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I am trying to reconstruct the real-world coordinates of 3D points from two images taken from the same camera. The camera is not calibrated, but the movement (translation and rotation) is known. In short:

Requirement:

  • No calibration

Extra constraints other than image point correspondences:

  • Known camera translation and rotation
  • Same camera used in all views

I understand that, from image point correspondences alone, a scene can be reconstructed only up to a projective transformation. With more constraints, an affine or similarity reconstruction may be done. In my case, I need a similarity reconstruction.

Given the above constraints, is a similarity reconstruction possible? If possible, how should I go about doing it?

I have tried to attack the problem from a few angles. Since I am not mathematically fluent, I try to use opencv as much as possible.

  1. findFundamentalMat() from the two images, hopefully extract the two camera matrices somehow, then triangulatePoints(). As you could have guessed, I got stuck in the middle, unable to obtain camera matrices from fundamental matrix.

    The textbook "Multiple View Geometry in Computer Vision" (by Hartley and Zisserman) gives an expression (p.256, Result 9.14) that expresses the camera matrices in terms of fundamental matrix and one of the epipoles. However, without knowing the camera's intrinsic parameters (requirement: no calibration), I don't see how I can get the epipole.

  2. I also try to treat my problem as a stereo system and use opencv's stereo*** functions. But they all seem to require human intervention to calibrate, which violates my requirement.

So, that's why I ask the question here today. The key is still, given those extra constraints, is a similarity reconstruction possible? I am not smart enough to understand the wealth of knowledge out there, and not able to come up with my own solution. Any help is appreciated.

Nick Lee
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  • if your camera intrinsics were given, would you be able to solve the problem? Typically guessing a calibration might give some results (maybe not fulfilling your desired accuracy) – Micka Dec 08 '16 at 10:54
  • If camera intrinsics were given, I think the problem would become trivial. Treat the first camera position as origin, apply translation and rotation to obtain the second camera pose, then `triangulatePoints()` would do the job. Am I correct? – Nick Lee Dec 08 '16 at 12:25

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