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 451

a small hole. In order to convert 3D spatial coordinates into 2D image coordinates, external
parameters such as the installation height and direction of the camera, and internal paramet-
ers such as the focal length and center point of camera are required. The focal length in the
internal parameter refers to a distance between the focal point and the image sensor charge
coupled device (CCD) and complementary metal oxide semiconductor (CMOS), which is rep-
resented by
(1)
Here, x screen and y screen refer to the coordinates on the 2D plane, whereas f is the distance
between the focal point and the image plane. In addition, Z is the distance between the object
and the focal point, whereas C is the displacement of the coordinate center in the projection
plane. Using Equation (1) , the location where the image appears on the 2D plane can be cal-
culated. However, because only a small amount of light passes through a pinhole camera, a
long exposure time is required to create an image. In order to collect a large amount of light,
a curved lens is used, thereby obtaining images by collecting the curved light. When the ob-
tained image is projected onto a 2D plane, a problem of image distortion can occur due to the
characteristics of the lens. The distortion by a lens can be divided into two types: radial dis-
tortion, which is generated more severely in an area farther from the center, and tangential
distortion, which creates an elliptical distortion distribution.
The typical type of lens which is installed in the vehicle is fish-eye lens and they can create
radial distortion. To resolve the radial distortion problem, three methods can be employed: the
method of using the center point of distortion, distortion parameters, and internal parameters;
the method of performing polynomial distortion iteratively to transform the distorted curves
caused by radial distortion into straight lines; and the method of using image information
only. Heikkila [ 1 ] proposed a method of finding the center of distortion and internal paramet-
ers by using chessboard-like images, in which a method to find parameters that can integrate
distortion correction and a camera calibration process was introduced. However, this method
has a drawback that could increase iterative calculation complexity when the distortion is ex-
cessively severe, although it can be efficient when distortion is moderately severe.
In Ref. [ 2 ] , three orthogonal planar paterns were introduced to cover an entire 180° image
with a speciic patern of asymmetrical distortion. This method locates a vanishing point
where distorted curves converge to a single point and then defines that as the center point of
distortion, thereby performing distortion restoration. This method does not depend on distor-
tion models of parameters due to the special structure of the apparatus, and therefore, it has
an advantage in that it can be applied to various lenses, although it is not appropriate for a
case where radial asymmetric distortion is generated.
In Ref. [ 3 ] , a center radius was defined using the center of a sphere and the position of a
single distorted point. A corrected position value was then used to restore the distorted curves
into straight lines. Then, new radii at all positions in the image were obtained to be applied in
the FOV model. This method can be used for real-time processing because it uses low-order