任意数量射影视图的临界配置分类
A Classification of Critical Configurations for any Number of Projective Views
AI总结：
本文利用新代数方法对任意数量射影相机的临界配置进行分类，证明其构成二次曲面等代数簇，并发现新配置与纠正以往误判。
摘要：
运动恢复结构是从一组图像中恢复相机和3D场景信息的过程。通常，在无噪声设置下，如果提供足够的图像和图像点，所有信息都能被唯一恢复。然而，在某些情况下，即使在理论上也无法进行唯一恢复；这些情况被称为临界配置。我们使用一种最近开发的代数方法对任意数量射影相机的所有临界配置进行分类。我们表明它们构成了众所周知的代数簇，例如二次曲面和次数至多为4的曲线。本文还改进了早期结果，既发现了先前未知的临界配置，又证明了一些先前被认为是临界的配置实际上并非如此。
英文摘要：
Structure from motion is the process of recovering information about cameras and 3D scene from a set of images. Generally, in a noise-free setting, all information can be uniquely recovered if enough images and image points are provided. There are, however, certain cases where unique recovery is impossible, even in theory; these are called critical configurations. We use a recently developed algebraic approach to classify all critical configurations for any number of projective cameras. We show that they form well-known algebraic varieties, such as quadric surfaces and curves of degree at most 4. This paper also improves upon earlier results both by finding previously unknown critical configurations and by showing that some configurations previously believed to be critical are in fact not.
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。
