Medial axes and symmetry sets of isophote curves

等光度曲线的中轴和对称集

• 批准号: EP/G000786/1
• 负责人: P Giblin
• 金额: $ 1.9万
• 依托单位: University of Liverpool
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2008
• 资助国家: 英国
• 起止时间: 2008 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FG000786%2F1
• 关键词: Medial; axes; symmetry; sets; isophote

For a (usually closed) curve in the plane the symmetry set and the medial axis are measures of the local symmetry of the curve. The medial axis plays the role of a skeleton, something that goes down the middle of the shape enclosed by the curve. It has the structure of a branched 1-dimensional set (a tree). It is used in shape analysis, comparison and recognition. For a 2-dimensional image (like a photograph of a 3D scene), at each point there is a brightness, measured say between 0 and 1. The brightness can be thought of as a third coordinate, after the first two which specify the point in the image. Lines of equal brightness are called isophotes and they are curves in the plane of the image. These curves are studied because they give much information about the image. We plan to carry out an investigation of the medial axes and symmetry sets of these curves, to obtain information which has not been available before.The principal investigator (Giblin) has carried out many similar investigations before but this problem has proved difficult with existing techniques. However recent work of the Visiting Researcher (Uribe-Vargas) introduces techniques which should make the investigation possible.

对于平面中的（通常闭合的）曲线，对称集和中轴是曲线局部对称性的度量。中轴起着骨架的作用，它沿着曲线所包围的形状的中间向下延伸。它具有分支一维集合（树）的结构。它用于形状分析、比较和识别。对于二维图像（如 3D 场景的照片），每个点都有一个亮度，测量值介于 0 和 1 之间。亮度可以被视为在指定该点的前两个坐标之后的第三个坐标在图像中。亮度相等的线称为等光线，它们是图像平面上的曲线。研究这些曲线是因为它们提供了有关图像的大量信息。我们计划对这些曲线的中轴和对称集进行研究，以获得以前无法获得的信息。主要研究者（Giblin）之前已经进行了许多类似的研究，但事实证明这个问题用现有技术很难解决。然而，访问研究员（Uribe-Vargas）最近的工作介绍了使调查成为可能的技术。

项目成果

Contact With Circles and Euclidean Invariants of Smooth Surfaces in R3

R3 中圆和光滑表面的欧几里得不变量的接触

• DOI: http://dx.10.1093/qmath/haab058
• 发表时间: 2022
• 期刊: The Quarterly Journal of Mathematics
• 作者: Giblin P