摘要翻译：
对于m个摄像机和n个点的运动问题，我们给出了结构的一个初等不等式。该结构从运动不等式出发，将空间维数、摄像机参数维数、摄像机个数和点个数与全局对称性联系起来，给出了一个严格的判据，该判据的重构概率为1是不可能的。在数学上，该不等式是基于Frobenius定理，它是线性代数基本定理的几何化身。本文还提供了从运动出发的结构问题的一般数学形式。它包括摄像机拍摄照片时点可以移动的情况。
---
英文标题：
《A structure from motion inequality》
---
作者：
Oliver Knill and Jose Ramirez-Herran
---
最新提交年份：
2007
---
分类信息：

一级分类：Computer Science        计算机科学
二级分类：Computer Vision and Pattern Recognition        计算机视觉与模式识别
分类描述：Covers image processing, computer vision, pattern recognition, and scene understanding. Roughly includes material in ACM Subject Classes I.2.10, I.4, and I.5.
涵盖图像处理、计算机视觉、模式识别和场景理解。大致包括ACM课程I.2.10、I.4和I.5中的材料。
--
一级分类：Computer Science        计算机科学
二级分类：Artificial Intelligence        人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
--

---
英文摘要：
  We state an elementary inequality for the structure from motion problem for m cameras and n points. This structure from motion inequality relates space dimension, camera parameter dimension, the number of cameras and number points and global symmetry properties and provides a rigorous criterion for which reconstruction is not possible with probability 1. Mathematically the inequality is based on Frobenius theorem which is a geometric incarnation of the fundamental theorem of linear algebra. The paper also provides a general mathematical formalism for the structure from motion problem. It includes the situation the points can move while the camera takes the pictures.
---
PDF链接：
https://arxiv.org/pdf/0708.2432