Radial distortion

카메라 렌즈에서 생기는 영상의 왜곡(distortion)현상은 크게 축 방향(radial)왜곡과 접선 방향

(tangential)왜곡으로 나눌 수 있다. 축 방향 왜곡의 경우 렌즈의 잘못된 곡면성형으로, 접선 방향 왜곡의 경우 렌즈와 카메라의 부적절한 조립으로 인해 생긴다.

아래 자료는 radial distortion에 대한 자료이다.

출처 : http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/FUSIELLO4/tutorial.html#x1-67001r131

A realistic model for a photocamera or a videocamera must take into account non-linear distortions introduced by the lenses, especially when dealing with short focal lengths or low cost devices (e.g. webcams, disposable cameras).

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The more relevant effect is the radial distortion, which is modeled as a non-linear transformation from ideal (undistorted) coordinates (u,v) to real observable (distorted) coordinates (û, ):

where r_d² = ² + ² and (u ₀,v₀) are the coordinates of the image centre.

Estimating k₁ Let us assume that the pinhole model is calibrated. The point m = (u,v) projected according to the pinhole model (undistorted) do not coincide with the measured points = (û, ) because of the radial distortion.

We wish to recover k₁ from Eq. (131). Each point gives two equation:

hence a least squares solution for k₁ is readily obtained from n > 1 points.
When calibrating a camera we are required to simultaneously estimate both the pinhole model’s parameters and the radial distortion coefficient.
The pinhole calibration we have described so far assumed no radial distortion, and the radial distortion calibration assumed a calibrated pinhole camera.
The solution (a very common one in similar cases) is to alternate between the two estimation until convergence.
Namely: start assuming k = 0, calibrate the pinhole model, then use that model to compute radial distortion. Once k₁ is estimated, refine the pinhole model by solving Eq. (130) with the radial distorion in the projection, and continue until the image error is small enough.

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