Construction of Statistical Shape Models from Minimal Deformations

Statistical shape models (SSM) capture the variation of shape across a population, in order to allow further analysis. Previous work demonstrates that deformation fields contain global transformation components, even if global preregistration is performed. It is crucial to construction of SSMs to remove these global transformation components from the local deformations thus obtaining minimal deformations prior to using these as input for SSM construction. In medical image processing, parameterized SSMs based on control points of free-form deformations (FFD) are a popular choice, since they offer several advantages compared to SSMs based on dense deformation fields. In this work, we extend the previous approach by presenting a framework for construction of both, unparameterized and FFD-based SSMs from minimal deformations. The core of the method is computation of minimal deformations by extraction of the linear part from the original dense deformations. For FFD-based SSMs, the FFDparameterization of the minimal deformations is performed by projection onto the space of FFDs. Both steps are computed by close-form solutions optimally in the least-square sense. The proposed method is evaluated on a data set of 62 MR images of the corpus callosum. The results show a significant improvement achieved by the proposed method for SSMs built on dense fields, as well as on FFD-based SSMs.