In this paper we present a fast new fully dynamic algorithm for the st-mincut/max-flow problem. We show how this algorithm can be used to efficiently compute MAP estimates for dynamically changing MRF models of labelling problems in computer vision, such as image segmentation. Specifically, given the solution of the max-flow problem on a graph, we show how to efficiently compute the maximum flow in a modified version of the graph. Our experiments showed that the time taken by our algorithm is roughly proportional to the number of edges whose weights were different in the two graphs. We test the performance of our algorithmon one particular problem: the object-background segmentation problem for video and compare it with the best known st-mincut algorithm. The results show that the dynamic graph cut algorithm is much faster than its static counterpart and enables real time image segmentation. It should be noted that our method is generic and can be used to yield similar improvements in many other cases that involve dynamic change in the graph.