Efficient MSPSO Sampling for Object Detection and 6D Pose Estimation in 3D Scenes

The point pair feature (PPF) is widely used in industrial applications for estimating 6D poses of known objects from unrecognized point clouds. The key to the success of PPF matching is to establish correct 3D correspondences between the object and the scene, i.e., finding as many valid similar point pairs as possible. Thus, a set of...

Counterexample to a Conjecture on an Infeasible Interior-Point Method

In [SIAM J. Optim., 16 (2006), pp. 1110–1136], Roos proved that the devised full-step infeasible algorithm has $O(n)$ worst-case iteration complexity. This complexity bound depends linearly on a parameter $\bar{\kappa}(\zeta)$, which is proved to be less than $\sqrt{2n}$. Based on extensive computational evidence (hundreds of thousands of...

Improved Full-Newton Step O(nL) Infeasible Interior-Point Method for Linear Optimization

We present several improvements of the full-Newton step infeasible interior-point method for linear optimization introduced by Roos (SIAM J. Optim. 16(4):1110–1136, 2006). Each main step of the method consists of a feasibility step and several centering steps. We use a more natural feasibility step, which targets the ?+-center of the next pair...

Full-step interior-point methods for symmetric optimization

In [SIAM J. Optim., 16(4):1110--1136 (electronic), 2006] Roos proposed a full-Newton step Infeasible Interior-Point Method (IIPM) for Linear Optimization (LO). It is a primal-dual homotopy method; it differs from the classical IIPMs in that it uses only full steps. This means that no line searches are needed. In this thesis, we first present an...