We present a new three-dimensional coupled optimal surface graph-cut algorithm to segment the wall of the carotid artery bifurcation from Magnetic Resonance (MR) images. The method combines the search for both inner and outer borders into a single graph cut and uses cost functions that integrate information from multiple sequences. Our approach requires manual localization of only three seed points indicating the start and end points of the segmentation in the internal, external, and common carotid artery. We performed a quantitative validation using images of 57 carotid arteries. Dice overlap of 0.86 ± 0.06 for the complete vessel and 0.89 ± 0.05 for the lumen compared to manual annotation were obtained. Reproducibility tests were performed in 60 scans acquired with an interval of 15 ± 9 days, showing good agreement between baseline and follow-up segmentations with intraclass correlations of 0.96 and 0.74 for the lumen and complete vessel volumes respectively.

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Abstract. We present a three-dimensional coupled surface graph cut algorithm for carotid wall segmentation from Magnetic Resonance Imaging (MRI). Using cost functions that highlight both inner and outer vessel wall borders, the method combines the search for both borders into a single graph cut. Our approach requires little user interaction and can robustly segment the bifurcation section of the carotid artery. Experiments on 32 carotid arteries from 16 patients show good agreement between manual segmentation performed by an expert and our method. The mean relative area of overlap is more than 85% for the lumen and outer vessel wall. In addition, differences in measured wall thickness with respect to the manual annotations were smaller than the image pixel size.

Purpose Accurate segmentation of the pulmonary arteries and aorta is important due to the association of the diameter and the shape of these vessels with several cardiovascular diseases and with the risk of exacerbations and death in patients with chronic obstructive pulmonary disease. We propose a fully automatic method based on an optimal surface graph‐cut algorithm to quantify the full 3D shape and the diameters of the pulmonary arteries and aorta in noncontrast computed tomography (CT) scans. Methods The proposed algorithm first extracts seed points in the right and left pulmonary arteries, the pulmonary trunk, and the ascending and descending aorta by using multi‐atlas registration. Subsequently, the centerlines of the pulmonary arteries and aorta are extracted by a minimum cost path tracking between the extracted seed points, with a cost based on a combination of lumen intensity similarity and multiscale medialness in three planes. The centerlines are refined by applying the path tracking algorithm to curved multiplanar reformatted scans and are then smoothed and dilated nonuniformly according to the extracted local vessel radius from the medialness filter. The resulting coarse estimates of the vessels are used as initialization for a graph‐cut segmentation. Once the vessels are segmented, the diameters of the pulmonary artery (PA) and the ascending aorta (AA) and the PA:AA ratio are automatically calculated both in a single axial slice and in a 10 mm volume around the automatically extracted PA bifurcation level. The method is evaluated on noncontrast CT scans from the Danish Lung Cancer Screening Trial (DLCST). Segmentation accuracy is determined by comparing with manual annotations on 25 CT scans. Intraclass correlation (ICC) between manual and automatic diameters, both measured in axial slices at the PA bifurcation level, is computed on an additional 200 CT scans. Repeatability of the automated 3D volumetric diameter and PA:AA ratio calculations (perpendicular to the vessel axis) are evaluated on 118 scan–rescan pairs with an average in‐between time of 3 months. Results We obtained a Dice segmentation overlap of 0.94 ± 0.02 for pulmonary arteries and 0.96 ± 0.01 for the aorta, with a mean surface distance of 0.62 ± 0.33 mm and 0.43 ± 0.07 mm, respectively. ICC between manual and automatic in‐slice diameter measures was 0.92 for PA, 0.97 for AA, and 0.90 for the PA:AA ratio, and for automatic diameters in 3D volumes around the PA bifurcation level between scan and rescan was 0.89, 0.95, and 0.86, respectively. Conclusion The proposed automatic segmentation method can reliably extract diameters of the large arteries in non‐ECG‐gated noncontrast CT scans such as are acquired in lung cancer screening.

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Optimal surface methods are a class of graph cut methods posing surface estimation as an n-ary ordered labeling problem. They are used in medical imaging to find interacting and layered surfaces optimally and in low order polynomial time. Representing continuous surfaces with discrete sets of labels, however, leads to discretization errors and, if graph representations are made dense, excessive memory usage. Limiting memory usage and computation time of graph cut methods are important and graphs that locally adapt to the problem has been proposed as a solution. Min-marginal energies computed using dynamic graph cuts offer a way to estimate solution uncertainty and these uncertainties have been used to decide where graphs should be adapted. Adaptive graphs, however, introduce extra parameters, complexity, and heuristics. We propose a way to use min-marginal energies to estimate continuous solution labels that does not introduce extra parameters and show empirically on synthetic and medical imaging datasets that it leads to improved accuracy. The increase in accuracy was consistent and in many cases comparable to accuracy otherwise obtained with graphs up to 8 times denser, but with proportionally less memory usage and improvements in computation time.

Centerline extraction of the carotid artery in MRI is important to analyze the artery geometry and to provide input for further processing such as registration and segmentation. The centerline of the artery bifurcation is often extracted by means of two independent minimum cost paths ranging from the common to the internal and the external carotid artery. Often the cost is not well defined at the artery bifurcation, leading to centerline errors. To solve this problem, we developed a method to cooperatively extract both centerlines, where in the cost to extract each centerline, we integrate a constraint region derived from the estimated position of the neighbor centerline. This method avoids that both centerlines follow the same cheapest path after the bifurcation, which is a common error when the paths are extracted independently. We show that this method results in less error compared to extracting them independently: 10 failed centerlines Vs. 3 failures in a data set of 161 arteries with manual annotations. Additionally, we show that the new method improves the non-cooperative approach in 28 cases (p < 0.0001) in a data set of 3,904 arteries.

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