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Is there a way to undistort and map a view to another without knowing the camera matrix ?

Goal is to transform this kind of view: enter image description here

to a 2D rectangle:

undistorted

using minimum number of distorted points.

The distorted view is not generated by a camera and looks like having a barrel distortion on the y axis. On the X axis, things look a little easier since it looks like a direct polar transformation.

baci
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  • Do you know the metric tensor for the view? You may not need opencv for it. – ACCurrent Aug 02 '16 at 10:17
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    [HERE](http://stackoverflow.com/questions/10196198/how-to-remove-convexity-defects-in-a-sudoku-square) you may find some usefull information about the transformation of the image. – Dainius Šaltenis Aug 02 '16 at 11:22
  • That link is about spatial 2D transformation, not undistortion – baci Aug 02 '16 at 12:10
  • is there a direct relation between the distoted quads and the undistorted quads? I though yes, but then I've seen that the bottim imge has 4 rows whike the top image has only 3 "rows"?!? – Micka Aug 02 '16 at 13:16
  • maybe youll find some hints in http://dl.acm.org/citation.cfm?id=513536 . If you just want to know how to interpolate between given sample correspondences you probably want to use some kind of 2d splines. – Micka Aug 02 '16 at 13:19
  • @Micka these views are drawn by hand for a visual understanding, of course there is not a direct relation – baci Aug 02 '16 at 13:31
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    @baci but do you know the direc relation between a grid of distorted and undistorted points (and just dont know how to perform the undistortion process)? you should present the known and unknown things or a real sample. In general: Undistortion CAN be done without knowing the camera matrix, if you know other things. – Micka Aug 02 '16 at 13:36
  • @Micka the relation is known for a sparse set of points. I just want to calculate a generalized homography – baci Aug 02 '16 at 14:41
  • edited the question, one can assume that relation between grid corners (30 points) are known – baci Aug 02 '16 at 14:51
  • should be possible with interpolation of parametrized surfaces like bezier surface patches or 2d splines. It's some time since I learned those things so maybe someone else can explain it or I'll need much more time to prepare a good answer :) – Micka Aug 02 '16 at 16:22
  • not sure whether simple bilinear interpolation of pixel positions (followed by anothrr bilinear interpolation of pixel values) could even be enough for your needs. – Micka Aug 02 '16 at 16:45

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