Beyond Gr\"obner Bases: Basis Selection for Minimal Solvers

Many computer vision applications require robust estimation of the underlying geometry, in terms of camera motion and 3D structure of the scene. These robust methods often rely on running minimal solvers in a RANSAC framework. In this paper we show how we can make polynomial solvers based on the action matrix method faster, by careful selection of the monomial bases. These monomial bases have traditionally been based on a Gr\"obner basis for the polynomial ideal. Here we describe how we can enumerate all such bases in an efficient way. We also show that going beyond Gr\"obner bases leads to more efficient solvers in many cases. We present a novel basis sampling scheme that we evaluate on a number of problems

Sensor Networks TDOA Self-Calibration: 2D Complexity Analysis and Solutions

Given a network of receivers and transmitters, the process of determining their positions from measured pseudo-ranges is known as network self-calibration. In this paper we consider 2D networks with synchronized receivers but unsynchronized transmitters and the corresponding calibration techniques,known as TDOA techniques. Despite previous work, TDOA self-calibration is computationally challenging. Iterative algorithms are very sensitive to the initialization, causing convergence issues.In this paper, we present a novel approach, which gives an algebraic solution to three previously unsolved scenarios. Our solvers can lead to a position error <1.2% and are robust to noise