Moving Frames & Computer Vision

移动框架

• 批准号: 9803154
• 负责人: Peter Olver
• 金额: $ 11.5万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-07-01 至 2002-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9803154&HistoricalAwards=false
• 关键词: Moving; Frames; & Computer; Vision

This project is devoted to innovative applications of the geometry ofmoving frames and the mathematical theory of differential invariants toproblems arising in computer vision, with emphasis on medical imaging. Since symmetry forms a basic component of the human visual system, it should benaturally incorporated into mathematical methods for image processing and objectrecognition. The image processing applications to be considered will includedenoising and smoothing, segmentation and edge detection, as well as objectrecognition, including symmetry detection and partial occlusions. Practicalimplementations will be based on the signature curve paradigm, that is based on the construction of suitable differential invariants for the symmetry group under consideration. Metrics that distinguish signature curves of different objects will be compared, with the goal being to recognize and extract objects from both two and three-dimensional images. Practical implementations of the image processing systems will rely on a new method of constructing symmetry-preserving numerical approximations to differential invariants that is to be developed as a part of this project. The applications will be based on a new, practical theory of moving frames, that can be applied to general group actions, both finite and infinite-dimensional. Part of the project will be devoted to the further development of this general theory. Various additional applications, to problems arising in physics, geometry, invariant theory, and the calculus of variations, will also be investigated.

该项目致力于在计算机视觉中引起的差异框架的几何形状和差异不变的数学理论的创新应用，重点是医学成像。由于对称是人类视觉系统的基本组成部分，因此应将其综合到数学方法中，以进行图像处理和对象识别。要考虑的图像处理应用程序将纳入和平滑，分割和边缘检测以及对象识别，包括对称检测和部分闭塞。实践实践将基于签名曲线范式，该范围基于正在考虑的对称组的合适差异不变剂的构建。 将比较区分不同对象的签名曲线的指标，目的是识别和提取从两个和三维图像中提取对象。 图像处理系统的实际实现将依赖于一种将对称性保存的数值近似值的新方法，该近似值将作为该项目的一部分开发。 这些应用将基于一种新的，实用的移动框架理论，该理论可应用于有限和无限维度的一般小组行动。 该项目的一部分将致力于这一一般理论的进一步发展。还将研究各种其他应用，这些应用在物理学，几何学，不变理论和变异的计算中引起的问题。