Convex Relaxations of SE(2) and SE(3) for Visual Pose Estimation
This addresses pose estimation in computer vision, offering a novel convex approach with proven exactness, though it builds on existing relaxation techniques.
The paper tackles rigid body pose estimation by proposing a convex relaxation method using spectrahedral representations of SE(2) and SE(3), which is shown to be exact in many settings and guaranteed for a large class of problems.
This paper proposes a new method for rigid body pose estimation based on spectrahedral representations of the tautological orbitopes of $SE(2)$ and $SE(3)$. The approach can use dense point cloud data from stereo vision or an RGB-D sensor (such as the Microsoft Kinect), as well as visual appearance data. The method is a convex relaxation of the classical pose estimation problem, and is based on explicit linear matrix inequality (LMI) representations for the convex hulls of $SE(2)$ and $SE(3)$. Given these representations, the relaxed pose estimation problem can be framed as a robust least squares problem with the optimization variable constrained to these convex sets. Although this formulation is a relaxation of the original problem, numerical experiments indicate that it is indeed exact - i.e. its solution is a member of $SE(2)$ or $SE(3)$ - in many interesting settings. We additionally show that this method is guaranteed to be exact for a large class of pose estimation problems.