Cross-manifold guidance in deformable registration of brain MR images

Manifold is often used to characterize the high-dimensional distribution of individual brain MR images. The deformation field, used to register the subject with the template, is perceived as the geodesic pathway between images on the manifold. Generally, it is non-trivial to estimate the deformation pathway directly due to the intrinsic complexity of the manifold. In this work, we break the restriction of the single and complex manifold, by short-circuiting the subject-template pathway with routes from multiple simpler manifolds. Specifically, we reduce the anatomical complexity of the subject/template images, and project them to the virtual and simplified manifolds. The projected simple images then guide the subject image to complete its journey toward the template image space step by step. In the final, the subject-template pathway is computed by traversing multiple manifolds of lower complexity, rather than depending on the original single complex manifold only. We validate the cross-manifold guidance and apply it to brain MR image registration. We conclude that our method leads to superior alignment accuracy compared to state-of-the-art deformable registration techniques.