From volumetric graphical objects to surface registration

Relatively recent developments in medical imaging allow the anatomical and functional noninvasive study of internal organs of the body. One of the most complex and interesting organs in our body is the brain. Many efforts are being carried out to try to understand how it works, its internal connections, how different zones interact with each other, why, in some cases, a zone takes in charge a functionality of another damaged one, etc.; the questions are innumerable and the answers, if any, are sparse. Recently, magnetic resonance imaging (MRI) equipments have been developed to capture the functional activity of the brain. Unfortunately, functional images suffer from a lack of spatial resolution. Thus, the need of combining them with anatomical ones, which have a much higher quality. Nowadays these images provide precious information for diagnosis purposes and this is the reason for the need of imaging tools to extract and analyze the information which is present in those images, and which sometimes is not appreciable for the human eye. Acquired MRI images are presented as volumetric sets of data with which one can reconstruct a three dimensional volumetric model of the scanned organ. Nevertheless, sometimes physicians are just interested in the surface of the organ, for example in brain functional activation studies. In addition, many times it is important to be able to carry out group studies, or to locate a lesion with respect to a standard reference. To do such studies it is necessary to perform a transformation of the surfaces in order to put them into correspondence. Such technique is called registration. Unfortunately, volumetric registration does not give satisfactory results for surface registration purposes. The solution is to work directly with surfaces instead of processing the volumetric data. Unfortunately we do not have information about the surfaces, hence the need of computer graphics and computer vision techniques. The present work proposes a number of methods to help in the task of providing information from volumetric objects to surface registration. To achieve that some stages are necessary. The proposed stages are independent one from another so they can be used, or not, depending on the particular need. They can even be used for other purposes than those presented in the present work. The first two stages address the problem of image quality. This is a very important "preprocessing" step because posterior processing will depend on the image quality. Usually MR images are corrupted with different artifacts; among them a spatial-dependent bias field and a Riciandistributed noise. For the former a supervised correction is proposed, and for the later a directional spatial filter using a novel diffusivity function. After both stages the volumetric MRI data is ready to be classified. The purpose of the proposed classification process is to extract the white matter of the brain, given that sulci are better extracted from white matt