The input to our algorithm is a set of 3D point clouds
representing one or more rooms of the interior of a building and
taken at known locations (with at least one scan inside each
room). We assume that the scans are registered in the same
reference frame and, without loss of generality, that the up-vector
is v up ¼ ð0; 0; 1Þ. We consider only buildings with planar, vertical
walls, but, like Lafarge et al. [18], we drop the more restrictive
Manhattan World assumption, and we also allow for non-convex
floor-plan room boundaries. The method produces a set of k closed
polyhedra as output, one for each room in the input scene.