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This paper presents a new active contour-based, statistical method for simultaneous volumetric segmentation of multiple subcortical structures in the brain. In biological tissues, such as the human brain, neighboring structures exhibit co-dependencies which can aid in segmentation, if properly analyzed and modeled. Motivated by this observation, we formulate the segmentation problem as a maximum a posteriori estimation problem, in which we incorporate statistical prior models on the shapes and intershape (relative) poses of the structures of interest. This provides a principled mechanism to bring high level information about the shapes and the relationships of anatomical structures into the segmentation problem. For learning the prior densities we use a nonparametric multivariate kernel density estimation framework. We combine these priors with data in a variational framework and develop an active contour-based iterative segmentation algorithm. We test our method on the problem of volumetric segmentation of basal ganglia structures in magnetic resonance images. We present a set of 2-D and 3-D experiments as well as a quantitative performance analysis. In addition, we perform a comparison to several existent segmentation methods and demonstrate the improvements provided by our approach in terms of segmentation accuracy.