Regularized image registration with line search optimization

Abstract

Image registration is normally solved as a regularized optimization problem. The line search procedure is commonly employed in unconstrained nonlinear optimization. At each iteration step the procedure computes a step size that achieves adequate reduction in the objective function at minimal cost.In this paper we extend the constrained line search procedure with different regularization terms so as to improve convergence. The extension is addressed in the context of constrained optimization to solve a regularized image registration problem. Specifically, the displacement field between the registered image pair is modeled as the sum of weighted Discrete Cosine Transform basis functions. A Taylor series expansion is applied to the objective function for deriving a Gauss-Newton solution. We consider two regularization terms added to the objective function. A Tikhonov regularization term constrains the magnitude of the solution and a bending energy term constrains the bending energy of the deformation field. We modify both the sufficient and curvature conditions of the Wolfe conditions to accommodate the additional regularization terms. The proposed extension is evaluated by generated test collection with known deformation. The experimental evaluation results show that a solution obtained with bending energy regularization and Wolfe condition line search achieves the smallest mean deformation field error among 100 registration pairs. This solution shows in addition an improvement in overcoming local minima.