Boundary-constrained inverse consistent image registration and its applications

This dissertation presents a new inverse consistent image registration (ICIR) method called boundary-constrained inverse consistent image registration (BICIR). ICIR algorithms jointly estimate the forward and reverse transformations between two images while minimizing the inverse consistency error (ICE). The ICE at a point is defined as the distance between the starting and ending location of a point mapped through the forward transformation and then the reverse transformation. The novelty of the BICIR method is that a region of interest (ROI) in one image is registered with its corresponding ROI. This is accomplished by first registering the boundaries of the ROIs and then matching the interiors of the ROIs using intensity registration. The advantages of this approach include providing better registration at the boundary of the ROI, eliminating registration errors caused by registering regions outside the ROI, and theoretically minimizing computation time since only the ROIs are registered. The first step of the BICIR algorithm is to inverse consistently register the boundaries of the ROIs. The resulting forward and reverse boundary transformations are extended to the entire ROI domains using the Element Free Galerkin Method (EFGM). The transformations produced by the EFGM are then made inverse consistent by iteratively minimizing the ICE. These transformations are used as initial conditions for inverse-consistent intensity-based registration of the ROI interiors. Weighted extended B-splines (WEB-splines) are used to parameterize the transformations. WEB-splines are used instead of B-splines since WEB-splines can be