between the output of the local branch Ú' and the feature map U, as follows:
Mh w| (U [t. h, w|, Ult, w|) A La(U (U, It, (,,,,), w], Uf: h, wl),
where Ú' (Z) and U - (Z). Similarly, the global anomaly map M is computed using the output from the global autoencoder Ô and the local reconstruction branch Ü"
hh, w| = (U [t h. w). Ul;, h, w|) Ag la [t, h, w|. Ul: hi wl),
(8)
where U" (-2 and - (-)
Since M' and M may have different ranges of anomaly scores, we normalize each map independently. This normalization ensures consistent score ranges and prevents noise one map from overwhelming anomalies detected in the other. Given the variability in anomaly score distributions across datasets, we adopt a quantile-based normalization method, which makes assumptions about the underlying score distribution.
To normalize the maps, we generate two sets of anomaly maps: M = {M' X E Dvatia) and M9 = {M X E Dvalia;; using images from the validation set Dvalid. For each set, we pool together the pixel values from all the anomaly maps in that set to compute the empirical quantiles at significance levels a and B. Specifically, for the local anomaly maps, the quantiles are denoted as da and g's, while for the global anomaly maps, the quantiles are denoted as la and dz- Values below Ja are considered normal, while those above ga are marked as highly abnormal.
Following Batzner et al. (2024), we define linear transformations t(() and t-)) for the local and global anomaly maps to map normal pixels values < 0 and highly anomalous pixels to values 0.1:
((M))= = 0.1 M' - (- d/a 933 9a
(M'-
1 ) (MMM) = 0.1 M
1 xw=
4a
where xw= matrix of ones. Mapping the empirical quantiles at a and to values of and 0.1 helps highlight the anomalous regions 0-to-1 color scale for visualization. Normal pixels are assigned score of O, while pixels with scores between Ja and gs gradually increase in color intensity. Pixels with scores exceeding is change more rapidly toward 1. Note that this transformation docs not affect AU-ROC scores, as these depend only on the ranking of the scores.
Finally, we compute the overall anomaly map M for the image X by averaging the normalized local and global maps:
L' ('(M') + (M99)
M
2
The final anomaly score for X is the maximum value in the combined anomaly map:
max he (1,2...... J.E (1, M(,, w).
4 Experimental Evaluation
In this section, we answer the following three questions: (i) How does ULSAD perform as compared to the SOTA methods? (ii) How effective is the local and global branch for the detection of structural and logical anomalies? (iii) How does each component in ULSAD impact the overall performance?
4.1 Setup
Benchmark Datasets. We evaluate our method on the following five LAD benchmarking datasets:
[1] BTAD (Mishra al., 2021). It comprises real-world images of three industrial products, with anomalies such body and surface defects. Training data includes 1,799 normal images across the three categories,
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while the test set contains 290 anomalous and 451 normal images.
[2] MVTTcc AD (Bergmann et al., 2019). It consists of images from industrial mamufacturing across 15 categories comprised of 10 objects and 5 textures. In totality, it contains 3,629 normal images for training. For evaluation, 1,258 anomalous images with varying pixel level defects and 467 normal images.
[3] MVTec-Loco (Bergmann et al., 2022). An extension of MVTec dataset, it encompasses both local structural anomalies and logical anomalies violating long-range dependencies. It consists of 5 categories, with 1,772 normal images for training and 304 normal images for validation. It also contains 1568 images, cither normal or anomalous, for evaluation.
[4] MPDD (Jezek et al., 2021). It focuses on metal part fabrication defects. The images are captured in variable spatial orientation, position, and distance of multiple objects concerning the camera at different light intensities and with a non-homogenoous background. It consists of classes of metal parts with 888 training images. For evaluation, the dataset has 176 normal and 282 anomalous images.
[5] VisA (Zou et al., 2022). contains 10,821 high-resolution images (9,621 normal and 1,200 anomalous images) across 12 different categorios. The anomalous images contain different types of anomalies such scratches, bent, cracks, missing parts or misplacements. For each lype of defect, there are 15-20 images, and an image can depict multiple defects.
Evaluation metrics. We measure the image-level anomaly detection performance via the area under the receiver operator curve (AUROC) based on the assigned anomaly score. To measure the anomaly localization performance, we use pixel-level AUROC and area under per region overlap curve (AUPRO). Furthermore, following prior works (Roth et al., 2022; Gudovskiy al., 2021; Bergmann et al., 2019), we compute the average metrics over all the categories for each of the benchmark datasets. Moreover, for ULSAD, report all the results over 5 runs with different random seeds.
Baselines. We compare our method with existing state-of-the-art unsupervised AD methods, namely PatchCore (Roth et al., 2022), PaDim (Defard et al., 2021), CFLOW (Gudovskiy et al., 2021), FastFLOW (Yu et al., 2021), DR.EM (Zavrtaník et al., 2021), Reverse Distillation (RD) (Deng & Ti, 2022), Efficient (Batzner ct al., 2024) and DFR (Yang et al., 2020). In this study, we only consider basclines that are capable of both anomaly detection and localization.
Implementation details. ULSAD is implemented in PyTorch (Paszke et al., 2019). For the baselines, we follow the implementation in Anomalib (Akeay et al., 2022), a widely used AD library for benchmarking. In ULSAD, we use a Wide-ResNNeL50-22 pre-trained on ImageNet (Zagoruyko & Komodakis, 2016) and extract features from the second and third layers, similar to PathCore (Roth et al., 2022). We use a CNN for the autoencoder No in the global branch and the feature reconstruction network No in the local branch. It consists of convolution layers with LeakyReLU activation in the encoder and deconvolution layers in the decoder. The architecture is provided in the Appendix A. Unless otherwise stated, for all the experiments, we consider an image size of 256 x 256. We train ULSAD over 200 epochs for each category using an Adam optimizer with a learning rate of 0.0002 and a weight decay of 0.00002. We set = 0.9 and 8 = 0.995 unless specified otherwise. For the baselines, we use the hyperparameters mentioned in the respective papers.
4.2 Evaluation Results
We summarize the anomaly detection performance of ULSAD in Table 1 and the localization performance Table 2. On the BTAD dataset, we improve over the DFR by approximately 2% in detection. Inspecting the images from the dataset, we hypothesize that the difference stems from the use of global branch in ULSAD as the structural imperfections are not limited to small regions. For localization, Reverse Distillation performs better owing to the use of anomaly maps computed per layer of the network. We can observe similar improvements over DFR on the MVTec dataset. Although PatchCore provides superior performance on MVTec, it should be noted that even without using a memory bank, ULSAD provides comparable results. Then, we focus on more challenging datascts such as MPDD and MOTo While MPDD contains varying external conditions such as lighting, background and camera. angles, MVTecLOCO contains both logical and structural anomalies. We can observe improvements over DFR (~ 12 16%) in both datasets. This
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highlights the effectiveness of our method. We visualize the anomaly maps for samples from the "pushpin" and "juice bottle" categories in Figure 6. It can be seen that while the global branch is more suited to the detection of logical anomalies, the local branch is capable of detecting localized structural anomalies.
Table Average Detection Performance in AUROC (%)). Style: best and second best
Method
BTAD
MPDD
MVTec
MVTec-LOCO
VisA
PatchCore (Roth al., 2022)
93.27
98.75
81.49
91.48
CFLOW (Gudovskly et al., 2021)
93.57
87.11
94.47
73.62
87.77
DR.EM (Zavrtanik et al., 2021)
73.42
74.14
75.26
62.35
77.75
EfficientAD (Batzner al., 2024)
88.26
80.62
91.21
FastFlow (Yu et al., 2021)
91.68
65.03
90.72
71.00
87.49
PaDiM (Defard et al., 2021)
93.20
68.48
91.25
68.38
83.28
Reverse Distillation (Deng & T4, 2022)
83.87
79.62
79.65
61.56
86.24
DFR (Yang al., 2020)
94.60
79.75
93.54
72.87
85.18
ULSAD (Ours)
96.17 0:45
95.73
0.45
97.65
0.38
84.1
0.86
92.46
0.45
Table 2: Average Segmentation Performance in AUROC (%) and AUPRO (%). Style: best and second best
Method
BTAD
MPDD
MVTTcc
MVTec-LOCK
VisA
PatchCore (Roth et al., 2022)
96.85
71.48
98.07
90.84
97.71
91.15
75.77
69.09
97.93
85.12
CFLOW (Gulovskiy al., 2021)
96.60
73.11
97.42
88.56
97.17
90.14
76.99
66.93
98.04
85.29
DRÆM (Zavrtanik al., 2021)
50.04
22.48
86.96
70.04
75.01
49.72
63.69
40.06
71.31
54.68
Effirient (Batzner et al., 2024)
54.37
97.03
90.44
96.29
90.11
70.36
66.96
97.51
84.45
FastFlow (Yu et al., 2021)
96.15
75.2
93.60
76.89
96.44
88.79
75.55
53.04
97.32
81.70
PaDiM (Defard et al., 2021)
97.07
77.80
94.51
81.18
96.79
91.17
71.32
67.97
97.09
80.80
Reverse Distillation (Deng & Li, 2022)
97.85
81.47
97.83
91.86
97.25
93.12 12
68.55
66.28
98.68
91.77
DFR (Yang et al., 2020)
97.62
59.06
97.33
90.46
94.93
89.42
61.72
69.78
97.90
91.72
96.73
75.41
97.45
92.02
97.61
91.67
80.06
73.73
98.24
87.12
ULSAD (Ours)
0.51
3.85
0.99
+ 0.64
1.30
+:
0.33
0.90
0.89
Logical Anomaly
Ground Truth
Global Map
Local Map
Final Map
Structural Anomaly
Ground Truth
Global Map
Local Map
Map
Logical Anomaly
Ground Truth
Global Map
Local Map
Final Map
Structural Anomaly
Ground Truth
Global Map
Local Map
Final Map
Figure 6: Example of anomaly maps obtained from global and local branches along with the combined map. Overall, ULSAD demonstrates competitive results in anomaly detection compared to the baseline methods across all benchmark datasets. Additionally, the difference in performance between ULSAD and the baselines
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for anomaly localization is minimal. The most notable difference is in the AUPRO score the BTAD, MVTec, and VisA datasets. Nonetheless, while the SOTA methods provide slightly better performance in the localization of structural anomalies, ULSAD provides similar performance across both logical and structural anomalies. We present anomaly maps obtained from different methods in Figure 9 of Appendix B. Extended versions of Tables 1 and are provided in Appendix B. Additionally, we provide the results on MVTecL.OCO, split between logical and structural anomalies, in Appendix B.1.
4.3 Ablation study
In this section, we analyze the impact of the key components of ULSAD, backbone architectures and the choice of a and 8 for normalization, using the MVTecI.OCO dataset.
Analysis of main components.
Table 3: Ablation of the main components of ULSAD.
We investigate the impact of key components ULSAD as presented in Table 3. Initially, we set both d and X to O, focusing solely on differences in magnitude when com- puting Lpg: Lig, and Cpt. The first row corresponds to using only the local branch. In the third row, the consistency loss E is applied to capture spatial relationships for de- tecting logical anomalies. However, when used in isolation, it limits ULSAD's performance to detecting only logical anomalies and fails to capture localized structural anomalies. Additionally, as discussed in Section 3.3, the global branch is prone to false positives in the presence of sharp edges or heavily textured surfaces. When incorporating Lig, which connects the global and local branches, we observe a significant improvement in performance, as shown in the fifth row. For the sake of completeness, we also consider here a variant of the consistency loss Lpx where we compute the lg distance between the feature maps instead of computing the self- and cross-attention maps. We refer to the alternative in the table as Lo We observe that the difference between the two variants becomes negligible when combined with Lig (row 4 and 5). Further, incorporating differences in direction when computing Lyg; Lig: and Lpt leads to improved performances across all settings shown in the last five rows. Overall, the best performance is obtained when both Lig and Epg is used while considering differences in both dircction and magnitude for computing the losses.
Local Branch
Global Branch
Performance (%)
A
Ex
Eap
LAUROG P-AUROG P-AUPRO
1
0.0
77.67
75.17
73.37
2
0.0
0.0
77.69
79.77
75.26
3
71.67
73.92
67.22
1
81.40
82.12
77.47
5
0.0
0.0
81.08
81.97
76.45
6
0.5
79.14
76.57
73.41
7
0.5
0.5
80.50
81.85
| 77.35
8
0.5
0.5
74.51
76.59
| 69.01
9
0.5
1 0.5
82.19
81.25
75.50
84.10
80.06
73.73
10
0.5
0.5
Effect of backbone. We investigate the impact of using different pre-trained backbones in ULSAD in Figure 7. We can obscrve that the overall best performance is obtained by using a Nelt 2 architecture in both detection and localization. More specifically, for detection, Wide-ResNet vari- ants are more effective than the ResNet architec- tures, whereas, for localization performance mea- sured using Pixel AUROC, the deeper networks such as 1esNet115 and Ne11-12 seem to have precedence over their shallower counterparts. Over- all, we can see that performance is robust to the choice of pre-trained model architecture. In our experiments, we utilize a Wide-ReeNNet50-2 architecture which is used by most of our baselines for fair comparison.
Performance (%)
84
Hool AUROC
mage AUROC
83-
82
81
80:
ResNet50
ResNet152
Mide-ResNee5502 MideRResNet101.2 Backbone
Figure 7: Ablation study of the backbone network
Effect of normalization. We analyze the impact of the quantile- normalization on the performance metrics by considering multiple values for a and B. The results are shown in Figure It can be seen that the final performance is robust. to the choice of a and B.
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04.0
72.13
15.5
0.8
50.8
73.0
0.9
0.50
07.31
25.75
33.45
10.33
13.82
05.24
01.05
5-13
00.33
14.04
03.0
0.57 0.95
0.9
42
-0.00
06 057 0.95
0.9
72.00
72:03
72.60
73:44
73.00
73.20
73:37
72.5
83:07
04.67
84.34
94.17
04.44
-2.5
00.50
000 46
60. 43
60.36
00:19
73.10
73.28
73.40
73.45
73.55
71.5
04.21
5--22
09.00
0.99
00.33
00.27
00.03
73.35
75.55
75.03
71.0
385
0.99
0.995
0.957
0.999
0.95
0.90
0.99
0.595
0.997
0.599
0.3
0.98
0.99
0.090
0.997
0.999
B
B
(a) Image AUROC
(b) Pixel AUROC
(c) Pixel AUPRO
Figure 8: Ablation study of a and 3 for normalization of anomaly maps with selected value highlighted.
Table 4: Memory and Computational Efficiency on MVTecLOCO dataset.
CFLOW
DR.M
FlstFlow
PaDiM
PatchCore
RD
DFR
EHAD
ULSAD
(2021)
(2021)
(2021
(2021)
(2022)
(2022)
(2020)
(2024)
(Ours)
L-AUROC 1
73.62
62.35
71.00
68.38
81.49
61.56
72.87
80.62
84.10 #
P-AUROC
76.99
63.69
75.55
71.32
75.77
68.55
61.72
70.36
80.06
P-AUPRO
66.93
40.06
53.04
67.97
69.09
66.28
69.78
66.96
73.73
Throughput (img/ s) f
11.69
10.06
30.21
33.45
32.70
34.87
15.08
23.33
33.42
GPU Memory (GB) 4
2.57
7.95
1.69
1.92
6.80
1.93
5.85
3.48
2.17
5 Memory and Computational Complexity
We report the computational cost and memory requirements of ULSAD compared to the baselines in Table 4. For this analysis, we ran inference on the test. samples in the MVTecLOCCO dataset using an NVIDIA A100 GPU. We measured throughput with a batch size of 32, as a measure of computational complexity, following EfficientAD (Batzner et al., 2024). Throughput is defined as the number of images processed per second when processing in batches. ULSAD demonstrates higher throughput than most baselines while maintaining competitive anomaly detection and localization performance. In addition to throughput, we also report peak GPU memory usage in Table 4 to highlight the memory efficiency of ULSAD. It is evident that ULSAD requires approximately one-third of the memory compared to retrieval-based methods such as PatchCore, which is one of the state-of- tht---rttt-- methods for IAD. For DFR (Yang et al., 2020), follow the authors' approach by using a multiscale representation, concatenating features from 12 layers of the pre-trained network No for anomaly detection. This approach results in reduced throughput and increased memory usage, as shown in Table 4. With our proposed modifications in ULSAD, we achieve superior performance using features from only 2 layers of Ng, drastically reducing memory requirements to approximately one-third of DFR's and increasing throughput by approximately two times.
6 Limitations
For training ULSAD, we follow the common assumption unsupervised anomaly detection (Ruff al., 2021; Chandola al., 2009; Roth et al., 2022; Batzner et al., 2024) that the training dataset is "clean", meaning it contains no anomalous samples. This setup is known in the literature one-class classification (Ruff et al., 2018). However, this assumption could impact performance in real-world scenarios where anomalies are unknown priori. Investigating the effects of dataset contamination (Wang et al., 2019; Jiang et al., 2022; Yoon et al., 2022; Perini et al., 2023; 2022) is an active area of research, which is beyond the scope of our current work. We leave for future research the analysis of contamination's impact on ULSAD and the development of strategies to make the learning process robust the presence of anomalies.
7 Conclusion
Our study focuses on Deep Feature Reconstruction (DFR), a memory- and compute-efficient method for detecting structural anomalics. We propose ULSAD, unified framework that extends DFR to detect both structural and logical anomalies using branch architecture. particular, we enhance the local branch's training objective to account for differences in the magnitude and direction of patch features, thereby improving
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structural anomaly detection. Additionally, introduce an attention-based loss in the global branch to capture logical anomalies effectively. Extensive experiments on five benchmark image anomaly detection datasets demonstrate that ULSAD achieves competitive performance in anomaly detection and localization compared to eight statc-of-the-art methods. Notably, ULSAD also performs well against memory-intensive, retrieval-based methods like PatchCore (Roth et al., 2022). Finally, ablation studies highlight the impact of various components ULSAD and the role of the pre-trained backbone on overall performance.
Acknowledgment
This work is supported by the FLARACC research project (Federated Learning and Augmented Reality for Advanced Control Centers), funded by the Wallonia region in Belgium
Reproducibility Statement
We provide extensive descriptions of implementation details (in Section 4.1), algorithm (in Algorithm 1) and code to help readers reproduce our results. Every measure is taken to ensure fairness in our comparisons by adopting the most commonly adopted evaluation settings in the anomaly detection literature. More specifically, we use the Anomalib library for our experiments, whenever applicable, for comparing their performance with ULSAD. For methods such as DFR (Yang al., 2020), which is not implemented in Anomalib, refer the original codebase provided by the authors.
Ethics Statement
We have read the TMLR Ethics Guidelines (https://bmlr.orgg) htr.allrrggt/ttrtrrr htt//chhhhhttii and ensured that this work adheres All benchmark datasets and pre-trained model checkpoints are publicly available and not directly subject to ethical concerns.
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Published in Transactions on Machine Learning Research (09/2024)
A Implementation Details
ULSAD is implemented in PyTorch (Paszke et al., 2019). Specifically, we used the Anomalib (Akeay et al., 2022) library by incorporating our code within it. helps us have a fair comparison as we use the implementations of baselines from Anomalib. Moreover, we used a single NVIDIA A4000 GPU for all the experiments unless mentioned otherwise. The architecture of FRN and global autoencoder-like model provided in Table 5 and 6, respectively.
Table 5: Feature Reconstruction Network of ULSAD.
Layer Name
Stride
Kernel Size
Number of Kernels
Padding
Activation
Conv-1
2
3 x
708
ReLU
BatchNorm-1
Conv-2
2
3
1536
ReLU
Encoder
BatchNorm-2
Conv-3
3
1536
ReLU
BatchNorm-3
Conv ToayTrasspee-111
708
ReLU
BatchNorm-4
Conv' Tranppaasppes-22
2
4 x 4
384
1
ReLU
Decoder
BatchNorm-5
Conv Transpose-
x
384
ReLU
BatchNorm-6
Table Global Autoencoder of ULSAD.
Layer
Padding
ReLU
BatchNorm-1
Couv-2
2
4
32
ReLU
BatchNorm-22
Conv-3
2
4 x
64
RoLU
BoteliNorm-3
Encoder
Conv-4
2
4 4x44
64
ReLU
BatchNorm-4
Comv-5
2
4 4x
64
RoL.
BatchNorm-55
Couv-6
8
ReLU
BateliNorm-6
Interpolato-1 (31, mode "bilinow"")
Couv-1
4x4
ReLU
BstchNorm-1
Interpolate-2 (8, mode= "bilinear")
Conv-2
4x4
64
RoLU
Beteh/Norm-2
Interpolate-3 (16, mode-. 'bilinoaz"
Conv-3
4
64
ReLU
BstehNorm-33
Decoder
Interpolate-4 (32, modes 'bilinea""
Conv-4
x
RoLU
BatehNNorm-4
Interpolato-5 (64, 'bilinou""
Conv-5
ReLU
BatehNorm-55
Interpolate-6 (32, mode= 'bilineaz"
Couv-6
ReLU
BatehiNorm-G
Couv-7
x
384
R+LU
20

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Published in Transactions on Machine Learning Research (09/2024)
B
Extended Results
Extended versions of the Table 1 and 2 are provided in Tables 7-21. It shows the performance of ULSAD per category of the benchmark datasets for anomaly detection and localization. Additionally, provide a visual comparison of the generated anomaly maps using the MVTecLOCO dataset in Figure 9.
Table 7: Anomaly detection based on Image AUROC on MVTTe dataset.
CFLOW
DRAEM
FastFlow
PaDiM
PatchCore
RD
DFR (2020)
EffA
ULSAD
Category
(2021)
(2021)
(2021
(2021)
(2022)
(2022)
(2024)
(Ours)
bottle
100.0
94.6
98.57
99.37
100.0
98.10
94.92
100.0
100.0 + 0.00
cable
93.46
74.29
89.30
86.94
98.54
95.41
79.54
94.61
97.92
capsule
91.74
65.46
86.04
88.43
97.93
81.01
96.01
95.57
94.61 + 0.28
carpet
98.26
57.70
98.76
97.31
97.91
57.90
97 .5
99.70
98.50 + 0.17
grid
93.57
76.02
99.08
84.04
97.24
93.07
94.57
100.0
92.67
hazelmut
100.0
84.43
81.57
86.07
100.0
99.82
100.0
93.39
99.93 + 0.05
leather
99.97
79.31
100.0
99.66
100.0
42.39
99. 99.46
99.92
100.0 + 0.00
metal nut
99.76
45.06
94.53
96.92
99.61
67.20
93.06
99.34 34
98.88
pill
90.73
44.65
87.53
88.52
94.35
54.66
92.06
99.08
96.17 + 0.39
screw
88.30
89.38
66.00
75.24
98.26
94.57
93 69
98. 09
95.20
0.15
tile
100.0
90.15
95.42
95.49
98.67
97.37
92.97
99.85
99.99
toothbrush
83.33
80.28
79.44
93.61
100.0
84.72
100.0
100.0
100.0 + 0.00
transistor
91.50
88.37
94.42
92.29
100.0
83.29
80 80.54
96.57
97 65 0.57
wood
98.33
90.96
97.54
98.33
99.30
53.16
98.77
98.13
98.81 1111
zipper
93.07
68.17
92.54
86.48
99.47
92.04
89.97
99.22
94.36
+ 0.13
Mean
94.47
75.26
90.72
91.25
98.75
79.65
93.54
98.23
97 97.65
Table 8: Anomaly segmentation performance based Pixel AUROC on MVTec dataset.
CFLOW
DRAEM
FlstFlow
PaDiM
PatchCore
RD
DFR (2020)
EffAD (2024)
ULSAD
Category
(2021)
(2021)
(2021
(2021)
(2022)
(2022)
(Ours)
bottle
98.58
76.53
97.8
98.3
97.98
98.31
90.83
98.31
96.21
cable
96.1
66.59
95.71
96.81
98.03
96.37
91.37
98.5
97.71 0.06
capsule
98.71
86.96
98.37
98.67
98.77
98.96
98 46
98. 48.33
98.95 0.03
carpet
98.57
71.95
98.27
98.68
98.67
99.05
98.46
94.83
99.18 0.06
grid
97.49
53.56
98.39
92.82
97.86
99.01
41
96.02
95.47 4: 1.09
hazelmut
98.64
84.66
94.79
97.85
98.43
98.91
98.53
96.15
98.81 + 0.93
leather
99.42
63.32
99.62
99.30
98.87
99.17
99.33
97.5
98.68
motal nut
97.97
80.25
97.01
96.71
98.51
97.68
93.02
98.07
97.62 1: 0.03
pill
97.
77.17
96.38
95.03
97.53
96.96
96.86
98.63
96.67 0.09
screw
97.64
83.38
89.87
97.89
99.19
99.43
99.07
98.50
99.33
tile
96.68
85.75
93.14
92.42
94.86
95.47
90.82
91.61
95.78 4: 0.05
toothbrush
98.16
90.70
97.50
98.83
98.67
98.99
98. .49
96.0
98.42
0.02
transistor
80.91
63.23
96.45
96.85
96.84
86.77
79.11 11
94.77
98.89
0.05
wood
94.70
71.73
95.71
93.83
93.31
95.06
95.36
90.85
95.20
+ 0.31
zipper
97.08
69.31
97.62
97.82
98.06
98.54
96.85
96.21
97.24
0.07
Mean
97.17
75.01
96.44
96.79
97.71
97.25
94.93
96.29
97.61
0.64
21

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Published in Transactions on Machine Learning Research (09/2024)
Table 9: Anomaly segmentation performance based Pixel AUPRO on MVTee dataset.
CFLOW
DRÆM
Flo
PaDiM
PatchCore
RD
DFR
EfFA
ULSAD
Category
(2021)
(2021)
(2021
(2021)
(2022)
(2022)
(2020)
(2024)
(Ours)
bottle
94.19
50.05
92.0
95.11
92.28
95.12
83.14
93.84
90.16 3.24
cable
85.85
28.58
86.65
89.65
90.77
90.32
83.09
92.53
88.63 + 0.48
capsule
90.47
81.11
90.15
92.62
92.4
93.93
96.33
91.09
93.77 77 + 0.16
carpet
92.64
48.64
94.63
95.59
92.7
96.41
95.47
90.99
96.39 + 0.24
grid
90.52
17.71
93.95
82.52
89.46
96.39
91.15
93.14
83.3 4: 3.96
hazelnut
96. 12
76.19
93.92
92.95
94.44
96.92
97.17
83.25
94.87 0.3
leather
98.39
52.1
99.06
97.91
96.33
97.97
98.34
97.32
97.44 4: 0.01
metal mut.
88.97
35.79
85.89
90.45
91.9
94.4
87.01
92.97
91.58 + 0.19
pill
93.67
64.26
91.0
93.88
93.92
94.76
95.86
95.93
94.5
screw
90.25
53.22
68.6
92.14
95.39
97.05
95.96
96.04
96.45 + 0.1
tile
91.49
58, 48
81.01
78.32
79.64
88.4
79.36
83.54
87.82 + 0.15
toothbrush
81.05
54.02
80.62
93.52
86.48
92.23
92.93
88.61
86. $6.28 + 0.46
transistor
78.75
51.37
88.92
89.04
94.06
75.05
64.25
82.82
91.61 + 0.68
wood
90.5
45.29
93.26
91.39
85.08
92.69
92.48
76.16
91.34 + 0.29
zipper
89.3
28.98
92.12
92.48
92.43
95.18
88.74
93.48
90.89
- 0.35
Mean
90.14
49.72
88.79
91.17
91.15
93.12
89.42
90.11
91.67
+ 1.36
Table 10: Anomaly detection performance based on Image AUROC on MVTecLOCO dataset.
CFLOW
DRÆM
FastFlow
PaDiM
PatchCore (2022)
RD
DFR
EfFAD (2024)
ULSAD
Category
(2021)
(2021)
(2021
(2021)
(2022)
(2020)
(Ours)
breakfast box
71.86
70.26
74.04
63.66
85.24
52.69
65.46
74.80
83.55
0.23
juice_ bottle
81.70
62.55
78.03
88.42
92.51
76.28
86.81
98.89
97.12
0.10
pushpius
73.43
51.32
61.20
61.30
75.54
50.72
72.68
80.58
86.85
0.94
screw bag
65.48
59.39
68.04
60.14
69.90
65.15
63.55
67.42
70.71
splicing__oonnectros connectors
75.63
68.25
73.71
68.40
84.24
62.95
75.87
81.39
82.30
Mean
73.62
62.35
71.00
68.38
81.49
61.56
72.87
80.62
84.1
Table 11: Anomaly segmentation performance based on Pixel AUROC on MVTeeLOCO dataset.
CFLOW
DRÆM
FlstFlow
PaDiM
PatchCore (2022)
RD
DFR
EFAD
ULSAD
Category
(2021)
(2021)
(2021
(2021)
(2022)
(2020)
(2024)
(Ours)
breakfast box
89.6
63.61
82.73
87.35
88.53
85.78
76.25
80.76
89.14
0.11
juice bottle
91.37
80.71
86.33
91.99
90.54
90.41
87.06
88.40
$9.07
pushpins
70.66
54.74
82.94
40.72
67.67
41.42
29.42
59.96
75.64
screw bag
69.94
65.23
58.07
65.35
62.40
67.33
59.74
61.64
71.35
splicing connectors
63.40
54.16
67.69
71.20
69.71
57.82
56.14
61.02
75.10
Mean
76.99
75.55
71.32
75.77
68
61.72
70.36
80.06
0.20
22

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Published in Transactions on Machine Learning Research (09/2024)
Table 12: Anomaly segmentation performance based on Pixel AUPRO on MVTecLOCO datasct.
CFLOW
DRÆM
FastFlow
PaDiM
PatchCore
RD
DFR
BEAD
ULSAD
Category
(2021)
(2021)
(2021
(2021)
(2022)
(2022)
(2020)
(2024)
(Ours)
breakfast box
67.27
36.11
63.8
74.28
73.08
69.67
63.56
58.44
71.36 0.38
juice bottle
80.75
51.51
77.90
88.78
85.42
84.95
82.88
86.51
87.72
pushpins
61.09
24.68
50.62
52.71
63.52
53.52
59.12
59.25
68.34
screw bag
54.39
31.27
38.1
61.42
56.12
59.66
71.66
62.45
66.52
0.33
splicingg_conneetiiiiie connectors
71.15
56.72
34.77
62.64
67.29
63.62
71.67
68.14
74.70
Mean
66.93
40.06
53.04
67.97
69.09
66.28
69.78
66.96
73.73 # 0.35
Table 13: Anomaly detection performance based on Image AUROC on MPDD dataset.
CFLOW
DRÆM
FastFlow
PaDiM
PatchCore
RD
DFR (2020)
EffAD (2024)
ULSAD
Category
(2021)
(2021)
(2021
(2021)
(2022)
(2022)
(Ours)
tubes
99.64
61.28
89.36
56.48
87.50
89.67
94.47
95.28
93.39 = 0.57
metal_ plate
97.42
80.05
86.92
42.69
99.72
91.87
68.31
100.0
93.81 = 0.28
connector
99.52
83.33
52.38
86.07
100.0
93.10
100.0
50.00
96.00
0.82
bracket white
79.89
84.00
50.78
80.33
89.67
83.67
54.55
96.48
100.0
bracket black
96.48
65.36
62.83
66.69
86.97
50.73
72.63
85.45
93.09 = 0.32
bracket. brown
49.70
70.81
47.89
78.66
95.78
68.70
88.54
85.32
98.08
0.14
Mean
87.11
74.14
65.03
68.48
93.27
79.62
79.75
85.42
95.73
0.45
Table 14: Anomaly segmentation performance based Pixel AUROC on MPDD dataset.
CFLOW
DRÆM
FastFlow
PaDiM
PatchCore
RD
DFR
EMTAD
ULSAD
Category
(2021)
(2021)
(2021
(2021)
(2022)
(2022)
(2020)
(2024)
(Ours)
tubes
99.15
76.87
98.44
91.35
98.45
99.08
98.62
98.98
98.55 0.10
metal mneta__patee
98.56
96.23
92.99
91.67
98.30
97-50
93.59
96.52
96.77
connector
97.38
90.01
92.69
97.93
99.11
98.55
98.68
99.32
99.40
bracket white
96.74
86.64
90.23
97.21
97.90
98.13
96.63 63
97.77
98.73 :: 0.1
bracket black
97.68
95.89
94.39
93.79
97.52
96.40
98.42
97.17
97.43 = 0.21
bracket brown
95.04
76.11
92.84
95.13
97.15
97.34
98.06
92.44
93.83
2.41
Mean
97.42
86.96
93.60
94.51
98.07
97.83
97.33
97.03
97.45
Table 15: Anomaly segmentation performance based on Pixel AUPRO on MPDD dataset.
CFLOW
DRÆM
FastFlow
PaDiM
PatchCore
RD
DFR (2020)
EtAAD (2024)
ULSAD
Category
(2021)
(2021)
(2021
(2021)
(2022)
(2022)
(Ours)
tubes
96.76
44.84
94.85
71.53
93.83
95.98
95.20
96.27
94.33
metal plate
91.53
82.83
74.62
75.47
92.50
92.00
83.99
83.59
90.07 = 0.22
connector
91.32
72.06
76.98
92.74
96.89
95.29
95.60
97.77
97.98
0.60
bhite
78.66
69.13
49.65
81.16
83.13
84.71
77.02
93.27
95.33
0.37
bracket black
89.48
93.12
79.65
83.51
93.65
89.14
95.57
89.98
90.17
0.67
bracket brown
83.62
58.29
85.62
82.69
85.07
94.04
95.37
81.77
84.24
Mean
88.56
70.04
76.89
81.18
90.84
91.86
90.46
90.44
92.02
2.64
23

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Published in Transactions on Machine Learning Research (09/2024)
Table 16: Anomaly detection performance based Image AUROC on BTAD dataset.
CFLOW
DRAE
Flow
PaDiM
PatchCore
RD
DFR
EffAD (2024)
ULSAD
Category
(2021)
(2021)
(2021
(2021)
(2022)
(2022)
(2020)
(Ours)
01
08.64
80.17
94.46
99.51
98.09
92.23
99.51
94.15
100.0 = 0.00
02
82.12
65.23
84.27
82.17
81.73
61.73
85.68
75.42
88.5 + 0.78
03
99.95
74.87
96.3
97.92
100.0
97.65
98.62
95.22
100.0
Mean
93.57
73.42
91.68
93.20
93.27
83.87
94.60
88.26
96.17 0.45
Table 17: Anomaly segmentation performance based on Pixel AUROC on BTAD dataset.
CFLOWW
DRÆM
Flow
PaDiM
CatchCore
RI
DFR
EfFAD
ULSAD
Category
(2021)
(2021)
(2021
(2021)
(2022)
(2022)
(2020)
(2024)
(Ours)
01
95.44
59.11
93.05
96.54
95.94
96.98
96.93
64.59
95.86 = 0.03
02
94.81
69.29
96.16
95.11
95.18
96.83
96.77
85.67
94.76 + 0.88
03
99.55
48.73
99.25
99.56
99.44
99.74
99.12
96.12
99.55 1. 0.02
Mean
96.60
59.04
96.15
97.07
96.85
97.85
97.62
82.13
96.73 +:
Table 18: Anomaly segmentation performance based on AUPRO on BTAD dataset.
CFLOW
DRÆM
FastFlow
PaDiM
PatchCore
RD
DFR (2020)
EffAD
ULSAD
Category
(2021)
(2021)
(2021
(2021)
(2022)
(2022)
(2024)
(Ours)
01
66.79
21.57
60.83
75.76
64.34
79.45
83.77
29.75
72.88 + 0.12
02
54.32
27.64
67.98
59.19
52.36
66.05
65.58
44.37
55. 16 + 6.83
03
98.21
18.24
96.99
98.45
97.76
98.92
27.83
88.98
98. 18 + 0.08
Mean
73.11
22.48
75.27
77.80
71.48
81.47
59.06
54.37
75.41 + 3.95
Table 19: Anomaly detection performance based on Image AUROC on VisA datasct.
CFLOW
DRÆM
FastFlow
PaDiM
PatchCore
RD
DFR (2020)
EHAD (2024)
ULSAD
Category
(2021)
(2021)
(2021
(2021)
(2022)
(2022)
(Ours)
candle
94.38
79.43
98. 18
86.19
98.59
85.54
89.65
80.52
87.11 = 0.29
capsules
69.9
72.77
81.05
61.72
69.92
87.37
76.75
63.73
79.61
0.72
cashew
94.7
95.5
87.78
90.91
96.29
85.38
93.80
96.11
94.72
chewinggum
99.02
83.68
95.18
98.20
99.29
81.92
99.22
98.27
99.49 0.12
fryum
92.98
70.46
92.60
85.06
93.5
77.94
96.58
95.70
95.86 0.14
macaronil
92.72
72.8
82.48
78.62
91.50
82.06
95.14
95.23
90.66 0.76
macaroni2
63.44
47.85
69.75
70.05
71.36
81.75
86.25
83.82
82.84 1.05
pebl
91.06
72.27
88.07
87.59
95.08
92.60
97.57
93. 78
92.92 0.11
peb2
79.95
91.17
86.47
83.20
92.46
87.57
91.55
94.95
93.67 0.18
peb3
82.23
81.29
81.47
72.79
92.46
90.87
97.27
95.92
93.62 -
pcb4
96.29
90.44
95.68
95.67
99.20
96.17
97.62
97.89
99.43 = 0.03
pipe fryum
96.54
75.32
96.16
89.28
98.07
85.68
98.36
98.59
99.61 0.11
Mean
87.77
77.75
87.49
83.28
91.48
86.24
85.18
91.21
92.46 0.45
24

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Published in Transactions on Machine Learning Research (09/2024)
Table 20: Anomaly segmentation performance based on Pixel AUROC
VisA dataset.
CFLOW
DR.EM
Flow
PaDiM
PatchCore
RD
DFR
EHAD (2024)
ULSAD
Category
(2021)
(2021)
(2021
(2021)
(2022)
(2022)
(2020)
(Ours)
candle
98.75
83.1
97.24
97.68
98.02
99.11
98.41
89.93
97.77
capsules
96.88
62.39
97.13
90.60
97.62
99.56
99.13
96.93
98.31 = 0.31
cashew
99.25
74.17
98.57
97.45
98.88
97.23
95.63
98.85
99.49 0.02
chewinggum
99.02
84.11
98.83
98.82
98.72
99.37
99.16
98.69
98.10
fryum
97.08
85.7
93.20
96.20
94.30
96.33
95.45
96.52
97. 0.19
macaronil
98. 71
63.95
98.60
97.85
98.13
99.48
99.73
99.59
99.00 0.13
macaroni2
97.35
79.02
94.65
95.40
96.79
99.33
99.43
98.84
98.20 0.25
pebl
99.05
27.98
99.29
98.67
99.47
99.65
99.30
98.98
99.61
pcb2
96.40
59.49
97.12
98.12
97.72
98.28
96.13
98.37
98.03 = 0.09
pcb3
97.23
76.43
97.
98.06
98.13
98.98
97.99
98.91
98.45
0.05
pcb4
97.97
83.42
97.51
97.00
97.83
98.29
96.58
95.49
95.22
pipe fryum
98.79
75.99
98.72
99.19
98.68
98.6
97.97
98.99
99.29
0.03
Mean
98.04
71.31
97.32
97.09
97.93
98.68
97.90
97.51
98,24
0.20
Table 21: Anomaly segmentation performance based on AUPRO on VisA dataset.
CFLOW
DR.EM
FlstFlow
PaDiM
PatchCore
RD
DFR (2020)
EIID
ULSAD
Category
(2021)
(2021)
(2021
(2021)
(2022)
(2022)
(2024)
(Ours)
candle
92.7
80.29
91.65
92.77
94.08
95.30
95.56
77.31
92.49 0.15
capsules
74.64
34.4
81.8
48.42
68.88
92.20
92.09
82.76 + 1.18
cashew
93.0
48.33
85.54
82.36
88.01
91.81
90.51
91.57
91.85 4: 1.15
chewinggum
89.58
62.66
84.69
84.33
83.86
88.57
85.52
74.87
84.34 1.0
fryum
85.62
71.94
72.39
75.54
78.25
84.8
92.08
82.93
85.47 + 0.66
macaronil
89.46
63.37
91.89
88.55
91.74
95.53
97.59
96.06
92.8 0.74
macaroni2
78.74
56.69
71.94
75.76
87.49
94.01
94.23
89.74
88.29 1.89
pcbl
87.24
27.43
85.89
86.39
89.07
95.0
93.55
90.53
90.22 - 0.28
pcb2
77.83
33.99
77.99
83.68
83.00
89.17
87.26
90.43
84.53 + 0.53
peb3
75.03
71.9
71.33
81.37
79.69
90.89
92.48
92.08
85.86
0.38
pcb1
86.53
73.26
83.41
82.17
84.91
89.17
84.38
75.25
73.37
pipe fryum
93.14
31.86
81.89
87.99
92.42
94.76
95.46
68.77
93.49 + 0.08
Mean
85.29
54.68
81.70
80.80
85.12
91.77
91.72
84.45
87.12 + 0.89
25

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Published in Transactions on Machine Learning Research (09/2024))
Podim
anomalles
EmcienzZD
PastF
Podim
Cotch
Reverse
rgicall
Ground
Dreem
Postf
Pedim
PatchCore
Raverse Fidd lietion
SAD
Stuctura anomalies
Ground Truth
CFlow
Draem
EffiiinttD
RistF ev
Podim
PatchCore
Reverse DiSt llation
U.SAD
orical anoma les
Ground Truth
CRlww
Dreem
EmfcienntD
FastF on
Podim
PatchCore
Reverse Dist flatonn
U.SAD
structura anomalies
Ground Thuth
CTTow
Dreem
ETTicenAAD
FastT DY
Padim
PatchCCre
Raverse Dist Flnteen
ULSAAD
ogicill anoma
Ground Bruth
Cliow
Droatt:
EfficinEA
Fasdl DY
Paeditt
PatchCCre
Raverne Didd Elation
ULSSD
auuctua anomalies
Ground Fuuth
Cflow
Dreem
EfficienADD
RootF ow
Padim
FandhCare
Reverse Dist llosion
ULSAD
nnicall anomales les
Ground Truth
CFiww
Dreem
EMficent2D
RadfF oz
Padim
PetchCCrn
Reverse Ditt lattion
dtustune ansmelis
Cheem
Redim
Uld
Figure 9: Visualization of anomaly maps on anomalous images from MVTecLOCO dataset.
26

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Published in Transactions on Machine Learning Research (09/2024)
B.1 Performance MVTecLOCO: Logical and Structural AD
In Tables 22, 23, 24, 25, 26, and 27, we report the anomaly detection and localization results MVTec LOCO separately for structural and logical anomalies. It can be observed that although PatchCore performs slightly better than ULSAD on structural anomalics, ULSAD delivers competitive results on logical anomalics. Moreover, as discussed previously in Section 5, the improvement in performance with PatchCore comes with three times the memory requirement. Therefore, we consider ULSAD be an efficient and effective approach for the detection and localization of both logical and structural anomalies.
Table 22: Anomaly detection performance based on Image AUROC on structural anomalies of MVTecLOCO dataset.
CFLOW
DRÆM
FastFlow
PaDiM
PatchCore
RD
DFR
EffAD
ULSAD
Category
(2021)
(2021)
(2021
(2021)
(2022)
(2022)
(2020)
(2024)
(Ours)
breakfast box
62.3
75.37
71.67
64.17
84.3
48.74
58.67
69.04
81.94 A: 0.74
juice_bottle bottle
73.45
52.18
76.52
86.17
96.47
78.
62.75
99.71
95.53
0.45
pushpins
71.03
66.51
60.17
72.4
77.42
50.17
40.06
92.07
85.17 17 0.65
screw bag
78.0
69.78
75.07
67.7
86.79
80.35
57.76
82.2
83.01
1.58
splicing connectors
74.35
80.33
70.31
66.85
88.67
63.04
55.84
90.2
80.59
0.35
Mean
71.83
68,83
70.75
71.46
86.73
64.12
55.02
86.64
85.25
Table 23: Anomaly segmentation performance based on Pixel AUROC on structural anomalies of MVTecLOCO dataset.
CFLOW
DRÆM
Fls
PaDiM
PatchCore
RD
DFR
RfADD
ULSAD
Category
(2021)
(2021)
(2021
(2021)
(2022)
(2022)
(2020)
(2024)
(Ours)
breakfast box
94.72
61.6
84.86
88.41
94.31
91.75
82.79
67.36
95.35
juice bottle
88,81
83.75
85.67
90.73
95.98
89.57
80.74
97.2
89.67
pushpins
91.4
46.14
85.54
90.82
95.16
87.83
48.52
89.48
88 38.38
bag
95.37
72.27
91.74
94.97
97.45
97.78
66.67
97.37
97.66
splicing__onneeetiee connectors
98.3
93.03
95.79
96.25
98.82
97.25
91.82
98.55
98.3
Mean
93.72
71.36
88.72
92.24
96.34
92.84
74.12
90.0
93.87
4 0.2
Table 24: Anomaly segmentation performance based MVTecLOCO dataset.
Pixel AUPRO on structural anomalies of
CFLOW
DRÆM (2021)
Flst
PaDiM
PatchCore (2022)
RD
DER
EifAD
ULSAD
Category
(2021)
(2021
(2021)
(2022)
(2020)
(2024)
(Ours)
breakfast box
41.92
71.29
81.97
78.71
76.67
26.67
65.87
75.43 1 0.67
juice_bottle bottle
80.56
50.44
87.61
92.64
90.81
61.67
92.08
# 0.31
pushpins
68.34
20.04
61.72
70.01
75.88
62.66
45.30
78.62
68.34
= 0.84
screw bag
82.07
39.41
73.69
85.1
88,92
93.
53. 53.95
91.38
91.98
: 0.73
splicing connectors
87.75
68.61
67.8
82.35
91.69
83.57
63.44
94.19
90.84
0.35
Mean
77.74
44.08
72.42
82.41
86.06
81.49
50.21
84.43
83.34
0.62
27

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Published in Transactions on Machine Learning Research (09/2024)
Table 25: Anomaly detection performance based on Image AUROC on logical anomalies of MVTecLOCO
dataset.
CFLOW
DRÆM
FastFlow
PaDiM
PatchCore
RD
DFR
DEAD
ULSAD
Category
(2021)
(2021)
(2021
(2021)
(2022)
(2022)
(2020)
(2024)
(Ours)
breakfast box
76.86
68.71
75.81
62.0
83.43
55.27
61.55
83.54
83.33 1.63
juice_ bottle
80.52
70.09
80.89
92.94
94.61
76.4
77.07
99.12
98.82
0.14
pushpins
71.15
37.9
58.81
50.72
74.53
52.98
60.27
72.0
85.23
screw bag
60.72
52.34
64.01
55.29
59.36
55.0
63.64
58.8
66.33
splicing__onneen connectors
67.5
56.15
74.54
69.43
80.27
61.74
53.10
75.64
86.27
Mean
71.35
57.04
70.81
66.08
78.11
60.3
63.13
77.82
84.0
Table 26: Anomaly segmentation performance based on Pixel AUROC on logical anomalies of MVTecLOCO
dataset.
CFLOW
DRÆM
FastFloo low
PaDiM
PatchCore
RD
DFR
EffAD (2024)
ULSAD (Ours)
Category
(2021)
(2021)
(2021
(2021)
(2022)
(2022)
(2020)
breakfast box
90.43
65.5
85.35
89.23
90.32
87.35
74.55
85.58
91.41 + 0.1
juice bottle
92.56
80.49
90.23
95.29
93.97
92.97
86.95
91.98
93.74 # 0.08
pushpins
70.38
56.06
82.91
41.95
69.39
41.86
67.93
61.12
75.96
1.11
screw bag
67.75
65.43
58.93
66.02
63.81
68.4
75.75
61.85
72.3
0.41
splicing__connectooe connectors
60.8
52.1
66.82
69.83
68.06
55.5
57.67
59.01
74.19 # 0.19
Mean
76.38
63.92
76.85
72.46
77.11
69.22
72.57
71.91
81.52
0.54
Table 27: Anomaly segmentation performance based on Pixel AUPRO logical anomalies of MVTecLOCO
dataset.
CFLOW
DRAM
Fast.Flow
PaDiM
PatchCore
RD
DFR
RFFADD
ULSAD
Category
(2021)
(2021)
(2021
(2021)
(2022)
(2022)
(2020)
(2024)
(Ours)
breakfast box
68.79
32.23
64.39
69.74
72.27
68.77
43.60
52.19
73.97
juice bottle
79.67
52.72
77.9
91.69
87.88
84.22
62.87
87.82
91.36
pushpins
59.07
26.21
47.71
51.93
63.47
53.84
41.80
58.36
68.78
1: 0.98
screw bag
50.7
25.58
53.92
46.8
48.72
54.59
52.8
61.48 4:
splicing connectors
65.86
53.71
26.66
57.66
62.21
58.85
34.72
62.7
72.66
0.27
Mean
64.82
38.37
48.45
64.99
66.53
62.88
47.52
62.77
73.65 4 0.61
28

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Published in Transactions on Machine Learning Research (09/2024)
C Extended Ablations
In this section, provide additional ablations on the local branch in Table 28 and the total architecture in Table 29. Lastly, in Table 30 provide the per-category results for the ablation the pre-trained backbone which is summarized in Figure 7.
Table 28: Abalations for local branch. Style: I-AUROC P-AUROC P-AUPRO.
estegory
A
0.01
0.5
A 0.9
breakfast
78.64
88.28
74.22
79.2
88.51
74.35
77.86
87.79
71.27
77.95
86.89
67.06
79.44
86.96
65.36
jutte_bottle
bottle
97.82
92.14
89.21
97.76
92.23
89.38
97.56
88.78
88.16
97.
84.39
84.63
97.08
83.61
83.47
pushpius
72.4
69.81
65.69
72.77
65.68
69.03
76.98
74.35
63.17
76.53
73.69
65.18
screw bag
66.42
66.6
64.39
67. 18
68.47
66.92
68.06
09.13
66.22
67.56
69.33
63.61
66.34
09.31
62.09
splicing
59.04
73.3
73.29
72.29 29
62.66
72.39
72.79
64.33
70.74
72.36
64.5
70.57
Mean
77.67
75.17
73.37
77.95
75.64
73.72
79.14
76.57
73.44
78.53
75.86
661.84
78.35
75.61
69.33
Table 29: Abalations for total architecture. Style: I-AUROC P-AUROC P-AUPRO.
category
Cig
Epg
Epgi
Lip
À
Ag
0.0
breakfast box
77.29
90.41
77.16
82.82
89.85
76.92
66.01
87.36
67.5
85.08
90.19
75.36
juice bottle
96.48
92.01
88.82
97.93
91.82
89.26
91.2
91.98
85.38
97.29
92.0
89.18
pushpins
70.89
80.89
70.67
78.66
88.09
79.11
74.67
77.37
58.75
74.61
85.86
76.33
screw bag
65.48
65.87
64.04
63.02
68.13
65.51
61.14
59.51
57.75
66.93
68.67
65.35
splicing connectors
78.29
69.68
75.61
84.55
72.71
76.54
65.31
53.4
66.74
81.5
73.11
76.01
Mean
77.69
79.77
75.26
81.4
82.12
77.47
71.67
73.92
67.22
81.08
81.97
76.45
A
A
0.5
breakfast box
79.22
90.87
78.32
82.45
88.49
71.03
71.36
87.64
67.38
83.36
89.34
72.36
juice_ bottle
96.3
91.17
88.89
98.08
87.06
88.05
91.14
91.84
85.92
97.46
88.81
87.71
pushpius
79.86
84.89
77.97
82.46
87.62
80.49
78.64
81.14
65.12
88.07
74.22
66.45
screw bag
66.58
68.83
66.11
65.11
70.04
62.81
62.09
67.32
62.92
70.6
71.58
67.01
splicing connectors
80.53
73.47
75.44
82.85
73.03
75.13
69.33
55.02
63.69
81.27
74.94
74.89
Mean
80.5
81.85
77.35
82.19
81.25
75.5
74.51
76.59
69.01
84.15
79.78
73.68
Table 30: Abalations for backbone on MvTec--OCO. Style: I-AUROC P-AUROC P-AUPRO.
Class
ResNet50
ResNet152
Wiide-ResNet50-2
Wide ResNet100-2
breakfast box
82.41
89.74
73.09
85.11
91.15
72.0
84.46
89.18
72.21
82.37
89.25
74.02
juice__ottee bottle
96.9
92.23
89.38
97.64
91.66
89.78
97.11
88.9
87.94
98.74
92.87
91.07
pushpins
81.79
79.49
75.15
73.28
76.49
63.71
85.48
75.46
67.82
82.48
76.55
70.67
screw bag
66.46
69.
67.01
68.06
68.63
66.97
71.14
71.57
66.82
73.1
68.99
66.88
splicing_coonectton
80.88
72.76
74.39
83.53
76.31
77.24
82.59
75.21
75.05
84.71
79.95
78.65
Mean
81.79
79.49
75.15
81.52
80.85
73.94
84.16
80.06
73.97
84.28
81.52
76.26
29


Reviews:
[{"review_id": "43XcQnh1Jj", "reviewer": "Reviewer_msCY", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "**Strengths**\n- Clearer performance improvements on more challenging cases (i.e.\n  MVTec-Loco including logical defects)\n- Generally clear exposition detailing the approach and the intended\n  purpose of each component and extension\n- Ablation tests to support the contribution of each component to\n  overall improvement\n- Code available and implemented in an AD framework which should\n  permit others to compare against this approach\n- Appendix provides relatively detailed performance information\n  (per-task in each dataset)\n\n**Weaknesses**\n- Relative performance on simpler structural-defect-only datasets\n  (those other than MVTec-Loco) is somewhat harder to judge,\n  improvements here, if any, are smaller\n- Could use additional discussion of trends in the results tables to\n  help readers understand them\n- Some measures appear to differ vs baseline works which tested on the\n  MVTec-Loco dataset. Comparisons here are self-consistent but this\n  may make it harder to compare results against other papers on that\n  dataset\n- Approach appears to be tuned (for ex. selection of parameters\n  lambda) on MVTec-Loco, which may contribute to reduced performance\n  on the other datasets", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper proposes a new approach to industrial anomaly detection\n(AD) capable of detecting both structural anomalies (local defects)\nand logical anomalies (requiring global analysis of the product). The\napproach extends an existing method, deep feature reconstruction\n(DFR), which uses features extracted by a pretrained network, to\nimprove identification of anomalies. Extensions include a modification\nof the loss to include the angular distance between network outputs\nand targets as well as a larger extension adding a second sub-network\nfor global analysis to detect logical anomalies. The authors test the\nnew approach on a variety of AD datasets and compare against existing\napproaches as a baseline, and perform ablation tests to measure the\nimprovements provided by the various components of the overall method.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "A couple things that I think would provide a nice improvement if they\nare feasible, then a few questions and minor notes. Overall, I\nappreciate the thorough ablation and tuning results.\n\n*[Important]* I think it would help contextualize performance if you\nare able to provide some estimate or discussion of the cost of ULSAD\nvs. some of the other approaches (in particular vs. nearest-neighbor\nmethods like PatchCore). You mention that the lack of a memory bank is\nan advantage which could compensate for slightly lower performance in\nsome cases. It would be nice to have some idea of how much of an\nadvantage this is, if possible (i.e. how much memory is saved by\nlosing the memory bank, or perhaps inference time improvements,\nsomething along those lines.). At least a rough idea to give readers\nsome context as to the costs of the memory or nearest neighbor search\non some of these tasks.\n\n*[Moderate]* It would be interesting to see the MVTec-Loco performance\nsplit between logical/structural errors if those results are\navailable, to compare performance against baselines between anomaly\ntypes. I understand, though, if this would not be possible without\nexcessive computational expense.\n\n*[Question]* among your baselines it appears that EfficientAD is the\nonly network that ran tests against MVTec-Loco, is that right?\n\n*[Question]* On the performance of EfficientAD vs. the source paper:\nthe original EfficientAD paper (Batzner, et al 2024) appears to report\nhigher anomaly detection performance on MVTec-Loco (roughly 90.0\naveraged across tasks) while your experiments hover closer to 80. Do\nyou know if you made any changes to the baseline that might account\nfor some of these differences?\n\nThe Batzner paper seems to indicate it uses AU-sPRO for the Loco\nresults, which may explain a difference for the segmentation; perhaps\nthere is something similar for the detection results. I don't doubt\nthat these are the results you obtained from testing, I am just\ncurious if you have thoughts on what might have produced the\ndifferences.\n\n*[Note]* the list of baselines in the body text under Table 2 is\nmissing EfficientAD.\n\n*[Note]* Are the tables of results in the appendices intended to have\n1st and 2nd place results bolded/underlined? This seems to only be\ntrue for some rows and tables.", "broader_impact_concerns": "No concerns", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "sghzHp6GoR", "reviewer": "Reviewer_xveU", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "**Strengths** \n\nThe authors address an important and challenging problem in machine learning. The paper is overall well written and the English level is satisfactory.\nThe proposed method improves upon state-of-the-art models in terms of AUROC for image-level anomaly detection. Segmentation-level performance is also promising, leading to results comparable to “Reverse Distillation.” \nThe paper includes several complementary evaluations demonstrating each component's role in their model, such as hyperparameters, backbone models, and loss terms.\n\n\n\n**Weaknesses**\n\nThe intuition behind some of the model components could be enhanced.\nThe proposed framework is based on several existing ideas. Nonetheless, I still consider the fusion of existing components into a new model a valid contribution to ML.  \n\nThe authors mention the advantage of their model in terms of memory and efficiency of computation, but I don’t see any such comparison in the paper between their model and existing schemes.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The authors address the problem of industrial anomaly detection, which is challenging due to the diversity of anomaly types. The proposed method relies on Deep Feature Reconstruction (DFR) and is designed to detect logical and structural anomalies. The model uses a pre-trained backbone for extracting features and contains global and local loss elements to detect both types of anomalies. The authors have evaluated their method using several datasets and compared them to recently proposed schemes. The results presented in the paper support the strength of the model both in terms of image level and pixel level anomaly detection capabilities. They further conduct an ablation to support each component of their model.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "On page 2, when you mention the pre-trained network \\theta, it is worthwhile to mention what type of architecture this is.\n\nPage 2, how are you selecting which layer $j$ to use?\n\nPage 2, the function f is simply a reshape?\n\nBased on section 3.2, I understand that the model is trained on clean samples. This type of training is often considered semi-supervised in AD. I believe this should be clarified early in the paper.\n\nFollowing the previous comment, have the authors evaluated the influence of contaminated training set on the performance? Are all baselines trained the same way?\n\nIt isn’t clear how \\tilde{U}’ and \\tilde{U}’’ are trained. The first seems like a simple reconstruction loss, but I don’t see an explanation for the latter.\n\nAn evaluation of memory and compute requirements is missing, especially in comparison to existing works.\n\nP11 “reverse distillation” is a name of a method? As such it should be capitalized.", "broader_impact_concerns": "No concerns", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "RNnU5IoDHV", "reviewer": "Reviewer_UCFP", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths.\n- ULSAD handles both structural and logical anomalies in the same frame work. \n\nWeakness\n\n- Novelty is limited or not clear for me. \n\nThe combination of L2 distance and cosine distance is the same as (Sahel et al., 2021) and there is no explanation why this combination improves performance. \n\nThe concept of attention-based loss seems to be similar to (Zhang et al, 2023)\n\n-\tOn Table 1, the performance of ULSAD is lower than DFR. \n-\tThe average segmentation performances of ULSAD on Table 2 are lower than state-of-the-art on several datasets.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper tackles Industrial Anomaly Detection (IAD) and handles structural anomalies (Bergmann et al., 2019) and logical anomalies (Bergmann et al., 2022). \nUnified framework for Logical and Structural Anomaly Detection (ULSAD) is proposed based on Deep Feature Reconstruction (DFR) (Yang 2020). Two modifications from DFR are proposed. \n- The combination of L2 distance and cosine distance between feature and reconstructed features is proposed for improving structural AD. \n- Attention-based loss based on global autoencoder-like network, is proposed for improving logical AD. \n\nThe experiments are conducted on 5 widely used datasets and compared with 8 SOTA methods.", "claims_and_evidence_yn": "No", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "-\tClarify the novelty of ULSAD. \n-\tCompare the model size and computational resources with SOTA methods to claim the computational efficiency. \n-\tExplain why adding $L_{pg}$ in the 3-th and 8-th rows of the results of Table 3 deceased the performance. \n-\tSec.3.3, proposes to use the cross-attention of Eq.(4) instead of the self-attention of Eq.(3). Compare these variants. \n-\tExplain what the difference of the last two rows of Table 3 is.", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: The authors have addressed all major concerns raised in the reviews. It is agreed that the paper is ready for publication.
Decision: Accept (poster)