Geometrical projection identity-based 3D reconstruction for fringe projection profilometry

This Letter reveals two special geometric points and a geometric projection identity (GPI) within an FPP system, thereby providing new 3D reconstruction equations for four common methods (Ver3, Hor3, OptE3, and HorVer4). We prove that the GPI-based and the traditional reconstruction frameworks are equivalent, but the former enables much faster point cloud computation and effective analysis of precision for metrology.