Constrained non-rigid registration using Lagrange multipliers for application in prostate radiotherapy

This paper presents a novel free-form deformation registration algorithm with non-rigid constraints to capture the transformation between the planning day and treatment day CT images used for external beam radiotherapy for prostate cancer. The non-rigid registration is constrained to the predetermined motion of segmented soft tissues, and the constrained optimization problem is solved by the method of Lagrange multipliers. The ultimate goal is for the nonrigid transformation to be used to update the radiotherapy plan to take into account soft tissue deformation. The performance of this hard-constrained nonrigid registration (H-CNRR) algorithm has been compared to those achieved using rigid, fully non-rigid, and soft-constrained nonrigid registration (S-CNRR). The results clearly indicate that this Lagrange multipliers based hard-constrained nonrigid registration algorithm presented in this paper performed better at capturing the motion of the constrained organs.