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 first term defines labels or seed points assigned to objects that the user wants to identify and the background. The second term carries out the diffusion of object and background labels and stops the diffusion when the interface between the object and the background is reached. The diffusion process is performed on a graph defined 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.