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I have a problem with measuring the real world length of a line between two known lines with only one single image.

Please have a look at this sketch:

Sketch of the problem

The following steps were realized:

  • Calibrated the camera
  • Detect the line end points in the image
  • Undistored the points with the calibrated camera data
  • Perspective correction with vanish lines

I have tried to solve this problem by rectify the image (removing projection and affine distortions) with this solution Image Rectification: Remove Projective and Affine Distortions from Rong Zhang.

But in my case, there is a missing second pair of orthognal lines (diagonals), because of the unknown length of c.

So there is my question: Is it possible to measure the real length of the line c with on single image, a calibrated camera and the known paramters (descripted in the sketch) ?

Luca Kiebel
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Basman
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  • how do you compute the perspective correction? Are A and B perfectly parallel afterwards? Did you try using the same metric for C? Do you have reference measures to play around? (assuming the pixel width and height are identical and no distortion => from your calibrated camera) – Micka Jul 28 '17 at 10:24
  • You mean (I think) that you don't know which ends of a and b are joined by line c. Well yes that's because your pattern for a and b is ambiguous - but can't you just take the shorter of the distances from one end of a to each end of b? – DisappointedByUnaccountableMod Jul 28 '17 at 11:16
  • Thank you for your quickly answers. @Micka The perspective correction is calculated by the vanish points from the parallel (in the real world) lines. The points will be distorted, until the vanishing line mappes at infinity. So the parallel lines (in world) will be also parallel in (the image) after distorting. To do this i need 4 lines, two pairs of parallel lines. So, there is also a parallel line oppsite to c. I will post a better sketch soon. – Basman Jul 28 '17 at 11:51
  • I think A and B are perfectly parallel, no matter what the line detection algo. does. For measurement i have only this two lines, no other features :( . I testet the measured pixel width in the image of the line, but this value was to unstable. – Basman Jul 28 '17 at 11:51
  • After perspective correction, is the middle of the lines in the image also the middle of the lines in real world (perspective foreshortening corrected)? Can you create a test sample where C is known (by measuring in real world) to evaluate some algorithm by knowing the ground truth (with all other assumptions like knowing the camera calibration etc.)? – Micka Jul 28 '17 at 11:57
  • Ok, i will create some test samples and upload them. – Basman Jul 28 '17 at 12:01

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