Optimal deformable surface models for 3D medical image analysis.

We present a novel method for building an optimal statistical deformable model from a set of surfaces whose topological realization is homeomorphic to a compact 2D manifold with boundary. The optimal parameterization of each shape is recursively refined by using hierarchical PBMs and tensor product B-spline representation of the surface. A criterion based on MDL is used to define the internal correspondence of the training data. The strength of the proposed technique is demonstrated by deriving a concise statistical model of the human left ventricle which has principal modes of variation that correspond to intrinsic cardiac motions. We demonstrate how the derived model can be used for 3D dynamic volume segmentation of the left ventricle, with its accuracy assessed by comparing results obtained from manual delineation of 3D cine MR data of 8 asymptomatic subjects. The extension of the technique to shapes with complex topology is also discussed.