Simultaneous Segmentation of Bladder and Prostate using Globally Optimal 3-D Graph Search Method

and size and also have serious mutual influence in position and shape between each other. We propose a novel method for simultaneoussegmentationofbladderandprostateusinga3-Dgraph-theoreticapproach.Thealgorithmcomputesaglobaloptimumofan objective function controlled by the cost function designed for each boundary surface. A geometric constraint is incorporated to avoid boundary leakage and to accurately detect the partially interacted boundaries of bladder and prostate. Our method is the first attempt at simultaneous segmentation of partially interacted surfaces, which admits a globally optimal solution in polynomial time. Materials/Methods: Our segmentation consists of the following steps: 1. Surface pre-segmentation. The geodesic active contours method is conducted for pre-segmentation of prostate and bladder. 2. Mesh construction. Partially interacted boundaries of prostate and bladder are defined according to the distance between two pre-segmented boundary surfaces. Then two triangulated meshes for pre-segmentedboundarysurfacesareconstructedusingisosurfacingalgorithm.3.Accuratesegmentationusinggraphsearchmethod. A graphisbuilt accordingtotwogeneratedmeshes.Thesurfacedistanceconstraintinpartiallyinteractedboundariesisincorporated by adding special edges in graph. Two globally optimal surfaces are computed by solving a maximum-flow problem in low-order polynomial time. Our method was applied on 10 CT images from 10 prostate-tumor patients with the resolution 0.90.9 3m m 3 . 50 slices of bladder and 50 slices of prostate were randomly selected to be manually traced by an expert as independent standard. The surface positioning errors were computed as the shortest distances between manually traced borders and computed surfaces. Results: All 10 images were successfully segmented. The mean unsigned surface positioning errors were 1.10±1.30 mm for bladder and 1.89±1.92 mm for prostate. The result is promising considering the low saliency of the boundary, especially for prostate segmentation. The bladder-prostate interface was correctly delineated by using a surface distance constraint. Conclusions:A novel method for simultaneous segmentation of bladder and prostate is demonstrated. The result shows good consistency with expert-defined independent standard.