1. Introduction
Planar regions in 3D scenes offer important geometric cues in a variety of 3D perception tasks such as scene understanding [42], scene reconstruction [3], and robot navigation [18], [56]. Accordingly, piecewise planar scene reconstruction has been a focus of computer vision research for many years, for example, plausible recovery of planar structures from a single image [16], volumetric piecewise planar reconstruction from point clouds [3], and Manhattan depthmap reconstruction from multiple images [11].