Projective reconstruction from line correspondences

Abstract

The paper gives a practical rapid algorithm for doing projective reconstruction of a scene consisting of a set of lines seen in three or more images with uncalibrated cameras. The algorithm is evaluated on real and ideal data to determine its performance in the presence of varying degrees of noise. By carefully consideration of sources of error, it is possible to get accurate reconstruction with realistic levels of noise. The algorithm can be applied to images from different cameras or the same camera. For images with the same camera with unknown calibration, it is possible to do a complete Euclidean reconstruction of the image. This extends to the case of uncalibrated cameras previous results of Spetsakis and Aloimonos on scene reconstruction from lines.

Indoor Manhattan spatial layout recovery from monocular videos via line matching

“…When point features are scarce, line features can be used instead. Computation of 3-D line segments and camera pose from three images of a set of lines is possible using the trifocal tensor [2,5,6,7,8,9,10]. This approach follows three general steps: (1) trifocal tensor computation from triplets of line correspondences, producing the three camera matrices; (2) 3-D line computation via triangulation from line correspondences; (3) non-linear optimization for refinement.…”

Affine Reconstruction from Lines.

“…More details about this can be found in [1]. 6 Reconstruction knowing the translation Knowing the translation up to a scale factor, we want now to reconstruct the scene in (F, i,j, k). We have t such that kt = T, where k is an unknown scalar.…”

“…Projective reconstructions differ from the true reconstruction by an arbitrary 3D projective transformation. They are feasible from points with two images [2], [8] or from lines with three images [6], [5].…”

Generalization of the Desargues Theorem for Sparse 3d Reconstruction

“…In the first category, images are considered at distant time instants and a large camera displacement is generally performed to obtain accurate results. The images can be taken two by two to obtain the so-called Stereovision Approach 1,2 where the fundamental matrix can be used to constrain the matching and to make a projective reconstruction from disparity maps, three by three for the Trifocal Approach 3 , and finally four by four for the Quadrifocal Approach 4 . These matching tensor techniques are essentially equivalent to implicit 3-D reconstruction methods and have two main drawbacks : the calibration procedure, which determines the intrinsic parameters of the sensor and its pose and orientation, and the inter-frame correspondence or features matching stage.…”