We describe a method for detecting anomalous faces in images. Our method uses a novel representation of appearance (auto-encoder residuals), and does not require any example anomaly in training. We demonstrate that our method significantly improves over a number of natural baselines.
Detecting anomalous faces has important applications. For instance, a machine operator might fall asleep or have a heart attack. Ideally, a monitoring system would identify this kind of problem by watching the operator’s face and trigger some form of intervention. The crucial difficulty in building such a system is that there aren’t datasets showing (say) people having heart attacks. Moreover, a reliable anomaly detection system must be built without seeing actual anomalies to generalize well.
This example presents serious difficulties for current methods for anomaly detection (briefly reviewed below), because previous anomaly detection systems tend to be evaluated on datasets where anomalies are very different from typical examples. But anomalous faces look quite similar to typical faces. Our method requires a representation of face appearance which exaggerates the relatively small changes that make a face image anomalous, without actually being shown. Worse, because face images are relatively high dimensional, there is no practical prospect of simply applying a density estimator to the example images. Our strategy is to learn a compression procedure that reconstructs faces well, but not other similar unseen images, and then look at the residuals. This is not a routine application because one must be sure that (a) training images reconstruct well (routine) but (b) other similar images do not (tricky, and unusual). We show that a carefully designed residual of a specially trained autoencoder has these two properties and therefore provides a strong feature for identifying facial anomalies.
Contributions: We augment the Celeb-A dataset (Liu et al., 2015) for evaluating image anomaly detection. We present a novel feature learning approach for anomaly detection using inpainting auto-encoders. We build a dataset of real anomalous faces and real typical faces to evaluate the proposed framework. We demonstrate that our feature works well in both supervised and unsupervised applications.
Anomaly detection has widespread applications, including: image matting (Hasler et al., 2003); identifying cancerous tissue (Alpert & Kisilev, 2014); finding problems in textiles (Serdaroglu et al., 2006; Mak et al., 2005); and preventing face spoofing (Arashloo et al., 2017). There is a recent survey in (Chandola et al., 2009)
. There are two distinct types of approach in the literature. In one approach, examples of both inliers and outliers are available, and discriminative procedures can be used to build representations and identify and select features. In the other, one can model only inliers, and anomalies are available only at test time.
Face anomaly detection
is a good example problem because (a) data resources of typical faces are abundant and (b) anomalous faces look a lot like typical faces; trivial methods perform poorly. We do not assume that anomalous faces are available at training time, because doing so creates two problems. First, anomalous face images are rare (which is why they’re anomalous) and highly variable in appearance, so a dataset of reasonable size is difficult to build. Second, the estimate of the decision boundary produced by any particular set of anomalous face images is likely to be inaccurate. The location of the decision boundary is determined by both the anomalies and the typical images; but the anomalies must be severely undersampled, and so contribute significant variance to the estimate of the decision boundary.
Instead, we assume that only typical faces are available at training time. We must now build some form of distribution model for true faces and exploit it to tell how uncommon the current image is. We focus on building a feature construction that allows simple mechanisms to compute an anomaly score. An alternative is to use a kernel method to build a distribution model (the one-class SVM of (Schölkopf et al., 2000)). We use this method as a baseline.
Our feature construction uses an autoencoder (Hinton & Salakhutdinov, 2006). Auto encoders use an encoder to compress a signal to a code, which can then be decompressed. The code is a low dimensional representation of content which has been shown to be useul for tasks such as: appearance editing (Yan et al., 2016; Lample et al., 2017); inpainting (Pathak et al., 2016)
; and colorization(Deshpande et al., 2017). Generative adversarial networks (GAN) (Goodfellow et al., 2014) have been used for anomaly detection in (Schlegl et al., 2017), but one must build a distribution for the code. (Schlegl et al., 2017) do explore using residuals in combination with the code likelihood. However, because their model is built on a GAN, their inference procedure is quite expensive, requiring many backprop and gradient steps, while our method is simply a forward run through an autoencoder. Our model also introduces a novel inpainting conditioning strategy for feature construction.
Evaluating anomaly detectors is tricky, because anomalies are rare. One strategy is to regard one class of image as typical, and another as anomalous. This strategy is popular (Zhai et al., 2016; Kliger & Fleishman, 2018; Deecke et al., 2018; Jindong Gu & Tresp, 2018) but may mislead. The danger is that one may unknowingly work with two very different classes, meaning that the quality of the distribution model for the typical class is not tested. In contrast, face anomaly detection has the advantage of being (a) intrinsically useful and (b) clearly difficult.
The set building method of (Zaheer et al., 2017) could be applied to face anomaly detection. This approach has been shown to be accurate at identifying the one special face in a set of 16. A direct comparison is not possible, because their method relies on identifying the one different face in a set (i.e. given 15 smiling faces and one frowning face, it should mark the frowning face). However, we adopt their evaluation methodology and use analogous scoring methods.
3 Anomaly Features
We view anomaly detection as feature construction followed by a simple unsupervised method. Natural choices of feature constructions are autoencoder codes, pretrained discriminative models (eg (Cao et al., 2017)), or autoencoder residual features. An anomalous face image will look mostly like a typical face image, but will display some crucial differences. The problem is we don’t know where those differences are or what they look like. A natural strategy is based on a generative models of typical face images. Write for a test image, and for a learned model that produces the typical face image that is ‘closest’ to the query image. We could then use the difference to compute a score of anomaly. In practice, “peeking” by the learned model (details below) means that this approach fails. The learning procedure results in a model that is biased to produce a that is closer to than it should be.
A simple variant of this approach is extremely effective. Rather than requiring to make the closest typical image, we conceal part of from and require it to extrapolate. We then compare the extrapolated region to to produce the anomaly signal.
3.1 Autoencoder Residuals as Anomaly Signals
We will build using an autoencoder. Autoencoders construct low dimensional latent variable models from high dimensional signals. An encoder estimates the latent variable (code; ) for a given input ; a decoder recovers the signal from that code. The two are trained together, using criteria like the accuracy of the signal recovery (ie ; (Bengio et al., 2009)). Variational versions which use Bayes priors on the code have been explored as well (Kingma & Welling, 2014). As we show in table 1, the code produced by the encoder is a poor guide to anomaly, likely because it is still fairly high in dimension, and an appropriate distribution model is obscure (Schlegl et al., 2017). The autoencoder image reconstruction residual, , is an alternative.
Straightforward experiments establish that the residual is a poor anomaly signal (Figure 1). The reason is interesting. An autoencoder is trained to reproduce signals from its training set, but this regime does not necessarily discourage reproducing other images as well. An autoencoder that is trained to reproduce face images accurately has not been trained not
to reproduce (say) cat images accurately, too. This means the autoencoder could reduce the training loss by adopting a compression strategy that works for many kinds of images. Therefore, a compression procedure that is good at compressing face images is not necessarily bad at compressing other images. This problem is not confined to neural networks. For example, choice of principal components that represents face images well(Sirovich & Kirby, 1987) may represent (say) cat images. Denoising in current implementations (Vincent et al., 2010) does not cure this problem. For example, a good denoising strategy is to construct a large dictionary of patches, then report the closest patch to the input. While a dictionary built on faces may reproduce some classes of image poorly, there is no guarantee in the training loss. Requiring a ‘small’ code (Hinton & Zemel, 1994) or adding code regularization (Kingma & Welling, 2014) does not cure this problem either, because it is not known how to account for the information content of the code. As a result, the model built by the autoencoder is not guaranteed to report the typical face image that is ‘closest’ to the query image; instead, it may pass through some of the query image as well (‘peeking’ at the query image), so resulting in a small residual and a poor anomaly signal. Experimental experience suggests that neural networks quite reliably adopt unexpected strategies for minimizing loss (‘cheating’ during training), meaning that we expect peeking to occur, and figure 1 confirms that it does. Peeking can be overcome by forcing the autoencoder to fill in large holes in the query image.
4 Beating Peeking with Inpainting
Write for an operator that takes an image and overwrites a box with zeros; write for an operator that overwrites all but the box with zeros. These boxes will be quite large in practice. We will train an autoencoder as below. We build an anomaly feature vector by constructing for a variety of boxes (as below). We will then apply simple decision procedures to this feature.
This feature works because the autoencoder cannot peek into within the box. Instead, it must extrapolate into , and that extrapolation is difficult to produce for multiple classes. In turn, the extrapolate is a much better estimate of what a typical face image would look like within , conditioned on the rest of . For example, if spans a mouth, then the auto encoder constructs a typical mouth conditioned on the face and compares it with the observed mouth, and if the mouth is anomalous the residual will be large (Figure 1).
This is similar to the inpainting problem explored in (Pathak et al., 2016), though we do not use an adversarial loss. The autoencoder is trained to inpaint randomly selected boxes. We use as a training loss, thus requiring the autoencoder to inpaint. The only difference between this and a denoising regime is the size of the boxes, which is large compared to gaussian noise.
Our encoder and decoder use standard convolutional architectures with a fully connected layer for code construction. Average pooling is used for downsampling, and bilinear interpolation is used for upsampling. Following(Berthelot et al., 2017)
, we use a higher capacity network for the encoder than the decoder which seems to help with reconstructing higher frequency information. We use the elu non-linearity and batch normalization after each conv layer, and a tanh non-linearity on the output from the decoder. We use thenorm for our training loss.
5 Eyeglass Experiment
|Regularized Logistic Regressor|
|Feature||Resnet50||AE Code||Res Patch|
|Feature||Resnet50||AE Code||Res Patches|
|Feature||Resnet50||AE Code||Res Patches|
|Feature||Resnet50||AE Code||Res Patches|
to codes from the autoencoder and state of the art Resnet features trained on face detection. We note that Resnet features work extremely well for supervised tasks, in fact in our simple dataset, Resnet features combined with an
regularized logistic regression performs nearly perfectly. However Resnet features do not perform well for either of the unsupervised classifiers. On the other hand, the inpainting residual features perform better than the autoencoder code regardless of the classifier type, and perform far better than Resnet for unsupervised classifiers.
Poor feature performance on a supervised task suggests that unsupervised methods will perform poorly too. Therefore in evaluating feature constructions, it can be useful to compare to an oracle. To do so, we construct a proxy anomaly experiment, where anomalous faces are those wearing eyeglasses, so allowing discriminative training of the oracle. Our oracle takes the form of a supervised -regularized linear regressor (we use glmnet (Friedman et al., 2010)) trained on data. While poor performance on the oracle suggests that unsupervised methods will perform poorly too, good performance on the oracle is not necessarily indicative of good unsupervised performance. We therefore also explore natural choices for unsupervised methods including one-class SVM (Schölkopf et al., 2000), one-class density estimates such as Mahalanobis Distance (Mahalanobis, 1936)
, and heuristic methods such as thenorm which are meaningful for our residual based feature.
We use the Celeb-A dataset (Liu et al., 2015), which is a collection of thousands of labeled faces. As in (Berthelot et al., 2017), we filter and crop with the Viola-Jones face detector (Viola & Jones, 2001), resulting in frontal faces in tightly cropped 128x128 boxes. For this experiment, we use 7700 images of people wearing eyeglasses as anomalies and 7000 images without eyeglasses as our unsupervised training set. We train our inpainting autoencoder with random for each sample on 90% of the non-eyeglass data. During test we use the same model to construct autoencoder codes as well as the inpainting features. For inpainting features, we use 32x32 boxes in a regular grid. We exclude the boxes that would lie directly on the image boundary. For Resnet features we use a pretrained resnet trained on face recognition from (Cao et al., 2017)
, we remove the final softmax layer, and use the resulting network as a feature constructor.
Our results shown in table 1 suggest that inpainting autoencoder residuals contain sufficient information for attribute classification. One class SVM’s are not a strong baseline for this problem. Mahoanobis distance is a decent baseline for our features. Inpainting autoencoder residual images are informative, even with the simplest heuristic classifier . We also show that autoencoder codes are less adept than inpainting residuals.
It is not surprising that the classifier works so well. Each inpainting feature is a local anomaly detector for the content under the box. Since the inpainting autoencoder was trained on images without glasses, when the box covers the eyeglasses, the inpanted content will not have eyeglasses. Consequently, the residual will be large. Taking the norm reports the score from the most violated box. Note that this experiment is not a true anomaly experiment, but it is similar to previous work (Zhai et al., 2016; Kliger & Fleishman, 2018; Deecke et al., 2018; Jindong Gu & Tresp, 2018) which uses attributes or class labels as proxies for anomalies.
6 Anomaly Experiment
We wish to determine whether we can detect true anomalies in a realistic setting. We use the Celeb-A dataset as our training data, filtering and cropping for frontal faces using Viola-Jones as in section 5. However rather than considering any specific attribute, we consider the entire Celeb-A dataset as typical data. We set aside 30,000 images for use in test, leaving us with 125,253 images for training. For our anomaly images, we collect a 100 image anomaly dataset. This set, which we call the anomaly set is comprised of strange or “weird” faces (Figure 1(c)). It includes extreme makeup, masks, photoshops, and people making extreme faces. We pass the images through the same Viola-Jones detector and cropper. This rejects many of the anomaly images, and in fact we only have about a 3% yield on anomaly images, meaning that we had to find roughly 3000 anomaly images in order to get 100. However, this construction is sensible: if Viola-Jones does not believe the images have a face, then they are too obviously anomalous. For example, a photograph of a cat would have a high anomaly score under our method, but a cat is also not likely to be identified as a face by a competent detector, so determining it is an anomaly is not particularly important or difficult.
We also wish to determine if anomaly detection is caused by special features of the Celeb-A dataset. An anomaly detector which identifies any image not from Celeb-A would not be particularly useful. We therefore collect a typical set of 100 images we do not believe to be anomalous images. It is comprised of pictures of celebrities that were taken after Celeb-A was created so there are no overlaps in pictures (Figure 1(b)). We also tried to find new celebrities, so that the people would be less likely to have appeared in the original Celeb-A dataset. This dataset is used to validate that a method is not memorizing images in Celeb-A or finding a particular feature of Celeb-A and rejecting any new images.
We show samples from Celeb-A, the typical set and the anomaly set in figure 2. By example it is reasonable to ask an anomaly detection method to identify images from the anomaly set without identifying images from the typical set.
Our experiments are modeled on the set experiment presented in (Zaheer et al., 2017). They form a set of 16 images from Celeb-A where 15 images share at two attributes, and one image differs. The goal is to identify the image with different attributes. We adjust this slightly. Large sets are more indicative of performance for real world anomaly detection, where the goal is to identify one image in thousands rather than one image in ten. However, using large sets is significantly more difficult so we report recall at 1, 5, and 10 rather than just reporting recall at 1. Note that at no point does any method have access to labels, which are revealed only to evaluate the experiment. We believe this is a better model for detecting rare anomalies.
Evaluating anomaly detection: We select one image from the anomaly set, and between 15 and 299 images from the 30,000 celeb-A held out images (without consideration of attributes, in contrast to (Zaheer et al., 2017)). We then score each image using our feature and a variety of scoring methods (section 6.1) to evaluate recall for the anomaly image, averaged over 10,000 sets. As figure 4 shows, recall is strong even from large sets, and the choice of score appears not to matter.
Control: Strong results could be caused by some special feature of celeb-A images. To control for this possibility, we repeat the anomaly detection experiment, but replacing the image from the anomaly set with an image from the typical set (100 typical images not from celeb-A). If celeb-A were wholly representative, then this experiment should produce recalls at chance. As figure 4 shows, the results are not at chance (there is something interesting lurking in celeb-A), but recall is very much weaker than for anomalies. The performance of the anomaly detector cannot be explained by quirks of celeb-A
6.1 Unsupervised Feature Learning
We use our regular grid of residual features for 32x32 patches with a 32 pixel edge exclusion and explore a variety of methods for turning the residual features into an anomaly score. The norm over the feature vector makes up our main method due to its simplicity and good performance. It is not obvious that this is a good choice, and for a general feature, this norm would be largely meaningless. However, as demonstrated in the attribute classification task our features are designed to be well suited to this norm. For our feature, the norm finds the most violated residual from the set of patches, which is obviously useful for anomalies that tend to occur locally.
The Mahalanobis Distance (mahal) estimates a mean and covariance from a set and then measures distance with respect to the mean and covariance. It is typical to estimate the mean and covariance on training data.The Equivariant Transform (equivariant) introduced in (Zaheer et al., 2017) can be applied in an unsupervised manner on a set of images. A sensible version looks like the Mahalanobis Distance. Recall the equivariant transform in matrix form:
Which for an element is equivalent to
Let be the inverse covariance of , then and compute a transformation which under the is the Mahalanobis Distance. This transformation is sensible and can be applied to the data prior to applying the norm to reweight the feature dimensions and take into account that some dimensions might be highly varying while others are not. For our autoencoder residual feature, we assume that our features are IID, so we can estimate a diagonal covariance, and we compute a robust mean and covariance by eliminating the largest and smallest values on each feature. Note that this is done without knowing which item is anomalous and thus does not violate train-test splits.
The Local False Discovery Rate
(lfdr) is a construction that identifies the probability that an item comes from a null distribution, without knowing what the null is(Efron, 2007). The method originates in multiple hypothesis testing, assuming that most observations come from the null. Assume the null distribution is , the non-null is , and the prior an item comes from the null is . Then the lfdr is
Small values suggest an item is worth investigating (i.e., anomalous). Estimation is complicated by the fact that neither nor are known; but the assumption that is large, and
is ‘close’ to a standard normal distribution allows fairly accurate estimation. We used the R programlocfdr. We estimated local false discovery rates using all 30200 test data items (doing so does not involve knowing which item is anomalous, so does not violate test-train protocols). We estimate using a standardized version of the L-infinity score, and a standardized version of the log of the L-infinity score.
As seen in figure 4, our feature performs well regardless of feature transformation applied. We report performance from (Zaheer et al., 2017) on the graph, even though their experiment is on different data. While they outperform our method for 16 image sets, using our auto-encoder residual features, we identify anomalies at rates significantly greater than chance even as the size of the set increases. Resnet-50 features (Cao et al., 2017) with a Mahalanobis Distance represents a strong baseline, however, we outperform it. There does seem to be some bias in the Celeb-A dataset being used to identify anomalies but our features and the Resnet-50 features do not identify typical images at anywhere near the same rate as anomalies. The gap between performance on typical images and anomalous images is apparent and clearly significant (eg. 40 vs 20 percent for recall at 1 in a 16 image set).
For qualitative comparison, we show the median image from each decile ranked by their anomalous score in figure 3. We also show a plot of how frequently they are ranked in the top images in a set of increasing size. Anomaly images are frequently identified as the most anomalous image in a 16 image set and as a top 10 anomalous image in 128 image sets. Typical images are almost never identified as the most anomalous image in any set, and almost never identified as the top 10 in any set larger than 16. The median least anomalous image is roughly as anomalous as the median typical image. These findings are consistent with our quantitative results, which show that images from the anomalous set are identified frequently and images from the typical set are identified more often than chance, but frequently less often than true anomalies.
We introduce the inpainting autoencoder residual as a feature for combating the overgeneralization of compression losses. This allows us to train our method solely on non-anomalous data, mimicking how a real anomaly detector must be trained. We demonstrate that our inpainting residual features are useful and work well in supervised and unsupervised settings. Though we did not see improvement in performance, it is easy to use inpainting autoencoder features with various feature transformation techniques. We also describe a standard anomaly detection experiment for evaluating future anomaly work on image sets, enabled through the collect two small datasets to augment Celeb-A.
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