A structure from motion inequality

Details A structure from motion inequality A structure from motion inequality

2007-08-18

arxiv.org/abs/0708.2432v1

Computer Science

Computer Vision and Pattern Recognition

15 pages, 22 figures

Scientific paper

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.

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