IIS: III: Small: Conformal Geometry for Computer Vision

IIS：III：小：计算机视觉的共形几何

• 批准号: 0916286
• 负责人: Xianfeng Gu
• 金额: $ 10万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-01 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0916286&HistoricalAwards=false
• 关键词: IIS; III; Small; Conformal; Geometry

This project investigates the computational conformal geometric methods applied for computer vision. The research team develops novel algorithms for shape analysis, surface matching and registration based on Ricci flow, and compared with conventional vision methods thoroughly. The basic of idea of the research is to conformally deform all surfaces as one of three canonical shapes, and then perform matching and registering these 3D surfaces in 2D planes. The research team uses the Ricci for shape analysis to preserve the intrinsic geometric characteristics, and to map the surfaces to the canonical shapes.. Ricci flow is the process to deform the metric proportional to the curvature, such that the curvature evolves according to a heat diffusion process. The research team conducts thoroughly comparison with conventional vision methods through extensive experiments using real world datasets. The research benefits many computer vision and visualization applications with methods for computing and visualizing conformal structures and conformal invariants on surfaces. The project also provides opportunity for training students in the areas of differential geometry, hyperbolic geometry, Riemannian geometry, computer vision.

本项目研究计算机视觉中应用的计算共形几何方法。研究小组开发了基于Ricci流的形状分析、表面匹配和配准的新算法，并与传统的视觉方法进行了彻底的比较。本研究的基本思想是将所有曲面共形变形为三种典型形状之一，然后在二维平面上进行匹配和配准。研究小组使用利玛窦进行形状分析，以保持固有的几何特征，并将表面映射到规范形状。里奇流是使度规与曲率成比例变形的过程，使得曲率按照热扩散过程演变。研究团队通过使用真实世界数据集的大量实验，与传统的视觉方法进行了彻底的比较。该研究为许多计算机视觉和可视化应用提供了计算和可视化表面上的共形结构和共形不变量的方法。该项目还为培养学生在微分几何、双曲几何、黎曼几何、计算机视觉等领域的能力提供了机会。