Trifocal Relative Pose from Lines at Points and its Efficient Solution

TL;DR

This paper introduces an efficient homotopy continuation solver for minimal relative pose problems from three views involving points and lines, outperforming existing methods in speed and robustness, especially under noisy conditions.

Contribution

The paper develops a novel, specialized homotopy continuation framework called MINUS for solving complex three-view pose estimation problems more efficiently and robustly than prior Groebner basis methods.

Findings

The proposed solver is significantly faster than previous methods.

It demonstrates high numerical robustness under image noise.

The method successfully handles difficult cases with limited or noisy data.

Abstract

We present a method for solving two minimal problems for relative camera pose estimation from three views, which are based on three view correspondences of i) three points and one line and the novel case of ii) three points and two lines through two of the points. These problems are too difficult to be efficiently solved by the state of the art Groebner basis methods. Our method is based on a new efficient homotopy continuation (HC) solver framework MINUS, which dramatically speeds up previous HC solving by specializing HC methods to generic cases of our problems. We characterize their number of solutions and show with simulated experiments that our solvers are numerically robust and stable under image noise, a key contribution given the borderline intractable degree of nonlinearity of trinocular constraints. We show in real experiments that i) SIFT feature location and orientation provide good enough point-and-line correspondences for three-view reconstruction and ii) that we can solve difficult cases with too few or too noisy tentative matches, where the state of the art structure from motion initialization fails.