Algebraic methods for direct and feature based registration of diffusion tensor images

We present an algebraic solution to both direct and feature-based registration of diffusion tensor images under various local deformation models. In the direct case, we show how to linearly recover a local deformation from the partial derivatives of the tensor using the so-called Diffusion Tensor Constancy Constraint, a generalization of the brightness constancy constraint to diffusion tensor data. In the feature-based case, we show that the tensor reorientation map can be found in closed form by exploiting the spectral properties of the rotation group. Given this map, solving for an affine deformation becomes a linear problem. We test our approach on synthetic, brain and heart diffusion tensor images.