4 research outputs found
A structure from motion inequality
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.Comment: 15 pages, 22 figure
Space and camera path reconstruction for omni-directional vision
In this paper, we address the inverse problem of reconstructing a scene as
well as the camera motion from the image sequence taken by an omni-directional
camera. Our structure from motion results give sharp conditions under which the
reconstruction is unique. For example, if there are three points in general
position and three omni-directional cameras in general position, a unique
reconstruction is possible up to a similarity. We then look at the
reconstruction problem with m cameras and n points, where n and m can be large
and the over-determined system is solved by least square methods. The
reconstruction is robust and generalizes to the case of a dynamic environment
where landmarks can move during the movie capture. Possible applications of the
result are computer assisted scene reconstruction, 3D scanning, autonomous
robot navigation, medical tomography and city reconstructions