Towards automatic geometric algorithms for solving fundamental problems in computer graphics, medical and biological imaging applications

An important goal of many computer vision an image processing techniques is to extract useful quantitative information contained in images in order to achieve some higher level task. For these tools to be of any practical use, common requirements are robustness and automation so bigger amounts of information can be reliably processed as increasingly demanded by computer graphics, computer vision, biological and medical applications. We develop a number of such techniques demonstrating their particular impact in non-photo realistic rendering, statistical analysis of HIV infected particles, video segmentation under severe occlusions and variability analysis of white matter structure in the brain.; Non-Photorealistic Rendering (NPR) is an important modality of computer generated stylized depiction. Virtually all state-of-the-art algorithms require manual or used assisted tasks when extracting scene and geometry features from either 2D images or full 3D models. Using multiple images as input, we propose a novel hybrid model that provides a degree of automation not achieved by any existing NPR technique.; Electron tomography allows determination of the three-dimensional architecture of subcellular assemblies and organelles at very high resolutions. Development of reliable quantitative approaches for interpretation of tomograms is a challenging problem because of the low signal-to-noise ratios that are inherent to biological images. We present methods for the automated segmentation of tomograms obtained from HIV-infected macrophages by developing a novel algorithm that finds image boundaries as global minimal surfaces.; Despite numerous efforts by researchers, successful tracking of moving objects that possibly change shape and are subject to occlusions still remains a challenging problem. We present an algorithm that handles particularly well the presence of severe and total occlusions by adopting an edge based segmentation approach that finds boundaries as a minimal surfaces in 3D space-time.; Diffusion Tensor Imaging (DTI) allows elucidation of neural paths in the white matter of the brain which is of paramount importance for understanding brain anatomy and has also implications for surgical planing. We will work on tensor based segmentation techniques for the automatic extraction of fiber bundles from DTI, using a novel statistical region based approach.