  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.
