Statistical representation of high-dimensional deformation fields with application to statistically constrained 3D warping

This paper proposes a 3D statistical model aiming at effectively capturing statistics of high-dimensional deformation fields and then uses this prior knowledge to constrain 3D image warping. The conventional statistical shape model methods, such as the active shape model (ASM), have been very successful in modeling shape variability. However, their accuracy and effectiveness typically drop dramatically in high-dimensionality problems involving relatively small training datasets, which is customary in 3D and 4D medical imaging applications. The proposed statistical model of deformation (SMD) uses wavelet-based decompositions coupled with PCA in each wavelet band, in order to more accurately estimate the pdf of high-dimensional deformation fields, when a relatively small number of training samples are available. SMD is further used as statistical prior to regularize the deformation field in an SMD-constrained deformable registration framework. As a result, more robust registration results are obtained relative to using generic smoothness constraints on deformation fields, such as Laplacian-based regularization. In experiments, we first illustrate the performance of SMD in representing the variability of deformation fields and then evaluate the performance of the SMD-constrained registration, via comparing a hierarchical volumetric image registration algorithm, HAMMER, with its SMD-constrained version, referred to as SMD+HAMMER. This SMD-constrained deformable registration framework can potentially incorporate various registration algorithms to improve robustness and stability via statistical shape constraints.