A generalized correlation coefficient: Application to DTI and multi-fiber DTI

Multi-fiber models have been introduced as an efficient and interpretable way of representing the diffusion signal in areas with crossing fibers. However, no metric has been provided to use multi-fiber features in registration. The normalized correlation coefficient is commonly used in registration of scalar images due to its invariance under linear transformations of the intensities. In this paper, we generalize the normalized correlation coefficient for tensor and multi-tensor images. The generalized invariance allows linear transformations of the diffusion eigenvalues in the logarithmic domain. We subsequently use it as a metric for block matching and show that multi-tensor features leverage the accuracy of the matching in areas with crossing fibers.