Automatic Construction of Correspondences for Tubular Surfaces

Statistical shape modeling is an established technique and is used for a variety of tasks in medical image processing, such as image segmentation and analysis. A challenging task in the construction of a shape model is establishing a good correspondence across the set of training shapes. Especially for shapes of cylindrical topology, very little work has been done. This paper describes an automatic method to obtain a correspondence for a set of cylindrical shapes. The method starts from an initial correspondence which is provided by cylindrical parameterization. The quality of the obtained correspondence, measured in terms of the description length, is then improved by deforming the parameterizations using cylindrical b-spline deformations and by optimization of the spatial alignment of the shapes. In order to allow efficient gradient-guided optimization, an analytic expression is provided for the gradient of this quality measure with respect to the parameters of the parameterization deformation and the spatial alignment. A comparison is made between models obtained from the correspondences before and after the optimization. The results show that, in comparison with parameterization-based correspondences, this new method establishes correspondences that generate models with significantly increased performance in terms of reconstruction error, generalization ability, and specificity.