Object Pose from 2-D to 3-D Point and Line Correspondences

Estimating a camera pose from 3D-2D correspondences - Perspective-n-Point - is one of the most fundamental problems in computer vision. Existing methods either solve a minimal problem or replace the objective with an easier one. Surprisingly, no scalable certifiable solver for the actual Maximum Likelihood Estimation (MLE) exists. We propose PnP*, the first practical solver that guarantees efficient computation and returns a certifiable globally optimal solution. We prove that the underlying convex relaxation is exact under moderate noise, which to our knowledge is the first stability guarantee for any relaxation for the MLE of PnP. Furthermore, we reduce the relaxation by exploiting chordal sparsity pattern and quotient ring reduction such that the relaxation is tractable and scalable. The stability and scalability results are verified numerically, as PnP* returns a provably correct camera pose at over 10 Hz.

We propose a novel method for iterative learning of point correspondences between image sequences. Points moving on surfaces in 3D space are projected into two images. Given a point in either view, the considered problem is to determine the corresponding location in the other view. The geometry and distortions of the projections are unknown as is the shape of the surface. Given several pairs of point-sets but no access to the 3D scene, correspondence mappings can be found by excessive global optimization or by the fundamental matrix if a perspective projective model is assumed. However, an iterative solution on sequences of point-set pairs with general imaging geometry is preferable. We derive such a method that optimizes the mapping based on Neyman's chi-square divergence between the densities representing the uncertainties of the estimated and the actual locations. The densities are represented as channel vectors computed with a basis function approach. The mapping between these vectors is updated with each new pair of images such that fast convergence and high accuracy are achieved. The resulting algorithm runs in real-time and is superior to state-of-the-art methods in terms of convergence and accuracy in a number of experiments.

Solving non-linear least-squares problem for pose estimation (rotation and translation) is often a time consuming yet fundamental problem in several real-time computer vision applications. With an adequate rotation parametrization, the optimization problem can be reduced to the solution of a~system of polynomial equations and solved in closed form. Recent advances in efficient closed form solvers utilizing resultant matrices have shown a promising research direction to decrease the computation time while preserving the estimation accuracy. In this paper, we propose a new class of resultant-based solvers that exploit Sylvester forms to further reduce the complexity of the resolution. We demonstrate that our proposed methods are numerically as accurate as the state-of-the-art solvers, and outperform them in terms of computational time. We show that this approach can be applied for pose estimation in two different types of problems: estimating a pose from 3D to 3D correspondences, and estimating a pose from 3D points to 2D points correspondences.