Introduction
Image registration seeks a transformation that will warp one image
onto another. Of course, in the absence of constraints, any image can be
warped to match another exactly. Usually constraints are derived from
the specific application.
A number of situations arise in medical imaging in which one wishes to
compute a transformation between two or more images. Image
registration between two medical images allows one to compare the same
subject across different imaging modalities, compare the same
anatomy in different subjects, or to monitor dynamic processes without
interference from subject motion. Image registration is an active area
of research in functional MRI.
In the simplest case, one merely wishes to correct for patient
motion. Here it is assumed that the imaging characteristics are
preserved across images, such that the same features appear in
both images being registered. In this case, relatively simple models
of motion can be used in which motion is said to be rigid. Simple
metrics of similarity can then be developed based on assumptions about
the effects of motion on intensity. For example, it may be assumed
that motion preserves intensity (Friston, Cox) or linearly scales
intensity (Woods). Alternatively, an intensity correction can
be performed before registering (Nestares). Small motion is often
assumed, allowing the system to be linearized (Friston,
Nestares). Although these assumptions may appear restrictive,
small motion approximations may be bootstrapped to handle large
motions (eg- using multi-resolution implementations, see Nestares).
This project considers the least-squares optimal calculation of two
simple models for motion, the rigid-body and affine
transformations. These models will be analyzed based on their
applicability to fMR patient motions.