The paper discusses the application of combinatorial graph cut algorithms to image segmentation, focusing on the simplest yet powerful method of using s/t graph cuts for object extraction. This approach combines boundary regularization with region-based properties, similar to Mumford-Shah functionals. The authors highlight the advantages of graph cuts, including global optima, practical efficiency, numerical robustness, and the ability to integrate various visual cues and constraints. They also explore connections between graph cuts and earlier segmentation methods like snakes, active contours, and level-sets. The paper provides a detailed technical description of the basic combinatorial optimization framework for image segmentation using s/t graph cuts, including the formulation of the segmentation energy, the integration of regional and boundary cues, and the handling of hard constraints. The authors demonstrate the effectiveness of their method through various examples and extensions, such as multi-scale approaches, hierarchical methods, and applications in video and medical imaging.The paper discusses the application of combinatorial graph cut algorithms to image segmentation, focusing on the simplest yet powerful method of using s/t graph cuts for object extraction. This approach combines boundary regularization with region-based properties, similar to Mumford-Shah functionals. The authors highlight the advantages of graph cuts, including global optima, practical efficiency, numerical robustness, and the ability to integrate various visual cues and constraints. They also explore connections between graph cuts and earlier segmentation methods like snakes, active contours, and level-sets. The paper provides a detailed technical description of the basic combinatorial optimization framework for image segmentation using s/t graph cuts, including the formulation of the segmentation energy, the integration of regional and boundary cues, and the handling of hard constraints. The authors demonstrate the effectiveness of their method through various examples and extensions, such as multi-scale approaches, hierarchical methods, and applications in video and medical imaging.