A variational method for registering or mapping like points in medical images is proposed and analyzed. The proposed variational principle penalizes a departure from rigidity, and thereby provides a natural generalization of strictly rigid registration techniques widely used in medical applications. The mathematical formulation is necessarily complex in order to meet a number of constraints and boundary conditions, and is, generally speaking, an optical flow technique.

A finite element technique is developed for solving the proposed problem. Several simple artificial examples are shown to illustrate how the technique works. The method is tolerant to image excision, making it applicable to a larger set of medical applications. A method for producing nonblurred interpolated images is provided, which could improve the matching of patient images to a medical atlas. Finally, the approach is applied to a pair of magnetic resonance images. Thirty-four references are given.