Precision distortion correction technique based on FOV model for wide-angle cameras in automotive sector - Emerging Trends in Image Processing, Computer Vision, and Pattern Recognition - page 454

(3)
The above equations are rearranged using radius R as
(4)
3.3 Distortion Coefficient Estimation of the FOV Model
According to the principle of the camera model [ 8 ] , a straight line in 3D should be a straight
line after being projected onto a 2D surface by a camera if there is no distortion. This means
that the larger the difference between an actual straight-line component and a projected
straight line, the larger the distortion is. Conversely, the less the difference is, the less the dis-
tortion is. The degree of camera distortion can be verified by the distortion coefficient ω of the
FOV model. In the FOV model, q ωi is a point of restoration of distorted point p i by the distor-
tion coeicient ω . The distortion parameter estimation from Ref. [ 9 ] expresses a relationship
of D - 1 ( ω, p i ) with regard to the distortion coefficient, which can solve the linear equation of the
least squares distance when the estimation is applied to the algorithms from p 1 to p n .
By solving the equation of the i and j functions where the error function E ij ( ω ) is minimized
with regard to the distortion coefficient ω , the distortion coefficient ω can be estimated. Using
this method, distortion correction can be performed by using the distortion correction coei-
cient with regard to the camera distortion center.
(5)
(6)