Nonlinear registration using variational principle for mutual information

We extend the multimodal image registration method described in Alexander and Summers [Fast registration algorithm using a variational principle for mutual information, Proc. SPIE Int. Soc. Opt. Eng. 5032 (2003) 1053–1063] to nonlinear registration. A variational principle maximizing mutual information leads to an Euler–Lagrange (EL) equation for the displacement field, represented here in a basis of cubic B-spline functions. A cost function is constructed from the sum of squares of the residuals of the EL equation at a subset of pixels where the magnitude of the spatial gradient of intensity exceeds a user-chosen threshold. The unknown coefficients in the displacement field representation are evaluated using a Levenberg–Marquardt minimization procedure. The proposed method was successfully applied to several image pairs of the same and different modalities, and an artificially constructed series of images containing nonlinear distortions and noise.