How Does Structured Sparsity Work in Abnormal Event Detection?

In traditional sparse modeling, it is assumed that a signal/feature/image can be either accurately or approximately represented by a sparse linear combination of atoms from a learned dictionary. Structured sparsity, which is beyond traditional sparse modeling, addresses collaborative structured sparsity to add stability and prior information to the representation. Specifically, in structured sparse modeling, the atoms are partitioned in groups, and a few groups are selected at a time for the sparse coding. Supposing there are n classes and mi training data for each class i, B[i] = [bi1...bimi ], i = 1...n and each bij ∈ R , the dictionary of the training data has a block structure where a few blocks of the dictionary correspond to the training data in each class. Thus, a test example can be represented as a linear combination of training data from a few blocks of the dictionary corresponding to its class. Structured sparsity has been found important in computer vision such as face recognition, motion segmentation, and activity recognition, since the data lie in multiple low-dimensional subspaces of a high dimensional ambient space in these applications. In fact, abnormal event detection can be another beneficiary given a testing frame, it should be identified as a normal frame if all the features within the frame preserves a structured sparsity: all features could be linearly represented by only a few atoms, more importantly, these a few atoms come from the same or similar behavior. Otherwise, it should be detected as an abnormal frame. This structured sparsity is illustrated in Fig. 1. It is straightforward to consider structured sparsity algorithms to achieve the structured sparsity shown in Fig. 1. However, it is infeasible to apply structured sparsity algorithms directly in abnormal event detection, which are mainly due to two reasons: 1) abnormal event detection has a highly biased training data only normal videos are used during the training, which is the due to the fact that abnormal videos are limited or even unavailable in advance in most video surveillance applications. As a result, there could be only one label in the training data which hampers supervised learning; 2) Even though there are multiple types of normal behaviors, how many normal patterns lie in the whole surveillance data is still unknown. This is because there is huge amount of video surveillance data and only a small proportion is used in algorithm learning, consequently, the normal patterns in the training data could be incomplete. As a result, any sparse structure learned from the training data could have a high bias and ruin the precision of abnormal event detection. Therefore, we in the paper propose an algorithm to solve the abnormality detection problem by sparse representation, in which local structured sparsity is preserved in coefficients. To better meet the needs of practical video surveillance applications, our method aims at dictionary learning preserving the structured Fig. 1. Ideal structured sparsity in normal and abnormal features. As normal features, their non zeros in coefficients should only distributed in the atoms with the same behavior; as abnormal features, their non zeros in coefficients should spread over atoms. sparsity through a relatively small training data. Our method contains three steps. Step 1: Initial dictionary construction, which selects initial atoms to form multiple dictionaries. These atoms are learned based on visual features; Step 2: Transferring atoms in Step 1 into feature space, and replace atoms in the initial dictionary with new feature atoms; Step 3: Dictionary refinement, which preserves local structured sparsity. We compare our method with state-of-the-art on the public dataset: UCSD anomaly dataset; moreover, we carry our experiments on the Anomaly Stairs dataset with a challenging setting: an incomplete normal patterns or a small set is used for training the model. Experimental results show the effectiveness of our method.