An Investigation of NURBS-Based Deformable Image Registration

Deformable image registration (DIR) is an essential tool in medical image processing. It provides a means to combine image datasets, allowing for intra-subject, inter-subject, multi-modality, and multi-instance analysis, as well as motion detection and compensation. One of the most popular DIR algorithms models the displacement vector field (DVF) as B-splines, a sum of piecewise polynomials with coefficients that enable local shape control. B-splines have many advantageous properties in the context of DIR, but they often struggle to adequately model steep local gradients and discontinuities. This dissertation addresses that limitation by proposing the replacement of conventional B-splines with a generalized formulation known as a Non-Uniform Rational B-Splines (NURBS). Beginning with the 1D fitting, heuristic rules are developed to determine the values of the additional free parameters introduced by NURBS. These rules are subsequently modified and extended to the 2D and 3D fitting of anonymized and publicly available patient DVFs. Based on the lessons learned from these increasingly complex test cases, a 2D DIR scheme is developed and tested on slices from a thoracic computed tomography (CT) scan. Finally, an automatic, non-uniform scheme is presented, and its registration performance is compared to the conventional uniform methods