METHOD FOR ANOMALITY DETECTION USING A GLOBAL LOCAL MODEL

Description

technical field

[0001] The present invention proposes a method for detecting anomalies in images. Prior art

[0002] Anomaly detection in images involves finding images, or regions of images, that do not conform to the rest of the data. This is an important problem in many industrial, medical, and biological applications. Detecting anomalies or defects on industrial objects is a complex problem that often requires operator intervention. This explains why visual or appearance quality control in production lines has historically been left to human operators. However, automating the process can accelerate production, reduce costs, and mitigate performance variations caused by operator fatigue [24, 33]. The problem remains a challenge for computer vision, though, because there is no clear and straightforward definition of normality in arbitrary data or of an anomaly in general, as use cases are highly varied.

[0003] Unsupervised anomaly detection for industrial applications has received considerable attention recently, particularly following the publication of a new reference dataset by MvTec [3]. The "unsupervised" requirement presents a challenge but could lead to a general solution. It is generally accepted that anomaly detection is not a classical classification problem

[30] . Indeed, anomalies do not form well-defined classes. They may be rare or inconsistent. New types of anomalies may appear later but must be detected as such based on past experience with normal data. This makes anomaly annotation inherently impossible. Conversely, normal data is abundant and can be used to model normality. This leads to viewing anomaly detection as a problem of detecting an event outside of a normal distribution.

[0004] Anomaly detection has been extensively reviewed in the literature [13, 23, 29]. The methods can be classified into three main categories: methods prior to deep learning, methods based on pre-trained networks, and finally, methods purely based on neural networks. Methods prior to deep learning

[0005] These methods focus on modeling normal data, also known as the background model. Homogeneous and stochastic methods [1, 12, 34, 35, 37] assume that the background model follows a known distribution. Center / environment methods [15, 16, 25] model anomalies as local events contrasting with their immediate surroundings. Sparsity-based methods [4, 6, 7, 21] learn a sparse dictionary representing normal data. Anomalies are defined as data that do not satisfy the sparsity condition. Nonlocal methods [10, 41] assume that each image patch in the normal data belongs to a dense cluster in the image patch space. Anomalies are located rather far from their nearest neighbors. Anomalies are measured by grouping small pieces of image, also called patches, which leads directly to a measure of sparsity.The method of Davy et al.

[10] bridges the gap with methods using pre-trained networks, as this method can be applied directly to image patches or to features of neural networks. Methods based on pre-trained networks.

[0006] Use of pre-trained networks. These methods use neural networks to integrate semantic information into the detection process. These networks can be pre-trained on general-purpose public databases such as COCO

[19] . SPADE [9] creates a feature database from a neural network pre-trained with reference images and uses the L2 standard between the features of an image and its K nearest neighbors, also known as kNN, in the reference database as a score. It involves features at different layers to perform multiscale analysis. MahaAD

[26] models each layer as a unique global Gaussian model. Anomalies are then detected by calculating and thresholding the Mahalanobis distance from this Gaussian. PaDim

[11] extends MahaAD

[26] by learning a positional Gaussian model instead of a global one. Neural networks and deep learning

[0007] Using a variational autoencoder (VAE), papers [1] and

[36] learn a representation of the normal data. To locate the anomaly, the Grad-cam attention technique

[32] is used: when the image is not an anomaly, attention should be uniform across the entire image; this changes when the image contains an anomaly. A weakly supervised version is also proposed. In

[17] , anomalies are found based on the distribution of gradients. Liu et al.

[20] propose a similar type of attention technique for detecting and locating the anomaly. In

[28] , a deep neural network is trained by minimizing the volume of a hypersphere surrounding the network representations of the data. Yi and Yoon

[38] suggest using image patches instead. The anomaly score is simply the distance between the encoded patch and its nearest neighbor. A P-style network is trained in

[40] .It learns to produce structural information from the image. The authors show that this information generally contains the anomaly and also helps during training to reconstruct the image. Li et al.

[28] use neural architecture search to find better deep learning architectures. Draem

[39] learns both a reconstruction model and a discriminating model using simulated anomalies. Aitor Artola et al. propose in [2] a neural normalization of the training set and then apply an anomaly detector based on the Non-Local Means algorithm. Finally, the most recent methods [14, 27] are based on stream normalization. Normalizing streams are invertible neural networks that learn a model transforming the data into a simpler, usually Gaussian, distribution. closest state of the art

[0008] With Padim

[11] , Defard et al. proposed learning a single multivariate Gaussian per pixel in a neural network feature space. Although they suggested reducing the dimensionality of the features using PCA or random selection, the dimensionality is still too large for most use cases. Indeed, the proposed dimensionality d = 100 or d = 550 would still require at least as many samples to estimate an unconstrained covariance matrix. This is not always possible in the MVTec dataset [3]. Moreover, potentially valuable information is lost by reducing the dimensionality. Another limitation of this model is the use of a single Gaussian at a given position. In fact, such a model could be too restrictive since it cannot model multimodal distributions.The publication "Deep Autoencoding Gaussian Mixture Model for Unsupervised Anomaly Detection", Bo Zong et al., ICLR 2018, also discloses an unsupervised anomaly detection method using a Gaussian mixture model.

[0009] One aim of the invention is to propose a method for detecting anomalies from descriptors which provides a solution to these problems. Description of the invention

[0010] According to a first aspect of the invention, an unsupervised anomaly detection method is proposed in one or a series of tested images, implemented by a computing unit, according to claim 1.

[0011] Preferably, conforming image data consists of features. Features can be extracted from a pre-trained neural network.

[0012] According to one possibility, conformal image data is extracted using Harris points or by means of wavelet decomposition.

[0013] Advantageously, the features can be extracted by a network pre-trained on aligned, so-called conformal, images.

[0014] Aligned conformal images can be determined by alignment to a reference image (Iref), or more generally a reference, from so-called conformal images.

[0015] Conformal image data can be pieces of conformal images.

[0016] The features can come from a wavelet decomposition of conformal images.

[0017] Determining the Gaussian mixture model of features can implement an online learning method.

[0018] Determining the Gaussian feature mixture model can implement a learning method with the K-MLE algorithm.

[0019] The method according to the invention focuses on modeling normal data. While state-of-the-art methods offered simple models based on Mahalanobis distance or heavy normalization of the flow network, the present invention proposes a global-local model that combines the flexibility of accurate local modeling with the robustness of a global Gaussian mixture model. The method according to the invention learns a global Gaussian mixture and then emulates a different model at each position by learning the mixture weights locally, thus avoiding the dimensionality issue when little data is available. Due to the sparsity of the model's weight maps, it is as efficient as the simpler models previously proposed and performs well on the MVTec dataset [3]. Description of the figures

[0020] Other advantages and features of the invention will become apparent upon reading the detailed description of implementations and embodiments, which are by no means limiting, with reference to the attached drawings in which: [ Fig.1 ] there [ Fig.1 ] illustrates a method for unsupervised anomaly detection according to the invention. Description of implementation methods

[0021] The embodiments described below are not exhaustive; variants of the invention may include only a selection of the described features, hereinafter isolated from the other described features, if this selection of features is sufficient to confer a technical advantage or to differentiate the invention from the prior art. This selection includes at least one feature, preferably functional, without structural details, or with only a portion of the structural details if this portion alone is sufficient to confer a technical advantage or to differentiate the invention from the prior art.

[0022] In the figures, an element appearing in several figures retains the same reference.

[0023] Inspired by image denoising methods, this description proposes to leverage the redundancy of structures in objects to learn a more accurate and expressive model than a single Gaussian, even under data constraints. Indeed, to overcome data limitations, non-local methods such as [5] take advantage of the redundancy, also called self-similarity, of natural images to estimate clean data models. This is why we propose the global-local model summarized in [ Fig.1 which we will present next.

[0024] As seen on [ Fig.1 ], the process includes a training step Ee and an inference step Ei.

[0025] In the example shown, the training step Ee includes: an optional step of aligning conforming images Inorm with respect to a reference image Iref, the step being optional in that it can be carried out prior to the implementation of the process according to the invention, an optional step of extracting ECNN features (also called image descriptors) on the aligned conforming images, the step being optional in that it can be carried out prior to the implementation of the process according to the invention, and also that it may or may not be carried out.

[0026] When the optional ECNN feature extraction step is implemented, the preferred but not exclusive mode of feature extraction proceeds by applying a pre-trained neural network to the aligned conformal images. Conformal image alignment

[0027] The conformal image alignment step is a step of normalizing the position of an image relative to a reference image.

[0028] Position normalization can be performed using an inverse compositional alignment algorithm (for English inverse compositional alignment ) and / or methods at times. These processes are known to those skilled in the art and will not be described further. Extracting the features

[0029] The feature extraction step receives aligned conformal images as input.

[0030] Feature extraction can be done from a neural network.

[0031] For example, this extraction can be performed using a neural network with 3 layers. Of course, other layer levels can be considered.

[0032] Advantageously, the neural network can be pre-trained. For example, it can be pre-trained on databases that are not specific to the use case addressed by the process.

[0033] Alternatively, the neural network can be trained on conformal images, including but not limited to the use of a normalization neural network or an image reconstruction neural network. Stage Ei

[0034] The Ei stage also includes the following steps: to determine (EGMM) a global Gaussian mixture model from conformal image data, said K-component Gaussian mixture exhibiting a set of Θ = ( π k , µ k , Σ k ) k= 1... K of parameters, such as for a given k, µ k is the average and Σ k the covariance of the Gaussian, π k being the weight of this Gaussian in said global model, for each Gaussian in the mixture of Gaussians, determine (ELWM) a set of local weights π k ( x ) to the position x,while keeping the covariance matrices and means fixed (to obtain a localization of the global Gaussian mixture model), determine a global model (EGLM) resulting by replacing the set of Gaussian mixture weights with the set of local weights determined.

[0035] Conformal image data can be conformal images. Alternatively, conformal image data can be conformal image features, obtained using one of the feature extraction methods.

[0036] Step Ei optionally includes, prior to the step of determining the Gaussian mixture of features from the features, a step of initializing the Gaussian mixture. Mixing initiation step

[0037] Zoran and Weiss

[42] showed that a Gaussian mixture can accurately represent the entire space of conformal image patches. The present invention develops the use of a Gaussian mixture as a global model for the set of features extracted from a neural network applied to a set of conformal sample images. In what follows, Θ = ( π k , µ k , Σ k ) k= 1... K is used to designate a Gaussian mixture model K components such as for a k given, ( µ k , Σ k ) define a Gaussian with mean µ k and covariance Σ k . The weight of this Gaussian within the model is represented by π k . 4 / Determination of a Gaussian mixture model of characteristics

[0038] Traditionally, Gaussian mixtures are learned using the expectation maximization (EM) algorithm. However, this algorithm is slow when applied with many Gaussians in high-dimensional samples.

[0039] For each layer c, the parameters of the Gaussian mixture are learned iteratively, as described below.

[0040] Preferably, the present invention implements the alternative K-MLE algorithm

[22] , which works for exponential family mixtures. This algorithm is analogous to the K-means algorithm and generalizes by using the properties of exponential families. It is faster because it assigns each sample ui to a single Gaussian index zi and therefore does not involve all samples in the calculation of each parameter. Given a dataset ( u ) i=1,, N in dimension d,its iterative attribution steps are written z i t + 1 = argmin k ∈ 1 K u i − μ k t T Σ k t − 1 u i − μ k t + loglog Σ k t + 2 loglogπ k t

[0041] Next, considering the sets C k t + 1 = z i = k The algorithm separately calculates the empirical parameters of each Gaussian mixture by: π k t + 1 = C k t + 1 N , μ k t + 1 = ∑ u ∈ C k t + 1 u C k And Σ k t + 1 = ∑ u ∈ C k t + 1 u − μ k u − μ k T C k

[0042] As an alternative to this learning method, the K-MLE algorithm can also be used with an online learning method

[31] .

[0043] Gaussian distributions with fewer than two samples are removed.

[0044] A regularization εId with ε > 0 is added the covariance estimated by the sample covariance estimator to estimate the covariance matrices.

[0045] According to a preferred embodiment, the method includes a shrinking regularizer [9] which takes the form of a convex combination of the empirical covariance of the samples Ŝ and the mean of its eigenvalues ​​multiplied by the identity F ^ = Tr Σ ^ d Id .

[0046] The convex coefficient ρ is chosen to minimize the expected mean squared error between the theoretical covariance Σ and its regularized estimator Σ̂ . E Σ − Σ ^ F 2 ρ tel que Σ ^ = 1 − ρ S ^ + ρ F ^

[0047] The optimal solution to the problem is the oracle. ρ 0. However, it requires knowledge of the theoretical covariance to be estimated. ρ 0 = E Σ − S ^ F ^ − S ^ E Σ ^ − F ^ F 2 ρ 0 = 1 − 2 d Tr Σ 2 + Tr 2 Σ N + 1 − 2 d Tr Σ 2 + 1 − N d Tr 2 Σ

[0048] Preferably, the Oracle Approximating Shrinkage (OAS) estimator [8] is used, which is better in terms of mean squared error when N d. This iterative estimator is defined as follows ρ j = 1 − 2 d Tr Σ ^ j S ^ + Tr 2 Σ ^ j N + 1 − 2 d Tr Σ ^ j Σ ^ + 1 − N d Tr 2 Σ ^ j Σ ^ j = 1 − ρ j S ^ + ρ j F ^ and we show that it converges to a limit ρ OAS equivalent defined by ρ OAS = 1 − 2 d Tr S ^ 2 + Tr 2 S ^ j N + 1 − 2 d Tr S ^ 2 Tr 2 S ^ d Return to the local model (ELWM)

[0049] At this stage, the Gaussian mixture model is global, and the probability of occurrence of each feature does not depend on its position. This simplification is excessive. It is clear that a feature can be normal at one position and anomalous at another. This is why we propose a method to add location information to the model, taking advantage of a prior alignment of the tested objects.

[0050] It is now described how, for each Gaussian of the Gaussian mixture model, one determines (ELWM) a set of local weights to obtain a localization of the global Gaussian mixture model.

[0051] The inventors adapted the k-MLE algorithm to learn the local weight map while maintaining fixed covariance matrices and means. If um ( x ) denotes the sample vector of the image m at position x, we obtain z i t + 1 x = argmin k ∈ 1 N u m x − μ k T Σ k − 1 u m x − μ k + log Σ k + 2 log π k t x C k t + 1 x = z m t + 1 x = k , ∀ m π k t + 1 x = C k t + 1 x N

[0052] To obtain more samples per position and reduce the number of false alarms caused by small deformations or slight variations in object position, the inventors propose to perform the x-weight calculation using the samples in a small circle of radius r centered on x. The value of r can, for example, be predetermined and equal to 1 pixel. EGLM Stage

[0053] To avoid overly localized analysis, according to one possibility of the invention, the global learned parameters ( µ k , Σ k ) Gaussian distributions are preserved, but it is proposed to deduce the mixture weights π k ( x ) dependent on the position from the Gaussian mixture. Inference step Ei

[0054] The interference step involves determining an anomaly score by applying said global model to one or a series of tested images.

[0055] During the test, the probability of a feature occurring at a specific position is estimated using the global-local model. An overall score and a decision are derived from the probability map.

[0056] Traditionally, samples are assigned to the nearest Gaussian to detect anomalies. The Mahalanobis distance to this Gaussian is then measured. However, this assignment ignores interactions between Gaussians. Yet, multivariate Gaussians in a mixture can have strong interactions and local maxima that differ from the centers of the Gaussians.

[0057] The Gaussian mixture model is the preferred mixture model in the invention, however the process can implement other mixture models from exponential families.

[0058] According to the invention, it is proposed to consider the mixture as a whole when analyzing a new sample Ei. Using the global-local model, the method involves calculating a probability Ec for each characteristic vector of an image using the mixture, thus forming a probability map. The image characteristic vector is obtained using the pre-trained neural network, from the aligned image Ec.

[0059] Most recent methods typically evaluate the image using the worst value (i.e., the lowest probability) of that map. The inventors propose using the quantile q, which is more robust with regard to false alarms.

[0060] The proposed method can also be made multiscale by taking characteristics from different layers of a network. To do this, the method includes a step of adjusting the mixture at each selected layer. The method then involves aggregating the probability maps by taking their product, which corresponds to assuming the independence of the layers.

[0061] The score is determined from the probabilities sorted in ascending order in the masked, and selection according to the q-quantile of these probabilities as being the score.

[0062] Of course, the invention is not limited to the examples just described, and many modifications can be made to these examples without departing from the scope of the invention. Furthermore, the various features, forms, variants, and embodiments of the invention can be combined in various ways, provided they are not incompatible or mutually exclusive. References

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Claims

1. Unsupervised method for detecting anomalies in an image or a series of images under test, which method is implemented by a computing unit, comprising the following steps: • a step (Ee) of determining a model from so-called conformal images, • an inference step (Ei) comprising determining an anomaly score by applying said model to said image or to the series of images under test, the model determination step comprising the following step: • determining (EGMM) a global Gaussian mixture model from conformal image data, said K-component Gaussian model having a set Θ = (πk, µk, Σk)k=1...K of parameters such that, for a given k, µk is the average and Σk is the covariance of the Gaussian, πk being the weight of this Gaussian in said global model, characterized in that the model determination step also comprises the following steps: • for each Gaussian of said Gaussian mixture, determining (ELWM) a set of local weights πk(x) at the position x while preserving the covariance matrices and fixed averages, • determining a local model, a so-called global local model (EGLM), by replacing the set of weights of the Gaussian mixture with the set of determined local weights.

2. Method according to claim 1, wherein the conformal image data are features.

3. Method according to claim 2, wherein the features are extracted from a pre-trained neural network.

4. Method according to claim 3, wherein the features are extracted (ECnn) by a network pre-trained using aligned, so-called conformal images.

5. Method according to claim 4, wherein the aligned conformal images are determined by alignment with a reference image (Iref) from the so-called conformal images.

6. Method according to claim 1, wherein the conformal image data are pieces of the conformal images.

7. Method according to claim 2, wherein the features originate from a wavelet decomposition of the conformal images.

8. Method according to any of the preceding claims, wherein determining (EGMM) the Gaussian mixture model of the features implements an online learning method.

9. Method according to any of the preceding claims, wherein determining (EGMM) the Gaussian mixture model of the features implements a learning method with the K-MLE algorithm.