AF: Small: Algorithms in Computational Geometry and Medical Applications

现代医学研究和成像技术一起向医生和临床医生展示了数量惊人的详细分子或细胞结构。例如，一个二维图像幻灯片可以包含数百万个单元格。事实上，病理学家使用显微镜一次只能检查数十或数百个细胞，遗漏了大多数细胞，也遗漏了中间范围内可能的模式。该项目致力于通过计算几何学中强大的计算和分析技术来研究细胞图像中的模式，并在医学研究和应用中验证这些算法技术和基于这些技术构建的软件。该项目提出了具有挑战性的几何和算法问题，这些问题出现在疾病(例如乳腺癌、炎症性肠病和类风湿性关节炎)的诊断、预后和分析中，不同类型的免疫细胞(例如中性粒细胞、嗜酸性粒细胞、浆细胞和淋巴细胞)的识别和分类，以及集体移动和聚集的细菌(例如黄色粘液球菌和铜绿假单胞菌)的跟踪和分析中，根据一类Voronoi图(由首席研究员开发)，在Voronoi图中细胞集合会影响附近的邻居。具体的几何技术包括聚类诱导的Voronoi图、耦合最优形状逼近和基于推土机距离的匹配。在重要的医学问题中探索这些几何结构不仅将带来组合优化和机器学习的新方法，以及新的公开可用的医疗应用软件，而且还将培养学生从几何算法、软件开发到医学应用的广泛的跨学科研究和教育。通过为医生提供适当的分析工具，该项目及其学生将有助于拯救生命。

Modern medical research and imaging technologies together present physicians and clinicians with mind-boggling amounts of detailed molecular or cellular structures. For example, one 2-dimensional image slide can contain millions of cells. In fact, pathologists use microscopes to examine only tens or hundreds of cells at a time, missing most cells, and also missing possible patterns in the intermediate range. This project addresses the need to study patterns in cell images through powerful computational and analytic techniques in computational geometry, and to validate these algorithmic techniques, and software built from them, in medical research and applications. The project formulates challenging geometric and algorithmic problems that emerge in the diagnosis, prognosis, and analysis of diseases (e.g., breast cancer, inflammatory bowel disease, and rheumatoid arthritis), identification and classification of different types of immune cells (e.g., neutrophils, eosinophils, plasma cells, and lymphocytes), and tracking and analysis of collectively moving and swarming bacteria (e.g., Myxococcus xanthus and Pseudomonas aeruginosa) in terms of a class of Voronoi diagrams (developed by the lead investigator) in which collections of cells influence nearby neighbors. Specific geometric techniques include clustering-induced Voronoi diagrams, coupled optimal shape approximation, and matching based on earth mover's distance.Exploring these geometric structures in important medical problems will not only lead to new methods in combinatorial optimization and machine learning, and new publically-available software for medical applications, but also train students in the broad range of interdisciplinary research and education from geometric algorithms, software development, to medical applications. By providing appropriate analysis tools for the physicians, this project and its students will help save lives.