Vehicle Behavior Learning via Sparse Reconstruction with $\ell_{2}-\ell_{p}$ Minimization and Trajectory Similarity

Vehicle behavior learning can be used in video surveillance systems to identify normal and abnormal vehicle motion patterns for the management of traffic operations, public services, and law enforcement. The purpose of this paper is to develop a novel adaptive sparse reconstruction method for vehicle behavior learning based on video surveillance systems. First, the <inline-formula> <tex-math notation="LaTeX">$\ell_{0}$</tex-math></inline-formula> minimization problem of sparse reconstruction is relaxed to the <inline-formula> <tex-math notation="LaTeX">$\ell_{p}$</tex-math></inline-formula> minimization problem <inline-formula> <tex-math notation="LaTeX">$(\text{0} <p <\text{1})$</tex-math></inline-formula>. A hybrid algorithm orthogonal matching pursuit—quasi-Newton is proposed to effectively find the sparse solutions. Then, a sparse reconstruction and similarity-based trajectory classifier is developed to learn vehicle behavior based on the sparse solutions and the trajectory similarity. In order to validate the performance and the effectiveness of the proposed method, four datasets, including CROSS, i-LIDA, Stop Sign, and I5 are used in the experiments. The results show that the classification and the anomaly detection accuracies of the proposed method are superior to the representative methods, including the Naïve Bayes classifier, <inline-formula> <tex-math notation="LaTeX">$k$</tex-math></inline-formula> nearest neighbor, support vector machine, and traditional sparse reconstruction-based trajectory learning methods.