A structure from motion inequality
Computer Vision and Pattern Recognition
2007-08-21 v1 Artificial Intelligence
Abstract
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.
Cite
@article{arxiv.0708.2432,
title = {A structure from motion inequality},
author = {Oliver Knill and Jose Ramirez-Herran},
journal= {arXiv preprint arXiv:0708.2432},
year = {2007}
}
Comments
15 pages, 22 figures