This paper proposes a method based on repulsive forces and sparse reconstruction for the detection and location of abnormal events in crowded scenes. In order to avoid the challenging problem of accurately tracking each specific individual in a dense or complex scene, we divide each frame of the surveillance video into a fixed number of grids and select a single representative point in each grid as the individual to track. The repulsive force model, which can accurately reflect interactive behaviors of crowds, is used to calculate the interactive forces between grid particles in crowded scenes and to construct a force flow matrix using these discrete forces from a fixed number of continuous frames. The force flow matrix, which contains spatial and temporal information, is adopted to train a group of visual dictionaries by sparse coding. To further improve the detection efficiency and avoid concept drift, we propose a fully unsupervised global and local dynamic updating algorithm, based on sparse reconstruction and a group of word pools. For anomaly location, since our method is based on a fixed grid, we can judge whether anomalies occur in a region intuitively according to the reconstruction error of the corresponding visual words. We experimentally verify the proposed method using the UMN dataset, the UCSD dataset and the Web dataset separately. The results indicate that our method can not only detect abnormal events accurately, but can also pinpoint the location of anomalies.
In both statistics-based models and topic-based models, high-dimensional features are often used to represent crowd events, which will cause the amount of training data to increase exponentially. Even worse, in real scenes, it is impossible to provide enough data to train a complete model that includes all possible crowd scenes. Therefore, some researchers have started using sparse coding to solve this problem @cite_4 @cite_37 @cite_12 . The underlying assumption is that normal events can be reconstructed by sparse coefficients with a small error, but for abnormal events, the reconstruction coefficients will be dense and a large error will be generated. Current sparse coding methods for abnormal event detection have overcome the high-dimensional problem and have achieved good results. However, this type of method still heavily relies on the expression capability of the underlying features. In dense crowds, the motion features extracted by current methods often contain a lot of noise, which greatly affects the final result. Additionally, the testing speed and dictionary updates @cite_4 of the sparse coding framework are still critical issues that need to be tackled.
@cite_37 @cite_4 @cite_12
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In crowded scenes, the extracted low-level features, such as optical flow or spatio-temporal interest point, are inevitably noisy and uncertainty. In this paper, we propose a fully unsupervised non-negative sparse coding based approach for abnormality event detection in crowded scenes, which is specifically tailored to cope with feature noisy and uncertainty. The abnormality of query sample is decided by the sparse reconstruction cost from an atomically learned event dictionary, which forms a sparse coding bases. In our algorithm, we formulate the task of dictionary learning as a non-negative matrix factorization (NMF) problem with a sparsity constraint. We take the robust Earth Mover's Distance (EMD), instead of traditional Euclidean distance, as distance metric reconstruction cost function. To reduce the computation complexity of EMD, an approximate EMD, namely wavelet EMD, is introduced and well combined into our approach, without losing performance. In addition, the combination of wavelet EMD with our approach guarantees the convexity of optimization in dictionary learning. To handle both local abnormality detection (LAD) and global abnormality detection, we adopt two different types of spatio-temporal basis. Experiments conducted on four public available datasets demonstrate the promising performance of our work against the state-of-the-art methods. We propose to detect abnormal events via a sparse reconstruction over the normal bases. Given a collection of normal training examples, e.g., an image sequence or a collection of local spatio-temporal patches, we propose the sparse reconstruction cost (SRC) over the normal dictionary to measure the normalness of the testing sample. By introducing the prior weight of each basis during sparse reconstruction, the proposed SRC is more robust compared to other outlier detection criteria. To condense the over-completed normal bases into a compact dictionary, a novel dictionary selection method with group sparsity constraint is designed, which can be solved by standard convex optimization. Observing that the group sparsity also implies a low rank structure, we reformulate the problem using matrix decomposition, which can handle large scale training samples by reducing the memory requirement at each iteration from O(k^2) to O(k) where k is the number of samples. We use the columnwise coordinate descent to solve the matrix decomposition represented formulation, which empirically leads to a similar solution to the group sparsity formulation. By designing different types of spatio-temporal basis, our method can detect both local and global abnormal events. Meanwhile, as it does not rely on object detection and tracking, it can be applied to crowded video scenes. By updating the dictionary incrementally, our method can be easily extended to online event detection. Experiments on three benchmark datasets and the comparison to the state-of-the-art methods validate the advantages of our method. In recent years, sparse signal modeling, especially using the synthesis model has been popular. Sparse coding in the synthesis model is however, NP-hard. Recently, interest has turned to the sparsifying transform model, for which sparse coding is cheap. However, natural images typically contain diverse textures that cannot be sparsified well by a single transform. Hence, in this work, we propose a union of sparsifying transforms model. Sparse coding in this model reduces to a form of clustering. The proposed model is also equivalent to a structured overcomplete sparsifying transform model with block cosparsity, dubbed OCTOBOS. The alternating algorithm introduced for learning such transforms involves simple closed-form solutions. A theoretical analysis provides a convergence guarantee for this algorithm. It is shown to be globally convergent to the set of partial minimizers of the non-convex learning problem. We also show that under certain conditions, the algorithm converges to the set of stationary points of the overall objective. When applied to images, the algorithm learns a collection of well-conditioned square transforms, and a good clustering of patches or textures. The resulting sparse representations for the images are much better than those obtained with a single learned transform, or with analytical transforms. We show the promising performance of the proposed approach in image denoising, which compares quite favorably with approaches involving a single learned square transform or an overcomplete synthesis dictionary, or gaussian mixture models. The proposed denoising method is also faster than the synthesis dictionary based approach. Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in statistics, machine learning, computer vision, as well as signal and image processing. In theory, this problem can be solved by the natural convex joint mixed relaxations (i.e., l 1 -norm and trace norm) under certain conditions. However, all current provable algorithms suffer from superlinear per-iteration cost, which severely limits their applicability to large-scale problems. In this paper, we propose a scalable, provable and structured robust bilinear factorization (RBF) method to recover low-rank and sparse matrices from missing and grossly corrupted data, i.e., robust matrix completion (RMC), or incomplete and grossly corrupted measurements, i.e., compressive principal component pursuit (CPCP). Specifically, we first present two small-scale matrix trace norm regularized bilinear factorization models for RMC and CPCP problems, in which repetitively calculating SVD of a large-scale matrix is replaced by updating two much smaller factor matrices. Then, we apply the alternating direction method of multipliers (ADMM) to efficiently solve the RMC problems. Finally, we provide the convergence analysis of our algorithm, and extend it to address general CPCP problems. Experimental results verified both the efficiency and effectiveness of our method compared with the state-of-the-art methods.