This project investigates a number of important computational geometry problems that arise in radiation therapy, medical imaging, and other applications. The target geometric problems include multileaf collimator leaf sequencing, field partitioning, shape approximation, sphere packing, and image segmentation and analysis. These problems play crucial roles in current medical research and clinical practice, especially in diagnostic imaging and radiosurgical treatment of cancers and other diseases. The project has broader impacts beyond computational geometry and computer science. It will produce efficient and effective algorithms and software for solving key problems in radiosurgery, medical imaging, and other related medical areas. New algorithmic approaches and software for computing radiosurgical plans of much better quality for cancer treatment than those used in current clinical practice will be developed. Optimal quality 3-D and 4-D medical image segmentation algorithms for various anatomical structures and their motions will be obtained. Thus, this study will help unite the powers of computer algorithms and modern medicine, and improve the quality of life for patients.
Theoretically, the target problems belong to fundamental topics of computational geometry such as geometric packing, covering, shaping, partitioning, and approximation, and present significant new challenges and new problem sources to computational geometry research. To develop new geometric techniques for solving these problems, diverse ideas and methods from other theoretical areas, such as graph algorithms, combinatorial optimization, and operations research, must be utilized. Algorithm implementation, experimentation, evaluation, and software development are a crucial component of this project. The investigator's group has been working with medical researchers and practitioners, and has access to real medical data and clinical radiation treatment systems for their experimental studies. The intellectual merit of this research includes: (1) providing new algorithmic techniques for solving a set of important geometric problems confronted by current medical research and practice; (2) introducing fresh and theoretically interesting problems and algorithms to computational geometry, enriching this area, and prodding further development of geometric techniques; (3) presenting new challenging problems and new approaches to other theoretical areas such as graph algorithms, combinatorial optimization, and operations research, and bringing new applications to these areas.
