Locally Orderless Registration for Diffusion Weighted Images

Registration of Diffusion Weighted Images (DWI) is challenging as the data, in contrast to scalar-valued images, is a composition of both directional and intensity information. The DWI signal is known to be influenced by noise and a wide range of artifacts. Therefore, it is attractive to use similarity measures with invariance properties, such as Mutual Information. However, density estimation from DWI is complicated by directional information. We address this problem by extending Locally Orderless Registration (LOR), a density estimation framework for image similarity, to include directional information. We construct a spatio-directional scale-space formulation of marginal and joint density distributions between two DWI, that takes the projective nature of the directional information into account. This accounts for orientation and magnitude and enables us to use a wide range of similarity measures from the LOR framework. Using Mutual Information, we examine the properties of the scale-space induced by the choice of kernels and illustrate the approach by affine registration.