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Optimal surface segmentation is a state-of-the-art method used for segmentation of multiple globally optimal surfaces in volumetric datasets. The method is widely used in numerous medical image segmentation applications. However, nodes in the graph based optimal surface segmentation method typically encode uniformly distributed orthogonal voxels of the volume. Thus the segmentation cannot attain an accuracy greater than a single unit voxel, i.e. the distance between two adjoining nodes in graph space. Segmentation accuracy higher than a unit voxel is achievable by exploiting partial volume information in the voxels which shall result in non-equidistant spacing between adjoining graph nodes. This paper reports a generalized graph based multiple surface segmentation method with convex priors which can optimally segment the target surfaces in an irregularly sampled space. The proposed method allows non-equidistant spacing between the adjoining graph nodes to achieve subvoxel segmentation accuracy by utilizing the partial volume information in the voxels. The partial volume information in the voxels is exploited by computing a displacement field from the original volume data to identify the subvoxel-accurate centers within each voxel resulting in non-equidistant spacing between the adjoining graph nodes. The smoothness of each surface modeled as a convex constraint governs the connectivity and regularity of the surface. We employ an edge-based graph representation to incorporate the necessary constraints and the globally optimal solution is obtained by computing a minimum s-t cut. The proposed method was validated on 10 intravascular multi-frame ultrasound image datasets for subvoxel segmentation accuracy. In all cases, the approach yielded highly accurate results. Our approach can be readily extended to higher-dimensional segmentations. 

Shape priors have been widely utilized in medical image segmentation to improve segmentation accuracy and robustness. A major way to encode such a prior shape model is to use a mesh representation, which is prone to causing self-intersection or mesh folding. Those problems require complex and expensive algorithms to mitigate. In this paper, we propose a novel shape prior directly embedded in the voxel grid space, based on gradient vector flows of a pre-segmentation. The flexible and powerful prior shape representation is ready to be extended to simultaneously segmenting multiple interacting objects with minimum separation distance constraint. The segmentation problem of multiple interacting objects with shape priors is formulated as a Markov Random Field problem, which seeks to optimize the label assignment (objects or background) for each voxel while keeping the label consistency between the neighboring voxels. The optimization problem can be efficiently solved with a single minimum s-t cut in an appropriately constructed graph. The proposed algorithm has been validated on two multi-object segmentation applications: the brain tissue segmentation in MRI images and the bladder/prostate segmentation in CT images. Both sets of experiments showed superior or competitive performance of the proposed method to the compared state-of-the-art methods.