One of the most important challenges in the development
of nonrigid registration techniques for functional-to-anatomical
brain image registration is the definition of appropriate
constraints to avoid excessive deformations. Regularization
methods, smoothness and diffeomorphic constraints have
been widely studied in the development of intersubject nonrigid
registration techniques [6] and are discussed in detail
in Section IV-B. These methods have also been used in the
above-mentioned studies on registration of functional EPI to
anatomical MRI; e.g., [155]–[158]. Other researchers have
investigated geometric constraints utilizing physical analysis
of distortion effects in EPI [157], [162]. Based on the analysis
of Spin Echo (SE) EPI, a logarithmic Jacobian correction
term has been incorporated into the optimization procedure
in [157]. A similar analysis has been performed in [162] for
gradient echo EPI, where a Jacobian correction term along
with a dephasing factor was incorporated into the optimization
framework. It should be noted that elastic regularization does
not necessarily need to comply with physical elastic properties
of the imaging material, especially pertinent in cases such as
EPI sequences used in fMRI, where the localized distortions
arise from artifacts in the imaging methods rather than changes
or differences in anatomy.