Quantifying deformation using information theory: The log-unbiased nonlinear registration

In the past decade, information theory has been studied extensively in medical imaging. In particular, maximization of mutual information has been shown to yield good results in multi-modal image registration. In this paper, we apply information theory to quantifying the magnitude of deformations. We examine the statistical distributions of Jacobian maps in the logarithmic space, and develop a new framework for constructing image registration methods. The proposed framework yields both theoretically and intuitively correct deformation maps, and is compatible with large-deformation models. In the results section, we tested the proposed method using a pair of serial MRI images. We compared our results to those computed using the viscous fluid registration method, and demonstrated that the proposed method is advantageous when recovering voxel-wise local tissue change.