Accelerated nonrigid image registration using improved Levenberg–Marquardt method

Abstract

B-splines have been successfully applied to nonrigid image registration and are popular in various applications. They offer a reduced computational overhead because changes in the control points only affect the transformation within a local neighborhood. Optimization is a key stage in image registration. Most optimization methods only use the gradient direction to determine the update step that may be not optimal. A suboptimal update step may result in a large number of iterations, thus significantly increases the computational time or decreases the accuracy of the registration results. Levenberg–Marquardt (L-M) optimization is a superior algorithm that provides more precise steps during the iteration process. However, because of the large number of parameters in nonrigid image registration, the L-M method suffers from high computational complexity. In this paper, a dedicated optimization method is proposed for nonrigid CT image registration based on L-M optimization. A regular L-M step along with an additional L-M step is computed as the optimal vector, which reduces the computation time because the Jacobian matrix is reused for two calculations in every iteration. Besides, the parameters change automatically according to the calculated results in each step to make the method more efficient. In addition, a linear search for the trial step is introduced to enhance performance. Experimental results indicate that the proposed method is effective and efficient.