Sequential sparsification for change detection

This paper presents a general method for segmenting a vector valued sequence into an unknown number of subsequences where all data points from a subsequence can be represented with the same affine parametric model. The idea is to cluster the data into the minimum number of such subsequences which, as we show, can be cast as a sparse signal recovery problem by exploiting the temporal correlation between consecutive data points. We try to maximize the sparsity (i.e. the number of zero elements) of the first order differences of the sequence of parameter vectors. Each non-zero element in the first order difference sequence corresponds to a change. A weighted l₁ norm based convex approximation is adopted to solve the change detection problem. We apply the proposed method to video segmentation and temporal segmentation of dynamic textures.