Log-unbiased large-deformation image registration

In the past decade, information theory has been studied extensively in medical imaging. In particular, image matching by maximizing mutual information has been shown to yield good results in multi-modal image registration. However, there has been few rigorous studies to date that investigate the statistical aspect of the resulting deformation fields. Different regularization techniques have been proposed, sometimes generating deformations very different from one another. 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 log-unbiased image registration methods. The proposed framework yields both theoretically and intuitively correct deformation maps, and is compatible with largedeformation models. In the results section, we tested the proposed method using pairs of synthetic binary images, two-dimensional serial MRI images, and three-dimensional serial MRI volumes. 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.