Automatic construction of 3D statistical deformation models using non-rigid registration

In this paper we introduce the concept of statistical deformation models (SDM) which allow the construction of average models of the anatomy and their variability. SDMs are built by performing a statistical analysis of the deformations required to map anatomical features in one subject into the corresponding features in another subject. The concept of SDMs is similar to active shape models (ASM) which capture statistical information about shapes across a population but offers several new advantages over ASMs: Firstly, SDMs can be constructed directly from images such as MR or CT without the need for segmentation which is usually a prerequisite for the construction of active shape models. Instead a non-rigid registration algorithm is used to compute the deformations required to establish correspondences between the reference subject and the subjects in the population class under investigation. Secondly, SDMs allow the construction of an atlas of the average anatomy as well as its variability across a population of subjects. Finally, SDMs take the 3D nature of the underlying anatomy into account by analysing dense 3D deformation fields rather than only the 2D surface shape of anatomical structures. We demonstrate the applicability of this new framework to MR images of the brain and show results for the construction of anatomical models from 25 different subjects.