How do you triangulate a three-dimensional point from a pair of stereo images?

Question

I work with a stereo pair of photos and try to get a set of three-dimensional points from coincident points in these two images. How exactly is a three-dimensional point triangulated? Do you cast a beam from the center point of the camera? Or do you cast a beam perpendicular to the photographs?

Answer 1

You must throw the beam from the center point of the camera.

The use of parallel rays would be appropriate only if the original images were created with orthogonal projection.

Answer 2

Reconstructing 3D points is greatly simplified if your images are corrected. This means that cameras are effectively parallel (looking in the same direction), and even if they are not images, they can be converted to meet this requirement. Then all you need to do to restore 3D is to know the effective horizontal movements of the camera (baselines). In short, Z = fB / D, X = uZ / f, Y = vZ / f, where B is the baseline, D is the mismatch, f-focal length, and u, v is the column and -row with the beginning in the center of the image.

However, what you showed in the picture is not a pair of cameras with a parallel optical axis. If you do not want to correct your images, you must consider the rotation and translation between cameras, which will complicate the recovery.