This paper focusses on anomaly detection using bio-inspired event-based cameras that register pixel-wise changes in brightness asynchronously in an efficient manner, which is radically different from how a conventional camera works. The asynchronous principle of operation endows event cameras     to capture high-speed motions (with temporal resolution in the order of ), high dynamic range () and sparse data. These low latency sensors have paved way to develop agile robotic applications , which was not feasible with conventional cameras. Only limited achievements have been accomplished in designing robust and accurate visual analytics algorithms for the event data, mainly because of unavailability of event cameras for commercial purposes and resultantly, dearth of large scale event datasets.
is a pervasive application of computer vision with its widespread applications as diverse as surveillance, intrusion detection etc. Anomaly detection can be posed as a foreground motion analytics task. This makes event camera an ideal candidate for video anomaly detection task as it comes with the ability to encode motion information at sensor level. WE argue that a vast majority of state-of-the-art frame-based anomaly detection networks rely on optical flow estimation orconvolution to explicitly model motion constraint to detect anomalies. It is pretty important to note that event cameras exhibits embedded motion information at the sensor level, which allows us to circumvent optical flow or convolution. Hence, direct application of existing conventional anomaly detection networks to event data is debatable.
In this paper, we introduce a solution towards solving event-based anomaly detection with a dual discriminator conditional Generative adversarial Network (cGAN), which has not been explored in prior works of event vision. Dual discriminator allows detection of spatial event anomalies, which would have not been feasible otherwise. However, data modality of event data does not directly fit this network due to its inherent difference from conventional cameras. State-of-the-art deep learning compatible event representations belong to feature engineering which mandates domain expertise. However, the advantages of deep learning to learn nested concepts from data has not been explored in event data representation. To alleviate this gap, we introduce a less computationally complex shallow encoder-decoder architecture (referred here as DL (Deep Learning) memory surface generation network) that learns a better latent-space sparse event representation while efficiently modeling motion analytics. To validate the efficacy of our algorithm, we introduce for the first time, a novel anomaly detection event dataset recorded from a type of event camera known as Dynamic Active Pixel Vision Sensor (DAVIS)  .
Event data representation:
The models that can cope with event data are biologically inspired neural networks acknowledged as Spiking Neural Networks (SNN). SNN has not become increasingly popular due to the lack of scalable training procedures. An alternative methodology followed in literature is an adaptation of event data to make them compatible with conventional networks.
Earlier works restrained themselves to encoding basic information such as polarity. In , list of events are converted into images by recording the occurrence of the recent event in the given time. The drawback of this representation is that it encodes solely the latest event information at each pixel value. In , a two-channel event image is created with histogram and of positive and negative events respectively. Storage of events of different polarity in different channels avoids the cancellation of events of opposite polarity at a given location. This choice proves to be better than that of . The predominant setback of the above basic strategies is that they discard the treasured time information that is obtained from event cameras.
Non-spatial time encodings contain useful motion information, including which will enhance the accuracy of vision algorithms. However, incorporating this information is a cumbersome task. In 
, time-stamp maps are created by using three distinctive techniques, pixel replication, temporal interpolation, and spatio-temporal correlation. These time-stamp maps are merged temporally for further processing, hence tending to lose the details of the time information obtained from the event camera.
In , the intensity image has been coded with the timestamp of each pixel of recent positive and negative events in the given integration time and around a spatial location of . This image was further used to construct features recognized as time surfaces. Following this,  encode the first two channels as number of positive and negative events that have occurred at each pixel and the last two channels as the time-stamp of the most recent positive and negative events. This representation discards all the other time information except that of the recent event. Moreover, this kind of encoding is very sensitive to noise.
 and  has attempted to improve the time channel information by expertly combining the time information. In , third channel stores average of the timestamp of the events that occurred at pixel in a given temporal window of size . 
improved it by allocating four channels that encode standard deviation of the timestamps of positive ad negative events (separately) that happened at that specific pixel in the given time intervalin addition to their average value.
Recently,  proposed an interesting approach to encode time information by introducing a representation (highly resistant to noise) known as memory surfaces which exponentially weighs the information carried by past events. Following this,  has proposed an event representation by discretizing the time domain. However, this representation might result in higher computational cost when applied on deep network has generated frames by accumulating constant number of events, thus claiming to have adaptive frame rate.
Anomaly Detection on Conventional Camera: As there is no prior work on event data anomaly detection, we briefly describe the frame-based deep learning algorithms for anomaly detection . Researchers build a statistical model (reconstruction modeling and predictive modeling) to characterize the normal samples and the actions that deviate from the estimated model are identified as anomalies.
The learning capability of deep networks used in reconstruction modelling      are too high that they don’t conform to the expectation of higher reconstruction error for abnormal events. This led to the new attractive phase of predictive models such as convolutional LSTM    and generative modeling. While convolutional LSTM learns the transformation required to predict the frames, generative models such as, Variational Auto-encoder (VAE)   and Generative Adversarial Network (GAN) 
, learn the probability distribution to generate the present from the history, which makes it a perfect candidate for anomaly detection. As this work is built on GAN, we limit our survey to GAN based conventional camera anomaly detection.
 proposed AnoGAN to identify the manifold of abnormal anatomical variability. AnoGAN is trained with a weighted sum of residual loss and discriminator loss (dissimilarity between intermediate feature representation of the original image and that of the reconstructed image). However, temporal information has been discarded in modeling anomalies.  proposed an anomaly detection framework that tries to model the anomalies based on motion inconsistency as well. The framework consists of two conditional GAN (cGAN)  networks, trained on cross channel tasks of generating frame of training video from the optical flow  and vice-versa. During test time, discriminators have been applied to detect anomalies. Similar architecture has been followed in . However, the significant distinction lies in the methodology used to detect possible anomalies.
 proposed a GAN solution by leveraging reconstruction loss, gradient loss and optical flow loss in addition to the adversarial loss. The constraint on the motion is modeled as the difference between the optical flow of predicted frames and the original frame. Recently,  has proposed 3D convolutional GAN to capture temporal information for anomaly detection. convolution increases the computational complexity of the network.
Contributions: In the context of the previous discussion, our contributions in this paper can be summarized as,
Event Data Representation: Shallow encoder-decoder module to generate an appropriate sparse representation of event data that inherently learns the temporal information from the data as opposed to state-of-the-art handcrafted features
2 Proposed Anomaly Detection Method
The pipeline of our event data prediction framework for anomaly detection is shown in Fig. 1. In our methodology, we present anomaly detection as a conditional generative problem that predicts future events conditioned on past events. To predict the future events, we train a dual discriminator conditional GAN with two discriminators (details of which is given in the forthcoming section), one under conditional setting and other under the unconditional setting. As the generator network of GAN is deep, the solution of predicting future events conditioned on the previous events will confront with computationally heavier model. To make the computation faster, we introduce a DL memory surface generation network (details of which are furnished in upcoming section), that tries to capture the coherence of motion from the given a set of events into a single structure known as DL memory surface, conditioned on which cGAN learns to predict the future events. To feed the DL memory surface network, we stack the events to produce a discretized volume (adapted from ), given a time duration and a set of discrete time bins each with duration.
2.1 DL Memory Surface Generation Network
In this work, we propose a novel event representation generated by a shallow, computationally inexpensive encoder-decoder network architecture with a loss function that comprises data term and sparsity term. Before dwelling into the loss function, we introduce the architecture of the encoder-decoder network.
2.1.1 Network Architecture
We adapt fully convolutional encoder-decoder architecture  with layers of the form convolution (with sigmoid activations) that maps a discretized volume of event data (explained above) to a single image known as DL memory surface with same spatial resolution at the bottleneck layer. The input and output are renderings of the discretized volume data.
In order to model only the temporal structure in the data without upsetting the spatial distribution, it is adequate if we restrict the convolution operation across the time dimension. Hence, we have constructed the network with convolution layers inspired by the papers , which was the first to introduce convolution. As studies have shown, CNN can learn complex tasks   with shallow architecture unlike its counterpart CNN, thereby resulting in ”small” network. We have utilized the potential of deep learning to model the motion, thereby capturing full information available from the data that they model in contrast to their state-of-the-art handcrafted frame generation counterparts.
2.1.2 Loss Function for Learning Temporal Information
The DL memory surface generation network tries to learn a function such that the target values is similar to that of the input , while the bottleneck layer models the temporal information encoded by the event camera. The architecture has two parts, encoder and decoder defined by the transformation functions and respectively with and being the parameters of decoder and encoder. As the event camera has built-in sparsity in data encoding, we would like to retain the sparsity in our encoding process as well. By placing sparsity constraints on the bottleneck layer, we will be able to discover an interesting representation that models the temporal information while preserving the sparse structure of the input event data. The addition of sparsity constraint to the loss function gives us the liberty to use shallow networks, but still force the network to learn more appropriate temporal information. The objective of the netwrok can be expressed as weighted sum of a data term and a sparsity term as follows,
In order to maximize the usefulness of the latent variable encoding, we put forth a data term that tries to model the probability distribution of getting the event discretized volume, , given the ideal DL memory surface, , by maximizing the forward divergence between the ideal distribution and our estimate (Eq. 2). Forward divergence will result in best latent variable that covers all the modes of probability distribution of normal videos.
As the first term does not depend on the estimated latent variable, it could be ignored. Hence, the second term of Eq. 2 boils down to maximizing the log likelihood of when the sample size tends to infinity. The output of the decoder can be modeled as a function of latent variable and noise as . This makes
a Gaussian distribution with mean. Thus maximizing the log likelihood turns out to minimizing
In order to impose sparsity constraint on the bottleneck layer, we define a sparsity term  as minimization of
Where, and are the spatial dimensions of the event data, is the Bernoulli probability distribution with parameter as low as . By modelling the probability distribution
as Bernoulli distribution with parameter, the divergence between the two Bernoulli distributions has an analytical expression as follows
Minimization of this will make sure that the output of encoder will be close to the sparsity parameter as much as possible.
2.2 Anomaly Detection Network
The framework adopted here is a dual discriminator conditional GAN architecture. A striking effect of stationary event camera under surveillance is that it captures moving objects alone, which results in inexpensive modeling of temporal anomalies. However, this has the effect of producing a silhouette of moving objects. Hence, cGAN results in poor characterization of spatial anomalies whose temporal modality overlaps with that of normal data. This could be attributed to the fact that cGAN penalizes the mismatch between input and output by modeling the joint distribution of input and output. In order to incentivize the detection of spatial anomalies in event data, we propose a variant of cGAN which pushes the generator distribution closer to the ground truth distribution while still sustaining the quality of match between input and output
We start this section with a brief review of conditional GAN architecture. For the sake of easy readability, we have used the notation and for and
respectively. Conditional GAN is a two-player game, wherein a discriminator takes two points x and y in data space and emits high probability indicating that they are samples from the data distribution, whereas a generator maps a noise vector z drawn fromand input sample drawn from to a sample that closely resembles the data . This is learned by solving the following minimax optimization
Preposition: For a fixed G, the optimal discriminator results in
With this given , the minimization of turns into minimizing the Jensen-Shannon divergence
Proof: Left hand side of Eq.2.2 can be expanded as
The above equation becomes
The optimal is estimated by differentiating the above equation with respect to and equating to zero,
On simplification, we get as given in Eq. 6. Substituting the optimum value of in the generator equation, it yields
Multiplying and dividing the terms inside by and using the fact , we get
The second and third term together is nothing but . Thus, the objective function of is minimized when
2.2.1 Dual Discriminator Loss Function of cGAN
We propose a three player game with two discriminators and and one generator. The disriminator sees the inputs and , whereas sees only . The new objective function becomes
Expanding as before, we get
By differentiating and equating to zero, we get the optimum values of and as Eq. 6 and as follows respectively
Substituting this optimal values and into the generator optimization function, we get
On simplification (as done for conventional conditional GAN), the above equation reduces to
The last four terms turns out to be sum of and . Hence generator achieves its minimum when and .
cGAN achieves optimum setting when , whereas dual discriminator cGAN enforces a constraint on the , which enables it to memorize the objects in the training set in addition to learning input-output image relation.
3 Experimental Validation
In this section, we provide the details of the dataset and the experiments conducted to validate the proposed algorithm
Although few event-based datasets are available for other vision-based tasks such as visual odometry , object recognition , there is no event-based dataset available for anomaly detection. To address this constraint and in order to evaluate the proposed algorithm, we introduce a new event dataset for anomaly detection. We present two variations of event dataset from two distinctive sets of environments, indoor lab environment, and outdoor corridor environment to set a realistic baseline for algorithm evaluation. This dataset is comprised of short event clips of pedestrian movements parallel to the camera plane, captured from static DAVIS camera with a resolution of . The normal and anomalous scenes are staged with typical training videos consisting of people walking, talking, sitting on a couch etc. The testing videos consist of the following variety of anomalous activities: people running, fighting, bending, and stealing bag. We summarize the statistics of the collected dataset in Table I.
|Sitting on sofa||11||Sitting on chair||3|
|Stealing bag||3||Stealing some object||3|
3.2 Evaluation Procedure
In this section, we evaluate different components of the proposed method on the event anomaly dataset proposed in this paper. We have conducted three different sets of experiments adapted to validate DL memory surface network, dual discriminator cGAN and anomaly detection system as a whole for varied event representations in literature.
3.2.1 Experiment A: DL Memory Surface
In this segment, we shed light on the qualitative and quantitative assessment of our proposed DL memory surface generation network on real event data. We applied the DL network on a training set of discretized event volumes of two different temporal classes, walking and running. Towards qualitative analysis, we provide the visualization (Fig. 2) of DL memory surfaces (of walking and running) and the temporal filters learnt by the network. The filters learned by the algorithm represent the different motion models of the events presented to the network.
To quantitatively evaluate the temporal modeling efficiency and sparsity of latent representation, we have conducted experiments that include tuning of the sparsity. As the sparsity acts as a regularizer, it could be demonstrated that an optimum sparsity is suitable for learning a better representation which could find its application in down-stream processing such as anomaly detection. Towards this, the DL memory surface network was trained on walking and running discretized event volumes with varied levels of sparsity imposed. Subsequent to freezing the model for each (Eq. 1
), DL memory surfaces are extracted from the bottleneck layer of the network for walking and running event volumes. To confirm the effectiveness of the temporal information captured by the proposed network, we evaluated it by examining the performance of them in classification task. Towards this, a convNet with 5 convolution layers and pooling layers, followed by 3 fully connected layers and a softmax output layer has been trained as two-class classifier with walking and running DL memory surfaces. Fig.3 (right) shows the classification accuracy for different levels of sparsity (). Higher accuracy for close to emphasizes the fact that an optimum sparsity enforces the network to learn the global motion model. Fig. 3 (left) shows the
t-SNE embedding of the features extracted from the last fully connected layer of the convNet trained with DL memory surfaces generated under optimum sparsity. Better clustering of feature is clearly evident.
3.2.2 Experiment B: Dual Discriminator cGAN
This section is dedicated to analysis of the dual discriminator cGAN in terms of anomaly detection subsequent to event prediction. In addition to this, we have also performed experiments to emphasize the role of unconditional discriminator in cGAN for anomaly detection. Towards this, a training set of normal activity clips such as pedestrians walking, talking, sitting, etc are provided to the network for learning the model.
Performance of dual discriminator cGAN: As part of qualitative validation, we provide the prediction output of the network for normal activity and abnormal activity in Fig. 4. It is evident that the prediction capability of the network is well pronounced for normal activities than that of anomalous activities.
So as to quantitatively evaluate the performance of the anomaly detection efficiency of dual discriminator cGAN, testing cases with intermittent events of abnormal activities such as running and fighting, etc were presented to the network. The proposed algorithm detects the presence of anomalous events at the event frame level by evaluating Mean Square Error (MSE) between the predicted events and the ground truth events. It should be noted that the co-occurrence of the spatial location of anomaly is not considered for evaluation. Fig. 5 shows the plot of MSE vs event frame number. It can be seen that MSE is higher for events such as running and fighting resulting from the fact that these kind of motion never appeared in the training set. Running has been distinguished as anomaly with higher probability than that of fighting sequence.
Significance of dual discriminator in anomaly detection: To evaluate the importance of dual discriminator in anomaly detection, we experimented by removing the unconditional discriminator from the objective function. The training set did not include events with a bag, hence the presence of bag has to be classified as an anomaly. In fig. 6, we show the future frame predicted, without (leftmost plot) and with (rightmost plot) unconditional discriminator. It can be seen that cGAN with a conditional discriminator alone can predict the bag in future event frame as it models the relation between the input DL memory surface and output events and hence results in failing to predict bag as anomaly. cGAN with dual discriminator results in distorted prediction of the bag, as it constrains the network to capture input data probability density in addition to the joint probability density between input and output. This proves the necessity to explicitly impose dual discriminator with conditional and unconditional setting to model shape-based anomalies in event domain.
3.2.3 Experiment C: Different Input Representations
In this section, we quantitatively assess the performance of the proposed system as a whole. As, anomaly detection is generally highly imbalanced problem, it has been stated in 
that Precision-Recall (PR) curve is the best suited metric. Henceforth, we have evaluated our models with the PR curve, generated by evaluating precision and recall at multiple threshold values.
As there is no work available for event-based anomaly detection, we compare our anomaly detection model by changing the input event representation. This is an interesting evaluation as this proves how well our DL memory surface network learns the temporal information from the data in contrast to the conventional fixed encoding of event data. The three different event representations that has been used for comparison are ,  and . Wherever the event representation results in multiple frames, they are treated as multiple channels of input. Fig. 7 shows the comparison of PR curves estimated using precision-recall-curve command of python. It could be visualized that the proposed DL memory surface generation learns the temporal information superior to other state-of-the-art methods, thus resulting in better performance in terms of PR.
In this paper, we presented the first baseline for event-based anomaly detection by potentially taking advantage of the most well-known deep learning models such as generative model and encoder-decoder model. The proposed solution involves cGAN with dual discriminator loss function, which permits capture of the spatial as well in event domain that might have gotten away from the cGAN with single discriminator. We have also proposed a first in the line deep learning solution to effectively encode the event data as sparse DL memory surface, where-in the motion information introduced by the event cameras at the sensor level is learnt adaptively from the data as opposed to state-of-the-art hard-wired event data representations. We have also provided an event-based anomaly dataset on which the proposed algorithm has been validated from different perspectives. Our analysis of other event data representations uncovers that the proposed DL based approach allows effective automatic learning of temporal pattern from the event data.
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