This paper describes the creation of 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 piecewise bilinear maps and tensor product B-spline representation of the surfaces. A criterion based on minimum description length was used to define the internal correspondence of the training data. The strength of the proposed method is demonstrated by deriving a concise statistical model of the left ventricle which has principal modes of variation that correspond to intrinsic cardiac motions. The extension of the technique to shapes with complex topology is also discussed.
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