一参数锚定多视图变种的欧几里得距离度
The Euclidean distance degree of one-parameter anchored multiview varieties
AI总结：
本文研究了一参数锚定多视图变种的欧几里得距离度，通过有理函数参数化曲线的公式推导，解决了计算机视觉中关于一维线多视图变种的猜想。
摘要：
多视图变种是用于描述由给定相机排列生成的图像特征对应关系的数学模型。它们具有一个不变量，称为欧几里得距离（ED）度，用于衡量在通过三角化计算场景结构时，确定最小再投影误差的3D特征的代数复杂性。在本文中，我们证明了一个公式，用于计算由有理函数参数化的曲线在温和通用性假设下的ED度。我们将结果应用于解决计算机视觉中由Duff和Rydell提出的关于一维线多视图变种的猜想。
英文摘要：
Multiview varieties are mathematical models for the set of image feature correspondences that can be produced by a given camera arrangement. They possess an invariant known as their Euclidean distance (ED) degree, which measures the algebraic complexity of determining the 3D features that minimize the reprojection error when computing the scene structure by triangulation. In this article, we prove a formula for the ED degree of curves parameterized by rational functions with mild genericity assumptions. We apply our results to resolve conjectures on one-dimensional line multiview varieties from computer vision proposed by Duff and Rydell.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
