In this paper, we propose a novel method to achieve both dense 3D reconstruction of the scene and estimation of the camera intrinsic parameters by using coplanarities and other constraints (e.g. orthogonalities or parallelisms) derived from relations between planes in the scene and reflected curves of line lasers captured by a single camera. In our study, we categorize coplanarities in the scene into two types: implicit coplanarities, which can be observed as reflected curves of line lasers, and explicit coplanarities, which are, for example, observed as walls of a building. By using both types of coplanarities, we can construct simultaneous equations and can solve them up to four degrees of freedom. To upgrade the solution to the Euclidean space and estimate the camera intrinsic parameters, we can use metric constraints such as orthogonalities of the planes. Such metric constraints are given by, for example, observing the corners of rectangular boxes in the scene, or using special laser projecting device composed of two line lasers whose laser planes are configured to be perpendicular.
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