Consistent Nonlinear Elastic Image Registration

This paper describes a new bidirectional image registration algorithm that estimates a consistent set of nonlinear forward and reverse transformations between two Ndimensional images. The registration problem is formulated in a N+1-dimensional space where the additional dimension is referred to as the temporal or time dimension. A periodic-in-time, nonlinear, N+1-dimensional transformation is estimated that deforms one image into the shape of the other and back again. The registration problem is solved numerically by discretizing the temporal dimension such that there is an incremental image and transformation at each time point. Nonlinear deformations from one image to the other are accommodated by concatenating the linear, small-deformation incremental transformations. An inverse consistency constraint is placed on the incremental transformations to enforce within a specified tolerance that the forward and reverse transformations between the two images are inverses of each other. Results are presented for 2D image registration problems. These results demonstrate the feasibility of accommodating both linear and nonlinear deformations.