Image Processing Reference
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polynomials to change curves into straight lines, although it has a weakness in terms of accur-
acy compared to other existing methods.
In Ref. [ 4 ] , distortion parameters based on the assumption that lines were straight prior to
distortion were found using the characteristics of the pinhole camera model in order to min-
imize the curvature of the lines, and then, they were applied to the tangential distortion cor-
rection method.
In Ref. [ 5 ], the longest curved lines were extracted and removed from 2D images, and then
the correction of the remaining curves was performed. However, this method has several
drawbacks in that curve detection is performed slowly whereas the removal of the curves may
not be carried out accurately owing to the use of a single fixed threshold value for curve re-
moval. To overcome these drawbacks, a method was proposed in Ref. [ 6 ] to detect and remove
the lines quickly using Hough transformation.
The FOV model, which is based on nonlinear lens distortion characteristics, corrects distor-
tion under the assumption that the center of an image and the center of lens distortion are the
same. However, in the case of cameras using lenses with special functions and a number of
layers, an error of the center point might occur during the manufacturing process, thereby cre-
ating a fine center point error in the projection onto the 2D plane. Therefore, not only can dis-
tortion correction not be performed correctly, but also additional distortion of the image can
occur after distortion correction. To solve this problem, a method was proposed in Ref. [ 7 ] to
correct distortion after estimating a center by selecting three straight lines in the image plane
to decrease computation complexity.
In addition, a method was presented in Ref. [ 6 ] to estimate the center of distortion by ex-
tracting a curve from the projected 2D image and modifying it into an undistorted straight
line, thereby finding the direction in which the center of the extracted curve is changed.
However, its accuracy varies depending on the number of detected lines and the existence of
lines around the distortion center.
This chapter proposes an accurate distortion correction method through the estimation of
the distortion center of a lens using the FOV model and 2D paterns in order to correct radial
3 Distortion center estimation method using FOV
model and 2D patterns
3.1 Distortion Correction Method Considering Distortion
Center Estimation
The process of distortion correction considering the distortion center is shown in Figure 1 . In
this chapter, a 2D planar image of a chessboard patern was used irst to correct distortion
of an image from a ish-eye lens quickly. Using the distorted chessboard patern, a distortion
coeicient was estimated by applying the FOV model.
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