Approximation-free running SVD and its application to motion detection

In different tasks such as adaptive background modelling, the Singular Value Decomposition (SVD) has to be applied in running fashion. Typically, this happens when the SVD is used in a sliding spatial or temporal data window. Each time the window moves on, the SVD should be calculated in the batch mode from scratch, or re-calculated using the previous solution. When the data matrix is relatively small, the batch mode is fast enough. When the matrix is large, the batch mode is prohibitive and fast re-calculation is needed. In background modelling for video surveillance, the data matrix is formed by consecutive frames and can be fairly large. The existing PCA or SVD based approaches use approximate solutions and divide the frame into small blocks to speed up the re-calculation. We present a fast approximation-free solution for running SVD and apply it to moving object detection in video. Photometric invariants are used for dynamic background with frequent shading. The proposed approach is compared on challenging sequences to the Multiple Gaussian Method which is a standard in adaptive background modelling.