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I'm trying to obtain the 3D metric reconstruction of the points I have in two different views of my scene by means of a pair of iPhone 4S (a rudimental stereo system).

To do so, I did calibrate the cameras, estimate the fundamental matrix and obtained an estimate of the essential matrix. Now, in Hartley&Zisserman "Multiple View Geometry in CV" book, I see that to any given E, they correspond 4 canonical cameras pairs, of which only one reconstructs as the "actual" stereo configuration.

The problem is that they say [cit.]"...the reconstructed point will be in front of both cameras in one of these four solutions only. Thus, testing with a single point to determine if it is in front of both cameras is sufficient to decide between the four different solutions for the camera matrix P'. ..."

Given that I know F, K_left and K_right, how does one establish whether a 3D point is in front of both cameras or not?

Thanks,

Riccardo

ripkars
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1 Answers1

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You can get the camera rotation and translation from essential matrix. So, you have the camera matrix P = [R, -R*t]. To test if point X = (x, y, z, 1) is in front of the camera, compute X' = P*X. X' = (x', y', z') will be position of point if camera is in the origin, looking toward z direction. So, if z' is positive, then X' is in front of the camera and X is in front of camera P. Else X is behind P.

fdermishin
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