Nonparametric statistical methods for image segmentation and shape analysis

Image segmentation, the process of decomposing an image into meaningful regions, is a fundamental problem in image processing and computer vision. Recently, image segmentation techniques based on active contour models with level set implementation have received considerable attention. The objective of this thesis is in the development of advanced active contour-based image segmentation methods that incorporate complex statistical information into the segmentation process, either about the image intensities or about the shapes of the objects to be segmented. To this end, we use nonparametric statistical methods for modeling both the intensity distributions and the shape distributions. Previous work on active contour-based segmentation considered the class of images in which each region can be distinguished from others by second order statistical features such as the mean or variance of image intensities of that region. This thesis addresses the problem of segmenting a more general class of images in which each region has a distinct arbitrary intensity distribution. To this end, we develop a nonparametric informationtheoretic method for image segmentation. In particular, we cast the segmentation problem as the maximization of the mutual information between the region labels and the image pixel intensities. The resulting curve evolution equation is given in terms of nonparametric density estimates of intensity distributions, and the segmentation method can deal with a variety of intensity distributions in an unsupervised fashion. The second component of this thesis addresses the problem of estimating shape densities from training shapes and incorporating such shape prior densities into the image segmentation process. To this end, we propose nonparametric density estimation methods in the space of curves and the space of signed distance functions. We then derive a corresponding curve evolution equation for shape-based image segmentation. Finally, we consider the case in which the shape density is estimated from training shapes that form multiple clusters. This case leads to the construction of complex, potentially multi-modal prior densities for shapes. As compared to existing methods, our shape priors can: (a) model more complex shape distributions; (b) deal with shape variability in a more principled way; and (c) represent more complex shapes. Thesis Supervisor: Alan S. Willsky Title: Professor of Electrical Engineering and Computer Science