In this work, we present a Direct Least-Squares (DLS) method for computing all solutions of the perspective-npoint camera pose determination (PnP) problem in the general case (n ≥ 3). Specifically, based on the camera measurement equations, we formulate a nonlinear least-squares cost function whose optimality conditions constitute a system of three third-order polynomials. Subsequently, we employ the multiplication matrix to determine all the roots of the system analytically, and hence all minima of the LS, without requiring iterations or an initial guess of the parameters. A key advantage of our method is scalability, since the order of the polynomial system that we solve is independent of the number of points. We compare the performance of our algorithm with the leading PnP approaches, both in simulation and experimentally, and demonstrate that DLS consistently achieves accuracy close to the Maximum-Likelihood Estimator (MLE).
In the Direct-Least-Squares (DLS) REF method, a nonlinear object space cost function is formulated and polynomial resultant techniques are used to recover the (up to 27) stationary points of a polynomial equation system of fourth order polynomials.
A Direct Least-Squares (DLS) method for PnP
2011 International Conference on Computer Vision
2011 International Conference on Computer Vision
Mathematics Computer Science