Within a specific medical application, the primary liver cancer curative treatment by a percutaneous high intensity ultrasound surgery, our study was designed to propose a fast 3D semi-automatic segmentation method of the liver, the tumor and the hepatic vascular networks. This method is characterized by a graph description of contrast medium injected CT volume where the links between the nodes describe either the degrees of similarity between voxels of the same class (region based approach) or the class changes between two neighboring voxels (boundary based approaches). The various weights describing these two properties are defined after a first interactive training phase. A Max-Flow/Min-Cut graph cut algorithm allowed partitioning the volume in two representative subsets of the segmented classes.