Characterizing changes in MR images with color-coded Jacobians.

Image registration is the process of establishing spatial correspondence between two images or between two image volumes. Registration can be achieved by rigid, elastic, or a combination of rigid and elastic transforms that attempt to bring the two images into coincidence. A rigid transform accounts for differences in positioning and an elastic transform describes deformations due to differences in tissue properties, temporal changes due to growth or atrophy, or differences between individuals. Deformation-based morphometry uses the resulting deformation fields from these transforms to evaluate differences between the images being registered. Three methods of registration were evaluated: rigid (affine) transformation, elastic optical flow transformation, and elastic spline transformation. All three methods produce vector deformation fields that map each point in one image to a point in the other image. A 12-color map of the transformation Jacobian was used to represent local volume changes. Using the three registration methods, color-mapped Jacobians were determined using a simulated three-dimensional block with known translation, rotation, expansion, contraction, and intensity modulations. Color-coded Jacobians were also generated for experimentally measured magnetic resonance image volumes of water-filled balloons and 7-year-old twin boys. Color-coded Jacobians overlaid on anatomical images provide a convenient method to identify regional tissue expansion and contraction.