Novel Methods for Multidimensional Image Segmentation
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Artificial vision is the problem of creating systems capable of processing visual information. A fundamental sub-problem of artificial vision is image segmentation, the problem of detecting a structure from a digital image. Examples of segmentation problems include the detection of a road from an aerial photograph or the determination of the boundaries of the brain's ventricles from medical imagery. The extraction of structures allows for subsequent higher-level cognitive tasks. One of them is shape comparison. For example, if the brain ventricles of a patient are segmented, can their shapes be used for diagnosis? That is to say, do the shapes of the extracted ventricles resemble more those of healthy patients or those of patients suffering from schizophrenia? This thesis deals with the problem of image segmentation and shape comparison in the mathematical framework of partial differential equations. The contribution of this thesis is threefold: 1. A technique for the segmentation of regions is proposed. A cost functional is defined for regions based on a non-parametric functional of the distribution of image intensities inside the region. This cost is constructed to favor regions that are homogeneous. Regions that are optimal with respect to that cost can be determined with limited user interaction. 2. The use of direction information is introduced for the segmentation of open curves and closed surfaces. A cost functional is defined for structures (curves or surfaces) by integrating a local, direction-dependent pattern detector along the structure. Optimal structures, corresponding to the best match with the pattern detector, can be determined using efficient algorithms. 3. A technique for shape comparison based on the Laplace equation is proposed. Given two surfaces, one-to-one correspondences are determined that allow for the characterization of local and global similarity measures. The local differences among shapes (resulting for example from a segmentation step) can be visualized for qualitative evaluation by a human expert. It can also be used for classifying shapes into, for example, normal and pathological classes.