An Efficient Solution to the Homography-Based Relative Pose Problem With a Common Reference Direction

International audienceIn this paper, we propose a novel approach to two-view minimal-case relative pose problems based on homography with a common reference direction. We explore the rank-1 constraint on the difference between the Euclidean homog-raphy matrix and the corresponding rotation, and propose an efficient two-step solution for solving both the calibrated and partially calibrated (unknown focal length) problems. We derive new 3.5-point, 3.5-point, 4-point solvers for two cameras such that the two focal lengths are unknown but equal, one of them is unknown, and both are unknown and possibly different, respectively. We present detailed analyses and comparisons with existing 6-and 7-point solvers, including results with smart phone images

A homography formulation to the 3pt plus a common direction relative pose problem

International audienceIn this paper we present an alternative formulation for the minimal solution to the 3pt plus a common direction relative pose prob-lem. Instead of the commonly used epipolar constraint we use the homog-raphy constraint to derive a novel formulation for the 3pt problem. This formulation allows the computation of the normal vector of the plane defined by the three input points without any additional computation in addition to the standard motion parameters of the camera. We show the working of the method on synthetic and real data sets and compare it to the standard 3pt method and the 5pt method for relative pose estima-tion. In addition we analyze the degenerate conditions for the proposed method