Metric Space Structures for Computational Anatomy

This paper describes a method based on metric structures for anatomical analysis on a large set of brain MR images. A geodesic distance between each pair was measured using large deformation diffeomorphic metric mapping (LDDMM). Manifold learning approaches were applied to seek a low-dimensional embedding in the highdimensional shape space, in which inference between healthy control and disease groups can be done using standard classification algorithms. In particular, the proposed method was evaluated on ADNI, a dataset for Alzheimer’s disease study. Our work demonstrates that the highdimensional anatomical shape space of the amygdala and hippocampi can be approximated by a relatively low dimension manifold.