## 2 Related work  
In this section, a review of the current main methods is presented. Initial studies gave attention to the use of the trajectory for anomaly detection [3; 4; 5; 19; 20; 21]. [PERSON] in [19] represented trajectories as sequences of transitions between nodes in a graph to detect abnormal movements. In another work, [PERSON] [20] combined the trajectory with Gaussian mixture and hidden Markov models to build activity models. [PERSON] [21] proposed an approximation algorithm implementing a hidden Markov model as one-class classifier, which can decide whether a given trajectory is normal compared to a model. Others works [6; 7; 8; 22; 23] were devoted to the extraction and analysis of low-level local features. [PERSON] in [6] generated behavior clusters based on behavior profile of a given pixel to construct probabilistic models. [PERSON] in [7] used optical flow to characterize the object's motion and proposed an adaptive codebook to obtain texture features. In the same process, [PERSON] [8] combined a histogram of optical flow orientation with one class support vector machine (SVM) for detecting abnormal motions. [PERSON] and [PERSON] [22] presented an approach based on spatio-temporal volumes and considered that if the event reconstruction using only the previous observations is impossible then this event is classified as abnormal. [PERSON] [9] proposed a method which is the improvement of [22], by using a codebook to group similar spatio-temporal volumes to reduce the dimension of the problem. This proposed method allows to reduce the computational complexity, and becomes applicable to real-time video analysis. [PERSON] in [23] proposed a sparse semi-non-negative matrix factorization (SSMF) to learn local patterns, and used a histogram of non-negative coefficients (HNC) as local descriptors. [PERSON] et al. in [24] used a dynamic texture (DTs) to design models of normalcy over both space and time. Spatial and temporal information is modeled with a mixture of DTs (MDT). Recently, various methods based on deep learning were applied for anomaly detection [15; 16; 17; 25; 26; 27]. [PERSON] [15] proposed a method for detecting and locating abnormalities based on spatiotemporal convolutional neural network. In this paper, the authors used a 3D-CNN to extract features related to motions and shapes. Although the results presented were encouraging, the supervised nature of this algorithm did not allow its use in real world systems monitoring. Indeed, both normal and abnormal events were used as training examples, which is not suitable in the field of video surveillance since it is very hard to reproduce all abnormalities. [PERSON] et al. in [26] used three initial layers of pre-trained 2D-CNN combined with a new convolutional layer, whose kernels were learned using sparse auto-encoder for abnormal event detection. One should notice here that the 2D convolution does not sufficiently take into account the temporal information. Same author in [27] used local and global descriptors generated with sparse auto-encoder to capture video properties. [PERSON] in [16] used a fully convolutional auto-encoder (AE), the learned AE reconstructs normal events with low error and give higher reconstruction error for abnormal events. For the same purpose, [PERSON] [25] proposed an AE with two parts, 2D convolutional layers for spatial features and use convolutional long short term memory for temporal information. [PERSON] in [17] proposed to use a generative adversarial nets (GANs), which are trained using normal frames and their corresponding representation generated by optical flow. In the testing phase, the real data are compared with the reconstruction generated by GANs, the use of optical flow in the detection of abnormalities can be time consuming. [PERSON] et al. in [28] presented an unsupervised deep learning framework for abnormal event detection in complex scenes. The proposed method is based on stacked denoising autoencoders (SDAE) to extract features, and multiples one-class-SVM to predict score of abnormalities.