Consistent Linear-Elastic Transformations for Image Matching

A fundamental problem with a large class of image registration techniques is that the estimated transformation from image A to B does not equal the inverse of the estimated transform from B to A. This inconsistency is a result of the matching criteria’s inability to uniquely describe the correspondences between two images. This paper seeks to overcome this limitation by jointly estimating the transformation from A to B and from B to A while enforcing the consistency constraint that these transforms are inverses of one another. The transformations are further restricted to preserve topology by constraining them to obey the laws of continuum mechanics. A new parameterization of the transformation based on a Fourier series in the context of linear elasticity is presented. Results are presented using both Magnetic Resonance and Xray Computed Tomography Imagery. It is shown that joint estimation of a consistent set of forward and reverse transformations constrained by linear-elasticity gives better registration results than using either constraint alone or none at all.