2007/08/18 by Oliver Knill, Knill, Oliver, Jose Ramirez-Herran +1
Computer Science · Engineering · #Advanced Vision and Imaging #Artificial Intelligence (cs.AI) #Computer Vision and Pattern Recognition (cs.CV) #Control and Dynamics of Mobile Robots #FOS: Computer and information sciences #I.2.10 #Robotic Mechanisms and Dynamics #cs.AI #cs.CV
paper · pdf · doi:10.48550/arxiv.0708.2432
15 pages, 22 figures
arxiv created 2007/08/18 · openalex publication_date 2007/08/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.