Combinatorial graph cut algorithms have been successfully applied to a wide range of problems in vision and graphics. This paper focusses on possibly the simplest application of graph-cuts: segmentation of objects in image data. Despite its simplicity, this application epitomizes the best features of combinatorial graph cuts methods in vision: global optima, practical efficiency, numerical robustness, ability to fuse a wide range of visual cues and constraints, unrestricted topological properties of segments, and applicability to N-D problems. Graph cuts based approaches to object extraction have also been shown to have interesting connections with earlier segmentation methods such as snakes, geodesic active contours, and level-sets. The segmentation energies optimized by graph cuts combine boundary regularization with region-based properties in the same fashion as Mumford-Shah style functionals. We present motivation and detailed technical description of the basic combinatorial optimization framework for image segmentation via s/t graph cuts. After the general concept of using binary graph cut algorithms for object segmentation was first proposed and tested in Boykov and Jolly (2001), this idea was widely studied in computer vision and graphics communities. We provide links to a large number of known extensions based on iterative parameter re-estimation and learning, multi-scale or hierarchical approaches, narrow bands, and other techniques for demanding photo, video, and medical applications.

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Abstract.A novel method is proposed for performing multi-label, semiautomated image segmentation. Given a small number of pixels with user-defined labels, one can analytically (and quickly) determine the probability that a random walker starting at each unlabeled pixel will first reach one of the pre-labeled pixels. By assigning each pixel to the label for which the greatest probability is calculated, a high-quality image segmentation may be obtained. Theoretical properties of this algorithm are developed along with the corresponding connections to discrete potential theory and electrical circuits. This algorithm is formulated in discrete space (i.e., on a graph) using combinatorial analogues of standard operators and principles from continuous potential theory, allowing it to be applied in arbitrary dimension.

We describe a means to automatically and efficiently isolate the outer surface of the entire heart in Computer Tomography (CT) cardiac scans. Isolating the entire heart allows the coronary vessels on the surface of the heart to be easily visualized despite the proximity of surrounding organs such as the ribs and pulmonary blood vessels. Numerous techniques have been described for segmenting the left ventricle of the heart in images from various types of medical scanners but rarely has the entire heart been segmented. We make use of graphcuts to do the segmentation and introduce a novel means of initiating and constraining the graph-cut technique for heart isolation. The technique has been tested on 70 patient data sets. Results are compares with hand labeled results.

Abstract. Various methods have been proposed to extract coronary artery centerlines from computed tomography angiography (CTA) data. Almost all previous approaches are data-driven, which try to trace a centerline from an automatically detected or manually specified coronary ostium. No or little high level prior information is used; therefore, the centerline tracing procedure may terminate early at a severe occlusion or an anatomically inconsistent centerline course may be generated. Though the connectivity of coronary arteries exhibits large variations, the position of major coronary arteries relative to the heart chambers is quite stable. In this work, we propose to exploit the automatically segmented chambers to 1) predict the initial position of the major coronary centerlines and 2) define a vessel-specific region-of-interest (ROI) to constrain the following centerline refinement. The proposed prior constraints have been integrated into a model-driven algorithm for the extraction of three major coronary centerlines, namely the left anterior descending artery (LAD), left circumflex artery (LCX), and right coronary artery (RCA). After extracting the major coronary arteries, the side branches are traced using a data-driven approach to handle large anatomical variations in side branches. Experiments on the public Rotterdam coronary CTA database demonstrate the robustness and accuracy of the proposed method. We achieve the best average ranking on overlap metrics among automatic methods and our accuracy metric outperforms all other 22 methods (including both automatic and semi-automatic methods).