Making minimal solvers inverse-free using null space computation

Hassan Bozorgmanesh, Janne Heikkila

Keywords: minimal solver, null space, inverse-free, camera-geometry

TL;DR: This paper proposes a novel inverse-free method based on null-space computations for minimal solvers in computer vision.

Abstract:

In this paper, we propose a novel resultant-based method for solving polynomial systems of equations that are commonly encountered in computer vision, particularly as minimal problems. Unlike traditional algorithms that rely on matrix inversion, the primary merits of the proposed method are the numerical stability of its formulation and the lack of need to compute the inverse of a matrix by leveraging null space computations. Additionally, its formulation paves the way for more computations to be performed in the offline stage by using the sparsity of coefficient matrices, thereby reducing the computational load in the online stage.
This inverse-free formulation is especially suited for sparse systems and offers improved robustness in scenarios where matrix inversion is unstable or infeasible. Experimental results demonstrate better accuracy compared to state-of-the-art methods such as SRBM and GAPS across a variety of camera geometry problems.

Submission Number: 314