(a) Illustration of semiautomatic segmentation process. (b)The user uses brush strokes of one color to identify the target structure, liver in this case, and brush strokes of a different color for background. (c) Segmentation result is shown shaded so the user can review and modify the result with additional brush strokes. (d) The brush strokes are automatically carried over to subsequent slices until they are no longer applicable, at which point the user can redraw the brushes.
The edge cost assignment of the graph to solve the minimization of three different energy functions using min s-t cut. A non-negative weight (cost) is assigned to each edge. Min s-t cut is usually solved through a maximum flow algorithm.22 The arrow of an edge shows the direction of the flow. (a) Greig's energy function in Eq. (1) for image binary denoising. (b) Boykov's energy function in which a heuristic boundary term B ij is defined in Eq. (2) for image segmentation. In addition, seed points for the classes, labeled h for target and j for nontarget, can be indicated by users. For those seed nodes, either a very large number K or zero is assigned to the cost of links to s and t to serve as hard constraints. (c) Our energy function, Eq. (3), derived from CRF, in which the probabilistic boundary term Eq. (5) is defined for image segmentation and is used for cost of edges connecting neighboring voxels. (d) An example of a minimum cut. Dashed lines indicate the edges being cut. The minimum cost of a cut to separate nodes 1, 2, and 3 into two separated groups is 2 + 4 + 8 + 2. After the cut, node 1 and 2 remain connected to s and are classified as target while node 3 remains connected to t and is classified as nontarget.
Graph-based interpolation. The solid line contours are segmented from our graph cut method on the two slices p and r. On the slice q being interpolated, the nodes in black do not need re-estimation since their adjacent nodes on slice p and r are assigned to the same class. Their edge costs are interpolated as Eq. (7) from slices p and r. The node in white needs re-estimation since its adjacent nodes on slice p and r are assigned to two different classes. A graph min-cut is then applied to the partially interpolated graph on slice q for segmentation.
Segmentation results from the phantom image. (a) On noise-free images, Boykov's boundary term favoring high contrast [Eq. (5)] is prone to leakage if a high contrast boundary is present in nearby tissue (arrow). (b) Additional brush strokes are needed to exclude neighboring tissue. (c) On an image with 4% Gaussian noise, using Boykov's boundary term and strongly weighted regional term results in an irregular boundary and pixels within the segmentation are excluded. (d) In contrast, our method SAASS requires fewer brush strokes and preserves piece-wise continuity.
Liver segmentation of a patient. Typical image slices from superior to inferior are shown. Physician-drawn contours in dark gray and SAASS contours are in light gray.
Kidney segmentation of a patient. Typical image slices from superior to inferior are shown. Physician-drawn contours in dark gray and SAASS contours are in light gray.
Comparison of liver segmentations: SAASS (dashed white), RG (black), MIPAV-LS (dark gray), and Seg3D-LS (light gray). RG, MIPAV-LS, and Seg3D-LS segmentations show leakage (arrows) since they are sensitive to low-contrast boundary and surrounding high contrast tissues.
Overlay analysis for liver and kidney segmentation. SAASS has the best DSC and smallest variation among the four methods compared.
Mean Hausdorff distance comparison in ten liver cases and eight kidney cases. Error bars show the minimum and maximum distances over the cases.
Sensitivity, specificity, and DSC measures comparison between SAASS graph-based interpolation and mesh-based interpolation. Mean of the measures in five liver cases are shown.
(Top row) Image slices where liver topology changes. The light gray contours in the middle slice are interpolated from the dark gray contours in the adjacent slices on the left and right based on surface tiling method, but suffer from topological change. The pale gray contours are result of our graph-based interpolation method (Sec. II E). (Bottom row) Even without topological change, our method still shows improved performance over surface tiling (middle), due the utilization of image information.
Bland–Altman plot of interobserver agreement in five kidney cases. Absolute value of the difference is used in y axis. SAASS shows better repeatability and the difference is irrelevant to the size of volumes.
Bland–Altman plots of intraobserver agreement for Observer 1 and Observer 2. In both observers, SAASS has better agreement compared to the manual method.
Comparison of performance of the manual method and SAASS. Mean time per slice for segmentations of five kidney cases is calculated from the two observers. The error bars show one standard deviation.
An example to demonstrate leakage. (a) The image shows blurred boundary between the liver left lobe and the apex of the heart. (b) Leakage of the initial segmentation due to blurred boundary. (c) An additional brush stroke to remove the leakage. The ground truth contour is shown.
Examples of segmentation on other organs and other modalities: (a) bladder and (b) heart in CT; (c) brainstem and (d) parotid in MR images. We note that MR inhomogeneity in pixel intensity should be corrected prior to intensity-based segmentation methods.
Scores of ten liver cases evaluated by three physicians. See text for details of the scoring rules.
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