3-D graph cut segmentation with Riemannian metrics to avoid the shrinking problem.

Though graph cut based segmentation is a widely-used technique, it is known that segmentation of a thin, elongated structure is challenging due to the "shrinking problem". On the other hand, many segmentation targets in medical image analysis have such thin structures. Therefore, the conventional graph cut method is not suitable to be applied to them. In this study, we developed a graph cut segmentation method with novel Riemannian metrics. The Riemannian metrics are determined from the given "initial contour," so that any level-set surface of the distance transformation of the contour has the same surface area in the Riemannian space. This will ensure that any shape similar to the initial contour will not be affected by the shrinking problem. The method was evaluated with clinical CT datasets and showed a fair result in segmenting vertebral bones.