Multiscale nonrigid data registration using adaptive basis functions

When performing registrations, it is often crucial to maintain certain structure of the template data T-the data being deformed into the subject data S-as well as to keep the deformation field smooth. Current approaches to registration often impose smoothness through heuristic means, but building it into the model has proven to be more difficult due mainly to computational constraints. In this paper, we view the registration problem as the following: find a deformation nu so that cost C(T, S, nu) is minimized. We model the deformation field as nu := Sigma (n)(i=1) c(i)phi (i), in which the {c(i)} are multipliers for basis functions {phi (i)} whose shape and size are chosen adaptively. This gives flexibility in incorporating automatic basis function selection methods and a priori information about T and S into the model. By selecting and placing basis functions appropriately, the number of basis functions required to produce a good deformation is reduced over uniform grid methods. Thus, this method should provide both improved computational speed and improved accuracy over such methods.