Planar Structures from Line Correspondences in a Manhattan World

Abstract

Traditional structure from motion is hard in indoor environments with only a few detectable point features. These environments, however, have other useful characteristics: they often contain severable visible lines, and their layout typically conforms to a Manhattan world geometry. We introduce a new algorithm to cluster visible lines in a Manhattan world, seen from two different viewpoints, into coplanar bundles. This algorithm is based on the notion of "characteristic line", which is an invariant of a set of parallel coplanar lines. Finding coplanar sets of lines becomes a problem of clustering characteristic lines, which can be accomplished using a modified mean shift procedure. The algorithm is computationally light and produces good results in real world situations.

Indoor Manhattan spatial layout recovery from monocular videos via line matching

“…The null space of solutions coincides with the second camera's projection plane of L. The only information we can derive about t/d is its projection t/d, u 2 (as the lever vector u 2 is orthogonal to this projection plane), which is equal to [3] (see the Appendix for a proof): Thus, the vector t/d lies on a plane that is parallel to the projection plane of L on the second camera, at a (signed) distance t/d, u 2 from it. We call this the n-characteristic plane Π(L, n) [3] (see Fig. 1, right panel).…”

“…If L and L 2 are parallel, the space of solutions is a line that is parallel to both L and L 2 (as should be expected: moving either camera parallel to the lines does not change the line images). This line takes the name of n-characteristic line L * [3]. The n-characteristic line of a pair of n-coplanar lines can be computed easily from their images in the two views, as the intersection of the associated n-characteristic planes.…”

“…In previous work [3] we introduced the characteristic lines (CL) algorithm to find sets of coplanar lines from two views of a Manhattan world, thus enabling SFM computation. The CL algorithm performs a clustering of n-characteristic lines, which are invariant representations of two views of parallel lines lying on a common plane with known orientation n. The CL algorithm is fast and robust, and was shown to produce good results with challenging image pairs [3].…”

“…The CL algorithm performs a clustering of n-characteristic lines, which are invariant representations of two views of parallel lines lying on a common plane with known orientation n. The CL algorithm is fast and robust, and was shown to produce good results with challenging image pairs [3]. In this paper we extend the CL method for the analysis of videos from a monocular camera.…”

Multi-planar Fitting in an Indoor ManhattanWorld

“…The lever vector [16] u L is the normal vector of the plane through the camera's optical center and the image line L (note that u L , which is easily computable given the intrinsic camera parameters, is orthogonal to the k-th vanishing direction.) Finally, we recompute {L k } based on the new vanishing direction, this time using a smaller threshold τ s = τ l /2.…”