Efficient large deformation registration via geodesics on a learned manifold of images

Geodesic registration methods have been used to solve the large deformation registration problems, which are hard to solve with conventional registration methods. However, analytically defined geodesics may not coincide with anatomically optimal paths of registration. In this paper we propose a novel and efficient method for large deformation registration by learning the underlying structure of the data using a manifold learning technique. In this method a large deformation between two images is decomposed into a series of small deformations along the shortest path on the graph that approximates the metric structure of data. Furthermore, the graph representation allows us to estimate the optimal group template by minimizing geodesic distances. We demonstrate the advantages of the proposed method with synthetic 2D images and real 3D mice brain volumes.