Computational Geometry Algorithms for Medical Problems in Radiation Therapy and Medical Imaging

放射治疗和医学成像中医学问题的计算几何算法这个项目研究了在放射治疗、医学成像和其他应用中出现的一些重要的计算几何问题。目标几何问题包括多叶准直器叶片排序、场划分、形状逼近、球体包装和图像分割与分析。这些问题在当前的医学研究和临床实践中起着至关重要的作用，特别是在癌症和其他疾病的诊断成像和放射外科治疗中。该项目的影响超出了计算几何和计算机科学的范畴。它将产生高效和有效的算法和软件，以解决放射外科、医学成像和其他相关医学领域的关键问题。将开发新的算法方法和软件，用于计算比目前临床实践中使用的质量要好得多的癌症治疗放射外科计划。对于不同的解剖结构及其运动，将得到质量最优的3-D和4-D医学图像分割算法。因此，这项研究将有助于将计算机算法和现代医学的力量结合起来，提高患者的生活质量。从理论上讲，目标问题属于几何填充、覆盖、整形、划分、逼近等计算几何的基本问题，给计算几何的研究提出了新的挑战和新的问题来源。为了开发新的几何技术来解决这些问题，必须使用其他理论领域的不同思想和方法，如图形算法、组合优化和运筹学。算法实现、实验、评估和软件开发是该项目的关键组成部分。研究小组一直在与医学研究人员和从业者合作，并为他们的实验研究获得真实的医学数据和临床放射治疗系统。这项研究的智力价值包括：(1)为解决当前医学研究和实践中面临的一系列重要几何问题提供了新的算法技术；(2)将新鲜的和理论上有趣的问题和算法引入计算几何，丰富了这一领域，并推动了几何技术的进一步发展；(3)为图算法、组合优化和运筹学等其他理论领域提出了具有挑战性的新问题和新方法，并为这些领域带来了新的应用。

Computational Geometry Algorithms for Medical Problems in Radiation Therapy and Medical Imaging 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.