Fast FEM-Based Non-Rigid Registration

In this paper, we present a fast and accurate implementation of the diffusion-based non-rigid registration algorithm. Traditionally, finite differences are used to implement registration algorithms due to their ease of implementation. However, finite differences are sensitive to noise, and they have a narrow numerical stability range. Further, finite differences employ a uniform grid. This is often not desirable in the case of registration, as finer resolution is needed to capture the displacement field in regions that have a high number of image features, as opposed to homogeneous regions with fewer features. On the other hand, the less explored Finite Element Methods are ideal for the non-rigid registration task, as they use a non-uniform discretization of the image domain, placing points based on the local image-feature information. We present such an FEM-based implementation of a popular diffusion-based registration algorithm~\cite{stefanescu04}. Originally, this algorithm was implemented using finite differences. Experimentally, we show that our implementation is much faster than the corresponding finite difference implementation, and that it achieves this In this paper, we present a fast and accurate implementation of the diffusion-based non-rigid registration algorithm. Traditionally, finite differences are used to implement registration algorithms due to their ease of implementation. However, finite differences are sensitive to noise, and they have a narrow numerical stability range. Further, finite differences employ a uniform grid. This is often not desirable in the case of registration, as finer resolution is needed to capture the displacement field in regions that have a high number of image features, as opposed to homogeneous regions with fewer features. On the other hand, the less explored Finite Element Methods are ideal for the non-rigid registration task, as they use a non-uniform discretization of the image domain, placing points based on the local image-feature information. We present such an FEM-based implementation of a popular diffusion-based registration algorithm [8]. Originally, this algorithm was implemented using finite differences. Experimentally, we show that our implementation is much faster than the corresponding finite difference implementation, and that it achieves this computational speed without compromising the accuracy of the non-rigid registration results. computational speed without compromising the accuracy of the non-rigid registration results. [8] R. Stefanescu, X. Pennec, and N. Ayache, "Grid powered nonlinear image registration with locally adaptive regularization", Medical Image Analysis, 8(3):325–342, 2004.