Geometrical constraint based 3D reconstruction using implicit coplanarities

Coplanarity is a relationship of a set of points that exist on a single plane. Coplanarities can be easily observed in a scene with planer surfaces, and these types of coplanarities have been widely used for 3D reconstructions based on geometrical constraints. Other types of coplanarities that can be observed from images are those observed as cross sections of planes and scenes; for example, points lit by a line laser, or boundary points of a shadow of a straight edge. Although these types of coplanarities have been implicitly used in variations of light sectioning methods, they have not been used in an unified manner with the former types. In this paper, we describe a new 3D reconstruction method based on coplanarities and other geometrical constraints. In particular, we make use of the above two types of coplanarities in an unified manner. This enables us to reconstruct 3D scenes scanned using line lasers or shadows of straight edges observed by a partially-calibrated single camera utilizing geometrical relationships between the planes in the scenes and the planes of line lasers or the planes of shadow boundaries.