Diffeomorphic Statistical Deformation Models

In this paper we present a new method for constructing diffeomorphic statistical deformation models in arbitrary dimensional images with a nonlinear generative model and a linear parameter space. Our deformation model is a modified version of the diffeomorphic model introduced by Cootes et al. The modifications ensure that no boundary restriction has to be enforced on the parameter space to prevent folds or tears in the deformation field. For straightforward statistical analysis, principal component analysis and sparse methods, we assume that the parameters for a class of deformations lie on a linear manifold and that the distance between two deformations are given by the metric introduced by the L₂-norm in the parameter space. The chosen L₂-norm is shown to have a clear and intuitive interpretation on the usual nonlinear manifold. Our model is validated on a set of MR images of corpus callosum with ground truth in form of manual expert annotations, and compared to Cootes´s model. We anticipate applications in unconstrained diffeomorphic synthesis of images, e.g. for tracking, segmentation, registration or classification purposes.