Fuzzy-based kernel regression approaches for free form deformation and elastic registration of medical images

In modern medicine, a largely diffused method for gathering knowledge about organs and tissues is obtained by means of merging information from several datasets. Such data are provided from multimodal or sequential acquisitions. As a consequence, a pre-processing step that is called “image registration” is required to achieve data integration. Image registration aims to obtain the best possible spatial correspondence between misaligned datasets. This procedure is also useful to correct distortions induced by magnetic interferences with the acquisition equipment signals or the ones due patient’s involuntary movements such as heartbeat or breathing. The problem can be regarded as finding the transformation, defined by a set of parameters, that best maps one dataset (namely the input or floating image) into the other (namely the target or base image). At the end of the process, corresponding pixels/voxels will have the same positions in both images/volumes. This chapter starts presenting a brief taxonomy of literature registration methods. Then, an excursus of novel registration methods is presented after a more detailed explanation of the Thin-Plate Spline approach (Bookstein, 1989), which is a milestone in the field. All of these schemes use a “fuzzy kernel-based” approach able to cope with many type of deformations. The described procedures are examples of landmark-based approaches that rely on a set of a priori known control points, even though the same concepts could be extended to area-based approach where no control points need to be detected. All of the methods use fuzzy membership maps in a probabilistic discriminative model, which is based on kernel regression. Such techniques are based on concepts derived by Fuzzy c-means clustering process (Dunn, 1973 and Bezdek, 1981). However, no clustering algorithm needs to be performed at all. The framework uses several measures, both quantitative and qualitative to evaluate the performance of the method. In all of the presented approaches the global mapping function is recovered as continue and smooth composition of local mappings. This philosophy allows dealing with subtle local deformations without the need of using extremely time consuming complex models. The methods were extensively tested and validated and the experimental results are reported. Final consideration and future work are then discussed.