How is point cloud data acquired from the structured light 3D scanning?

Question

I am trying to understand the 3D reconstruction of Object using 3D structured Lighting scanner and I am stuck at the point where a method of decoding set of camera and projector correspondences to use to reconstruct a 3D point cloud. How exactly is 3D point cloud information acquired from the information obtained from those correspondences? I want to understand the mathematical implementation, not the code implementation.

Answer 1

assuming you used structured light method which uses some sort of lines (vertical or horizontal - like binary coding or de-brujin) the idea is as follows:

1. a light plane goes through the projector perspective center and the line in the pattern.

2. the light plane normal needs to be rotated with the projector rotation matrix relative to the camera (or world depends on the calibration). the rotation part for the light plane can be avoided if if treat the projector perspective center as system origin.

3. using the correspondences you find a pixel in the image that match he light plane. now you need to define a vector that goes from the camera perspective center to the pixel in the image and then rotate this vector by the camera rotation (relative to the projector or world. again' depending on the calibration).

4. intersect the light plane with the found vector. how to compute that can be found in wikipedia: https://en.wikipedia.org/wiki/Line%E2%80%93plane_intersection

the mathematical problem (3d reconstruction) here is very simple as you can see. the hard part is recognizing the projected pattern in the image (easier than regular stereo but still hard) and calibrating (finding relative orientation between camera and projector).