Nonrigid Image Registration With Crystal Dislocation Energy

Abstract

The goal of nonrigid image registration is to find a suitable transformation such that the transformed moving image becomes similar to the reference image. The image registration problem can also be treated as an optimization problem, which tries to minimize an objective energy function that measures the differences between two involved images. In this paper, we consider image matching as the process of aligning object boundaries in two different images. The registration energy function can be defined based on the total energy associated with the object boundaries. The optimal transformation is obtained by finding the equilibrium state when the total energy is minimized, which indicates the object boundaries find their correspondences and stop deforming. We make an analogy between the above processes with the dislocation system in physics. The object boundaries are viewed as dislocations (line defects) in crystal. Then the well-developed dislocation energy is used to derive the energy assigned to object boundaries in images. The newly derived registration energy function takes the global gradient information of the entire image into consideration, and produces an orientation-dependent and long-range interaction between two images to drive the registration process. This property of interaction endows the new registration framework with both fast convergence rate and high registration accuracy. Moreover, the new energy function can be adapted to realize symmetric diffeomorphic transformation so as to ensure one-to-one matching between subjects. In this paper, the superiority of the new method is theoretically proven, experimentally tested and compared with the state-of-the-art SyN method. Experimental results with 3-D magnetic resonance brain images demonstrate that the proposed method outperforms the compared methods in terms of both registration accuracy and computation time.