Multiscale Approach for Three-Dimensional Conformal Image Registration

Abstract

Image registration, especially for three-dimensional (3D) image registration, is widely used in clinical medicine. Many 3D image registration models have been proposed during the last decades. All these models achieve the minimum of the cost functional with some prior regularization. In addition, the physical mesh folding phenomenon is not taken into consideration in most models. This raises a question of whether one can achieve/approach the infimum of the cost functional without a regularization term and ensure no mesh folding. To give an answer to this question, a multiscale approach for 3D conformal image registration is presented in this paper. This approach ensures no mesh folding and gets close to the infimum of the cost functional without any regularization on the 3D conformal set. The 3D multiscale approach contains a series of deformation composition processes and the convergence of the process is presented. Furthermore, a numerical algorithm for this multiscale approach is proposed and the convergence of the numerical algorithm is proved. Moreover, several numerical tests are also listed to show the good performance of the proposed algorithm.