A Homography Formulation to the 3pt Plus a Common Direction Relative Pose Problem

In this paper we present an alternative formulation for the minimal solution to the 3pt plus a common direction relative pose problem. Instead of the commonly used epipolar constraint we use the homography 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 estimation. In addition we analyze the degenerate conditions for the proposed method.