How is a lens distortion model applied to undistort an image?
Asked 4/7/2016
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I understand that models like Brown–Conrady or the pinhole camera model use calibration parameters such as focal length, principal point, and radial/tangential distortion coefficients. Conceptually, how are those parameters used during distortion correction? In particular, how does the algorithm map pixels from the distorted image to the corrected one, and what role do interpolation and pixel area changes play?
Originally by Photography Stack Exchange contributor. Source · Licensed CC BY-SA 4.0
Photography Stack Exchange contributor
10y ago
2 Answers
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The model specifies a mapping from an ideal picture on a rectangular grid where the scene is projected in a rectilinear way to a distorted picture on another rectangular grid. It tells you where the pixels that should have appeared at some coordinate (x,y) can be found in the distorted image that you actually have. The problem is then that the gray values you need a some location in the corrected image can be found according to the mapping at some factional value, so you need to use interpolation.
Also, you need to take into account that one pixel in the corrected image will, in general, cover an area in the uncorrected image that is different from the area of one pixel in the uncorrected image. The gray value of the pixel in the corrected image is then determined by demanding that the total amount of light that falls in the area is the same as the light that fell in the corresponding area in the uncorrected image.
Originally by user28357. Source · Licensed CC BY-SA 4.0
user28357
10y ago
0
Generated from our catalog & community — verify before relying on it.
A distortion model defines a coordinate mapping between an ideal rectilinear image and the distorted image captured by the lens.
In practice, undistortion usually works like this:
- For each pixel location in the corrected output image, the algorithm computes where that point would fall in the original distorted image using the calibrated parameters (focal length, principal point, radial and tangential distortion terms).
- That mapped location is often not exactly on a source pixel center, so the pixel value must be estimated by interpolation from nearby pixels.
- Because distortion changes local magnification, one output pixel may correspond to a differently sized area in the input image. A good resampling method should account for this so brightness/energy is preserved as well as possible.
So the model itself is not “removing distortion” directly; it supplies the geometric transformation. The actual correction comes from resampling the recorded image onto a new rectangular grid using that mapping.
This is why calibration parameters matter: they determine the exact warp from ideal image coordinates to distorted sensor coordinates.
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