NURBS-Based Deformable Image Registration
T Jacobson*, M Murphy, Virginia Commonwealth University, Richmond, VAMO-F-BRA-3 Monday 4:30:00 PM - 5:15:00 PM Room: Ballroom A
Purpose: To develop and investigate the efficacy of optimization schemes for Non-Uniform Rational B-Splines (NURBS) in deformable image registration (DIR).
Methods: Previously, we developed a method for fitting a known DIR displacement vector field (DVF) using non-uniform knot placement in one- and two- dimensions. In this method, an initial fit was made with uniform knot spacing. The error generated by this fit served as an attractive force pulling on the knots, acting against a resistive spring force in an iterative equilibration scheme. This two-step approach has been extended to three-dimensional deformable image registration by allowing the difference image to serve as the attractive force, which now acts on planes of knots. We compare the force equilibration scheme with a simplex search for the optimized rectilinear positioning of the planes of knots. In addition, we investigate the efficacy of simplex and gradient descent searches for optimizing the control points and their associated weights.
Results: In one- and two-dimensional B-spline fits to known DVFs, the force equilibration scheme was shown to produce non-uniform knot patterns that reduced both the overall sum of squared errors and the frequency of large errors. Non-rational B-spline fits to surface DVFs were found to be more accurate than rational B-spline fits with the same number of total free parameters.
Conclusions: Non-uniform B-splines offer an attractive alternative to uniform B-splines in modeling DVFs. Specifically, knot placement offers increased local control as well as the ability to explicitly represent topological discontinuities in the deformation. We are investigating the most effective method to solve for NURBS configurations in the problem of three-dimensional deformable image registration.