Learning object trajectory patterns by spectral clustering

We develop a trajectory pattern learning method that has two significant advantages over past work. First, we represent trajectories in the HMM parameter space, thus we overcome the normalization problems of existing methods. Second, we determine common trajectory paths by analyzing the optimal cluster number rather than using a predefined number of clusters. We compute affinity matrices and apply eigenvector decomposition to find clusters. We prove that the number of clusters governs the number of eigenvectors used to span the feature affinity space. We are thus able to determine automatically the optimal number of patterns. We show that the proposed algorithm accurately detects common paths for various camera setups