CAREER: Application and Theory of Geometric Shape Handling

这项研究的目的是在实践中帮助提高形状处理的速度、质量和生产率。几何形状是包括计算机视觉、计算机辅助设计(CAD)、机器人学、生物信息学、计算生物学、医学成像、地理信息系统(GIS)和药物设计在内的众多前沿技术领域的核心，在这些领域中，必须高效和可靠地处理和处理几何形状。本研究基于两个研究轨道：(I)形状处理应用和(Ii)形状处理理论。研究人员将继续促进跨学科交流，为应用问题提供更多的理论依据，并追求更坚实的理论基础，以此作为更广泛应用的基础。具体地说，这项研究涉及几个应用项目，包括但不限于计算蛋白质组学、计算神经科学和时空交通数据库。半自动算法将与理论专业知识相结合，为在数据非常嘈杂的地区进行高通量处理铺平道路。理论项目包括曲线和曲面的匹配和距离测量问题，多曲线匹配，启动测地线距离测量的一般研究，其中距离测量使用曲面上的最短路径来测量，以及形状简化。将研究下界，以便更好地了解问题的结构，并将设计应用友好的算法，如输出敏感算法和近似算法，以便更好地处理异常值和噪声输入。

The objective of this research is to help increase speed, quality, and productivity of shape handling in practice. Geometric shapes are at the core of a wide range of cutting-edge technological sectors including computer vision, computer aided design (CAD), robotics, bioinformatics, computational biology, medical imaging, geographical information systems (GIS), and drug design, in which a multitude of tasks for manipulating and handling geometric shapes have to be performed efficiently and reliably.This research is based on two research tracks: (i) shape handling applications and (ii) shape handling theory. The investigator will continue to foster interdisciplinary communication, contribute more theoretical soundness to applied problems, and pursue a stronger theoretical foundation which can be the basis for a wider range of applications. Specifically, this research involves several applied projects including, but not limited to, computational proteomics, computational neuroscience, and spatiotemporal traffic databases. Semi-automatic algorithms will be combined with theoretical expertise in order to pave the road for high-throughput processing in areas with very noisy data. Theoretical projects include matching and distance measure problems for curves and surfaces, multi-curve matching, initiation of a general study of geodesic distance measures in which distances are measured using shortest paths on a surface, and shape simplification. Lower bounds will be investigated in order to gain better insight into the structure of the problems, and application-friendly algorithms such as output-sensitive algorithms and approximation algorithms will be devised in order to better cope with outliers and noisy inputs.