An algebraic solution to rigid registration of diffusion tensor images

We present an algebraic solution to direct registration of diffusion tensor images under various local deformation models. We show how to linearly recover the 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. Given the tensor reorientation map, we show that solving for a rigid deformation becomes a linear problem. We test our direct approach on synthetic, brain and heart DT images