Recent developments in medical imaging technology have changed the practice of medicine, providing physicians with powerful, non-invasive methods for studying the internal anatomy and function of the human body. These advances in imaging techniques offer both a great opportunity and a tremendous challenge for the image processing community to develop new tools to help the analysis and interpretation of the vast amount of complex medical imaging data now made available. The work presented in this thesis is motivated by the fascinating task of studying the structural and functional relationship of the human brain, with the specific aim of developing automatic, geometrically accurate, and topologically correct methods for reconstructing the brain cortical surfaces from 3D magnetic resonance brain images.; This dissertation makes four main contributions. First, we have developed an efficient and automatic topology correction algorithm, which can be applied to remove all the handles from an initial segmentation of the human brain cortex having the wrong topology. Second, we have proposed a class of new topology preserving geometric deformable models, which improve upon the traditional geometric deformable models by imposing topological control. Third, we have designed an updated system for the automatic reconstruction of the inner, central, and outer surfaces of the brain cortex. Finally, we have developed a moving grid technique to help resolve the resolution problem of geometric deformable models.
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