Estimation of omnidirectional camera model from epipolar geometry

Author: Micusik

Year: 2004

Notes:

Calibration of a spherical camera model with automatic correspondences based on epipolar constraint

Camera model:

projection equation: $$ \alpha g(Au' + t) = PX \ \alpha \in \mathbb{R}, \ g(u,v) = (u, v, f(u,v)) $$
non linear funtion $g$ compute 3D vectors with $f$ rotationnally symmetric wrt to $z$
what is the digitized image? $$ f(\mathbf{u},a,b) = \frac{r}{\tan(\frac{ar}{1+br^2})} $$
With model simplification calibration can be performed with 9 points RANSAC
The model is linearized $p = as + bt$

Model estimation with epipolar constraint:

constraint $p^T F p = 0$
Leads to a QEP with concatenation of n points
use the error between the ray and a epipolar plane (??)
u /= 1000 for better numerical stability

Commentaires:

Notations pourries, on s'y perd