Geometric and Combinatorial Algorithms for Optimal Surface Segmentation in Medical Images

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Efficient detection of globally optimal surfaces representing object boundaries in volumetric images is fundamental and remains challenging in modern computer-assisted medical diagnosis and treatment and many other important medical applications. This research deals with specific problems of detecting optimal single and multiple interacting surfaces in volumetric image datasets. It permits identification of optimal surfaces of terrain-like shapes, cylindrical shapes, and complex shapes. Image data sets we consider have various different image features, such as edge, texture, and shape. The essence of these problems is to solve a number of important geometric optimization problems belonging to the fundamental topics of computational geometry, such as surface identification, geometric partitioning, geometric k-means clustering, and metric labeling. The research focus of this project is on developing efficient algorithms and novel techniques for solving these crucial problems with a provably global optimality. The application of geometric and combinatorial techniques to medical problems is intellectually deep and can result in advances in both theoretical computer science and medicine. The proposed image analysis methods allow evaluating the image data objectively in a quantitative manner, promising to substantially impact image-based clinical care. An important goal of this research is dissemination of implemented algorithms in software to application domains. In doing this, it helps to bring together the computer science and the medical community.Intellectual Merit: We expect this project to make a number of theoretical contributions: (1) providing new algorithmic techniques for solving a set of crucial computational problems confronted by current medical research and applications; (2) introducing fresh and theoretically interesting problems and algorithms to geometric and combinatorial optimization, enriching and prodding further development of the field; (3) presenting new challenging problems and new approaches to other theoretical areas such as graph algorithms and operations research, and bringing new applications to these areas.Broader Impacts: The successful completion of this project will result in methodologies that greatly accelerate the pace of 3-D and 4-D medical image processing. The automated image segmentation software will be platform independent and will directly address the needs of a broad base of end users across a wide range of disciplines from basic research to clinical medicine. The proposed image analysis tools will provide clinicians with the means to assess diseased organs in 3-D and 4-D, rather than in 2-D as is typically done in conventional practice. In addition, infusion of the research results into the classroom provides students with a unique opportunity to study and practice in the emerging important interdisciplinary area involving computer science and modern medicine, promotes interdisciplinary learning, and enables the training of more versatile scientists.