Variational techinques with applications to segmentation of medical images

Abstract

During the last decades, medical imaging has experienced an increasing importance in clinical practice with the development of new image acquisition techniques of the human body. The huge amount of information that becomes available with the images has promoted the development of image processing methods to automatically analyse and interpret the images in a reliable way. Both segmentation and registration of medical images have been identified as key problems in medical image analysis becoming challenging areas of active resarch. This Thesis aims at the development of methods for the segmentation and registration of medical images in the framework of challenging applications. The common fact existing between these methods is that they are formulated from variational problems defined in their respective spaces of solutions. First, we have proposed a method for automatic segmentation of the cerebral vasculature from angiographic data. The method is based on a region-based implicit deformable nipdel implemented within the level set paradigm. Region-based information is computed from the probabilities associated to the main tissue 'types present in the medical images. In our method, a non-parametric model for probability estimation is assumed. The feature space is composed of high-order multi-scale differential image descriptors that have shown efficient enough to discriminate vessels from other structures. The method has been successfully applied to the segmentation of cerebral aneurysms in 3D-RA,and CTA showing to outperform some of the region-based implicit deformable models that could compete in performance for this application. Second, we have focused on the study of the Riemannian manifold of diffeomorphisms and the devise of efficient methods for diffeomorphic registration intended to spread the use of diffeomorphisms in clinical research studies. Our method includes the stationary parameterization of diffeomorphisms in the Large Deformation Diffeomorphic Metric Mapping (LDDMM) paradigm. We have formulated the variational problem related to the registration scenario and derived the associated Euler-Lagrange equations. Our method has shown to provide similar or even improved results while drastically reducing memory and time requirements with respect to reference LDDMM. In addition, we have proposed a Gauss-Newton method for optimization in order to introduce efficiency and robustness during registration that has been favorably compared to other efficient diffeomorphic registration algorithms that were proposed in the literatúre simultaneously to our conference results. Our algorithm has been successfully used in the generation of 3D statistical brain atlases"from statistics on populations of diffeomorphisms.