SU-F-J-79: Extension of Fixed-Point Iteration Algorithm for Inverse Deformation




(I) To present a modification of the fixed point iteration algorithm to assure the convergence for a wide range of cases such as rotation and scaling deformations and (II) to provide implementation details with results from simulations and clinical images and emphasize more on practical considerations, such as how to choose good initial values to improve the speed of convergence. Inverse deformations are often applied to images, contours, and dose.


The 2D or 3D inverse deformation field is iteratively found by taking a partial step size parameter (< 1) in a given direction which depends on the forward deformation field as opposed to a full step size parameter (= 1) as in the original fixed-point inverse deformation paper. The step size parameter controls the size of the change in the inverse deformation field during each iteration. The step size parameter is also dynamically changed to achieve convergence faster.


The new method was implemented in Matlab and tested for both 2D simulated cases and 3D clinical cases. We started the main iteration loop with step size parameter = 1 and then dynamically changed it to achieve convergence of maximum voxel error of 0.01. The same method was implemented for deformation fields from deformable registration of three patients to another set of patient data. Convergence of the inverse deformation fields was also achieved for the patient cases.


If the step size parameter is small enough, then the improved iterative algorithm achieves convergence for a wider array of cases such as rotations and scaling of the image. The method is demonstrated to be successful for 2D simulated data and 3D patient data sets and allows for the finding of inverse deformation fields for a wider range of cases.

Supported by Cancer Prevention & Research Institute of Texas (CPRIT) - ID RP150485