Femur statistical atlas construction based on two-level 3D non-rigid registration

The statistical atlas is a 3D medical image analysis tool to enable more patient-oriented and efficient diagnosis. The atlas includes information on geometry and its variation across populations. The comparison with information from other patients is very useful for objective quantitative diagnosis. The statistical atlas can also be used to solve other challenging problems such as image segmentation. As a key to the construction of statistical atlases, 3D registration remains an important yet unsolved problem in the medical image field due to the geometrical complexity of anatomical shapes and the computational complexity arising from the enormous size of volume data. In this work we developed a two-level framework to efficiently solve 3D non-rigid registration, and applied the method to the problem of constructing statistical atlases of the femur. In contrast to a general multi-resolution framework, we employed an interpolation to propagate the matching instead of repeating the registration scheme in each resolution. The registration procedure is divided into two levels: a low-resolution solution to the correspondences and mapping of surface models using Chui and Rangarajan's thin-plate spline (TPS)-based algorithm, followed by an interpolation to achieve high-resolution matching. Next, principal component analysis (PCA) is used to build the statistical atlases. Experimental results show the shape variation learned from the atlases, and also demonstrate that our method significantly improves the efficiency of registration without decreasing the accuracy of the atlases.