What do I do with the fundamental matrix?

Question

I am trying to reconstruct a 3d shape from multiple 2d images. I have calculated a fundamental matrix, but now I don\'t know what to do with it.

I am finding multiple co

Answer 1

With your fundamental matrix, you can determine the camera matrices P and P' in a canonical form as stated (HZ,pp254-256). From these camera matrices you can theoretically triangulate a projective reconstruction that differs to the real scene in terms of an unknown projective transformation.

It has to be noted that the linear triangulation methods aren't suitable for projective reconstruction as stated in (HZ,Discussion,p313) ["...neither of these two linear methods is quite suitable for projective reconstruction, since they are not projective-invariant."] and therefore, the mentioned recommended triangulation technique should be used to obtain valueable results (that is actually more work to implement).

From this projective reconstruction you could use self-calibration approaches that can work in some scenarios but will not yield the accuracy and robustness that you can obtain with a calibrated camera and the utilization of the essential matrix to compute the motion parameters.