We propose a semi-supervised image segmentation method that relies on a non-local continuous version of the min-cut algorithm and labels or seeds provided by a user. The segmentation process is performed via energy minimization. The proposed energy is composed of three terms. The ¯rst term de¯nes labels or seed points assigned to objects that the user wants to identify and the background. The second term carries out the di®usion of object and background labels and stops the di®usion when the interface between the object and the background is reached. The di®usion process is performed on a graph de¯ned from image intensity patches. The graph of intensity patches is known to better deal with textures because this graph uses semi-local and non-local image information. The last term is the standard TV term that regularizes the geometry of the interface.We introduce an iterative scheme that provides a unique minimizer. Promising results are presented on synthetic textures a nd real-world images.