Diffeomorphic Transformations for Automatic Multi-modality Image Registration

DIFFEOMORPHIC TRANSFORMATIONS FOR AUTOMATIC MULTI-MODALITY IMAGE REGISTRATION by Ramkrishnan Narayanan Co-Chairs: Charles R. Meyer and Jeffrey A. Fessler Image registration is usually the first step before performing any post-processing operations such as surgical planning, volumetric measurements, diagnosis, etc. There are numerous registration algorithms that use any of several geometric interpolants to warp images. The deformation can be modeled by a suitable parameterization of the interpolant, through a uniform grid placement of control points or adaptively, where control points are only placed where images are misaligned. Nonparametric approaches do not use control points at all, e.g., fields regularized by elastic constraints. There are two main challenges in control point based approaches: the choice of deformation model and the method of parameterization. While some transformations focus on modeling local changes, some on continuity and invertibility, there is no closed-form nonlinear parametric approach that satisfies all these properties. This dissertation presents a class of nonlinear transformations that are controllably local and continuous, and invertible under certain conditions. They are straightforward to implement, fast to compute and can be used as alternatives to splines and radial basis functions. The second challenge is the method of parameterization, that is, the location and scale at which control points are placed. Poor choice of parameterization results in deformations not being modeled accurately or over-parameterization, where control points may lie in homogeneous regions with low sensitivity to cost. This lowers computational efficiency due to high complexity of the search space and might also provide transformations that are not physically meaningful, and possibly folded. This dissertation proposes a method to find mismatched locations in images and the spatial scale at which they are misregistered. Mismatch is specified based on location and smooth spatial scale (mismatch vector) at which local joint entropy is high. First we show that mismatch vectors found by our method are in good agreement with known deformations applied to synthetic images. Next we use these attributes to parameterize our iterative registration method to demonstrate registration performance. The result is a completely automatic multimodality registration algorithm that achieves high accuracy of alignment (voxel sized errors) for the registration of brain structures in MR images.