= Solution
TODO: Biology deferred at the user's request: clinical registration applications and their validation requirements.
Generic <image registration> estimates a coordinate transformation aligning corresponding features in two images. A rigid transform permits translation and rotation, an affine transform additionally permits linear deformation, and a nonrigid model permits spatially varying displacement. The transformation class expresses assumptions about what changes between the acquisitions.
One can minimize a discrepancy between $I_1(T(\mathbf x))$ and $I_2(\mathbf x)$, using interpolated image values and an explicit <optimization> procedure. Squared intensity differences suit some comparable acquisitions; <mutual information> can compare statistical dependence when image contrasts differ. Landmarks, feature descriptors or additional geometric constraints provide other information. Smoothness or other <regularization> controls overly flexible transformations. A favorable objective value does not by itself prove correct feature correspondence.
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