Non-linear Registration Using Block-Matching and B-Splines

Medical image registration techniques are of particular importance to improve and facilitate working with images of the body interior. The main idea in medical image registration is to find a transformation that maps a source image as close as possible to a target image by determining a corresponding position for each point of the source. To find a mapping between two images that takes anatomic variabilities into account, the respective transformation must be non-linear. In this thesis, an algorithm is implemented that calculates a non-linear transformation to register 2D or 3D images. The transformation estimation is based on a block-matching technique that identifies a displacement field between two images. Using this set of correspondences as sampling points, the transformation is approximated by cubic B-Spline functions. In order to compute the approximation, a Least Squares estimator is employed which is extended in a second step to a weighted Least Squares approach to gain robustness. The minimization is solved by the conjugate gradient algorithm. For a high accuracy of the result, the transformation estimation is performed in an iterative manner that is in addition nested in a pyramidal approach. For reasons of noise influence and lack of sampling points in homogeneous regions, a biharmonic regularization term is integrated to smooth the unfavourable effects. Results are presented obtained by experiments on different artificial testing images as well as on images of histological slices of the brain. As highlighted, the non-linear approach yields satisfying registration results for most ...?. The implementation of the B-Spline transformation completes a program that registrates two images fully automatically in a linear or non-linear way.