Total Variation Minimization and Graph Cuts for Moving Objects Segmentation

Abstract

In this paper, we are interested in the application to video segmentation of the discrete shape optimization problem $$ \lambda J(\theta)+\sum_{i} (\alpha-f_{i})\theta_{i} \label{eq:func} $$ (1) incorporating a data f = (f i ) and a total variation function J, and where the unknown θ = (θ i ) with θ i ∈ {0,1} is a binary function representing the region to be segmented and α a parameter. Based on the recent works [1], and Darbon and Sigelle [2,3], we justify the equivalence of the shape optimization problem and a weighted TV regularization in the case where J is a “weighted” total variation. For solving this problem, we adapt the projection algorithm proposed in [4] to this case. Another way of solving (1) investigated here is to use graph cuts. Both methods have the advantage to lead to a global minimum.Since we can distinguish moving objects from static elements of a scene by analyzing norm of the optical flow vectors, we choose f as the optical flow norm. In order to have the contour as close as possible to an edge in the image, we use a classical edge detector function as the weight of the weighted total variation. This model has been used in the former work [5]. We also apply the same methods to a video segmentation model used by Jehan-Besson, Barlaud and Aubert. In this case, it is a direct but interesting application of [1], as only standard perimeter is incorporated in the shape functional.