A New Solution to the Relative Orientation Problem Using Only 3 Points and the Vertical Direction

Abstract

This paper presents a new method to recover the relative pose between two images, using three points and the vertical direction information. The 1 arXiv:0905.3964v1 [cs.CV] 25 May 2009 vertical direction can be determined in two ways: 1-using direct physical measurement like IMU (inertial measurement unit), 2-using vertical vanishing point. This knowledge of the vertical direction solves 2 unknowns among the 3 parameters of the relative rotation, so that only 3 homologous points are requested to position a couple of images. Rewriting the coplanarity equations leads to a simpler solution. The remaining unknowns resolution is performed by an algebraic method using Gröbner bases. The elements necessary to build a specific algebraic solver are given in this paper, allowing for a real-time implementation. The results on real and synthetic data show the efficiency of this method.

Tracking orthogonal vanishing points in video sequences for a reliable camera orientation in Manhattan World

“…They have been used to initialize EM estimators to converge to the correct VP. Other optimal solutions rely on analytical approach often based on time consuming algorithms [3], [11], [16]. In this last paper, it is interesting to note that, even if they are non deterministic, the RANSAC-based approaches hold comparable results against exhaustive search for the number of clustered lines.…”

“…In man-made urban environments, many line segments are oriented along three orthogonal directions aligned with the global reference frame. Under this so-called Manhattan world assumption, vanishing lines or points are pertinent visual cues to estimate the camera orientation [1], [7], [10], [11], [12] [14]. This is an interesting alternative to structure and motion estimation based on features matching, a sensitive problem in computer vision.…”

Underwater Photogrammetry for Archaeology

“…Using the SIFT (Lowe, 2004;Munich et al, 2006) algorithm to detect homologous points, we will make all the possible relative orientations using the Stewenius algorithm (Kalantari et al, 2011;Nister, 2004;Stewenius et al, 2006). …”

Multi-view 3D reconstruction for scenes under the refractive plane with known vertical direction

“…Although the accuracy of the heading measured by the digital compass is not good enough due to magnetic filed disturbances, the roll and pitch angles can be measured accurately even with low-cost IMUs [16]. Therefore, attempts have been made to take the advantage of two known angles (i.e., the vertical direction) to simplify the relative pose estimation [9,14] and absolute pose estimation [16] for settings involving only one medium.…”