Multilinear rank support tensor machine for crowd density estimation

Crowd density estimation, which aims to analyze the density level of people in a crowded scene, has become a major topic in intelligent video surveillance. Different methods have been proposed, but there are still many difficulties and challenges such as occlusions mitigating making it a focus of research. Considering that many types of features are actually tensor formed data, and it is common to use different types of features in the same time to enhance the performance, we introduce a multilinear rank support tensor machine (MRSTM) taking a tensor collection as input to the problem of estimating the density level of crowd. Furthermore, an alternating support vector machine approach is proposed to train a MRSTM classifier. Our method is tested on crowd datasets PETS 2009, Mall and a ground truth image sequence recorded at Hebei Normal University. Experimental results and statistical analysis show that, by using simple tensorial features such as pixel values, gray level dependence matrix based features or the combination of them, we are likely to get higher accuracy while spending less testing time compared to using the corresponding vectorial features and support vector machine, and the method based on higher-order singular value decomposition, especially when the training set is small.