Applying a statistical constraint to the 3D reconstruction of the un-textured surface's cross-sections using a structured light system consists of two cameras and a planer laser

In this paper, a simple structured light system is designed to produce the three-dimensional points cloud from the un-textured surfaces. The system consists of two cameras and a planer laser, in which the 3D contents are produced through the stereo images taken from the light reflected by the intersection of a planer laser and the 3D surface of an object. There was no control over how the laser swept through the surface and the instantaneous parameters of the laser plane were not known in advance. Considering the knowledge of the internal camera calibration parameters and the relative orientation of the stereo-pairs, the video captured by the cameras are normalized during the epipolar re-sampling process. Next, in each pair of simultaneous frames, the matched points located at the 3D section of the laser’s plane are then identified. During the simultaneous space intersection of the matched points, a constraint is applied to enforce the singularity of the covariance matrix of 3D points lie in the intersection of the laser's plane and the 3D surface of an object to ensure their co-planarity. By applying this statistical constraint, the precision of the surface 3D reconstruction was improved up to 41% in this structured light system.