This paper presents a new method for image registration based on jointly
estimating the forward and reverse transformations between two images
while constraining these transforms to be inverses of one another. This
approach produces a consistent set of transformations that have less
pairwise registration error, i.e., better correspondence, than traditional
methods that estimate the forward and reverse transformations independently.
The transformations are estimated iteratively and are restricted to
preserve topology by constraining them to obey the laws of continuum
mechanics. The transformations are parameterized by a Fourier series
to diagonalize the covariance structure imposed by the continuum mechanics
constraints and to provide a computationally efficient numerical implementation.
Results using a linear elastic material constraint are presented using
both Magnetic Resonance and X-ray Computed Tomography image data. The
results show that the joint estimation of a consistent set of forward
and reverse transformations constrained by linear-elasticity give better
registration results than using either constraint alone or none at all.