IIS: III: Small: Conformal Geometry for Computer Vision

该项目研究应用于计算机视觉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深入的比较。研究的基本思想是将所有的曲面共形变形为三个标准形状之一，然后在二维平面上进行匹配和配准。研究小组使用Ricci进行形状分析，以保留固有的几何特征，并将表面映射到规范形状。里奇流是使度量与曲率成比例地变形的过程，使得曲率根据热扩散过程而演变。研究小组通过使用真实的世界数据集进行广泛的实验，与传统的视觉方法进行了彻底的比较。该研究有利于许多计算机视觉和可视化应用的方法计算和可视化的共形结构和共形不变量的表面。该项目还提供了机会，培养学生在微分几何，双曲几何，黎曼几何，计算机视觉领域。

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.