Anotace:
Medical images are increasingly used within healthcare for diagnosis, planning treatment, and monitoring disease progression. The images acquired at different times, with different imaging modalities, from different subjects etc. often provide an additional clinical information that is not revealed in the separate images. The spatial relation between the images has to be found and this process is called image registration. In our contribution, we use elastic registration which assumes that the images are two different observations of an elastic body which is discretized by the finite element method. We are especially interested in the problems where the requirements on the registration prevent the application of standard FFT based solvers to the solution of auxiliary linear problems, which is the case when the part of the two observations can be related by a rigid body motion. Because the medical images usually contain a large area of background and a small area of changes, a regular discretization results in waste of computational resources due to the fine refinement of the space outside the region of interest (especially in 3D). To avoid this, we use coarser grid with local refinement that takes into account specific features of the images and their differences. The related elasticity problems are solved by TFETI, which is a variant of the Finite Element Tearing and Interconnecting (FETI) domain decomposition method for massively parallel numerical solution of elliptic Partial Differential Equations (PDE) with optimal complexity.