The research of this project is at the interface between computational geometry and surgery related to cardiovascular diseases. Cardiovascular diseases (such as vessel narrowing and blockage) have been major causes of death in the United States for a long time. The primary method for dealing with such diseases is to conduct interventional procedures, such as angiography, angioplasty, and coronary stent implant, in a minimally invasive manner. The research focus of this project is on developing efficient algorithms and techniques for solving a set of important geometric problems arising in these interventional procedures.
The target geometric problems include imaging geometry determination, high dimensional maximum inscribed sphere, k-set correspondence, projective curve-level, curve and point-set clustering, and minimum energy paths. New algorithms for these problems not only provide more efficient solutions to key problems in these interventional procedures, but also have the potential to be used in many other applications. The application of computational geometry techniques to medical problems is intellectually deep and can result in advances in both computational geometry and medicine. An important goal of this research is dissemination of implemented algorithms in software to application domains. In doing this, it will help to bring together the computer science and the medical community.
