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Two DOF Camera Pose Estimation with a Planar Stochastic Reference Grid

Determining the pose of the camera is a need to many higher level computer vision tasks. We assume a set of features to be distributed on a planar surface (the world plane) as a Poisson point process, and to know their positions in the image plane. Then we propose an algorithm to recover the pose of the camera, in the case of two degrees of freedom (slant angle and distance from the ground). The algorithm is based on the observation that cell areas of the Voronoi tessellation generated by the points in the image plane represent a reliable sampling of the Jacobian determinant of the perspective transformation up to a scaling factor, the density of points in the world plane, which we demand as input. In the process, we develop a transformation of our input data (areas of Voronoi cells) so that they show almost constant variances among the locations, and analytically find a correcting factor to considerably reduce the bias of our estimates. We perform intensive synthetic simulations and show that with few hundreds of random points our errors on angle and distance are not more than few percents.