W-PnP Method: Optimal Solution for the Weak-Perspective n-Point Problem and Its Application to Structure from Motion

Abstract

Abstract:Camera calibration is a key problem in 3D computer vision since the late 80's. Most of the calibration methods deal with the (perspective) pinhole camera model. This is not a simple goal: the problem is nonlinear due to the perspectivity. The strategy of these methods is to estimate the intrinsic camera parameters first; then the extrinsic ones are computed by the so-called PnP method. Finally, the accurate camera parameters are obtained by slow numerical optimization. In this paper, we show that the weak-perspective camera model can be optimally calibrated without numerical optimization if the L 2 norm is used. The solution is given by a closed-form formula, thus the estimation is very fast. We call this method as the Weak-Perspective n-Point (W-PnP) algorithm. Its advantage is that it simultaneously estimates the two intrinsic weak-perspective camera parameters and the extrinsic ones. We show that the proposed calibration method can be utilized as the solution for a subproblem of 3D reconstruction with missing data. An alternating least squares method is also defined that optimizes the camera motion using the proposed optimal calibration method.