Generalized Pose-and-Scale Estimation using 4-Point Congruence Constraints

TL;DR

The paper introduces gP4Pc, a fast and robust method for estimating the absolute pose and scale of a generalized camera using four point-ray correspondences, based on shape congruence constraints.

Contribution

It presents a novel parametrization and polynomial solver for pose-and-scale estimation, including an efficient variant for coplanar points, improving speed and robustness.

Findings

gP4Pc is among the fastest pose-and-scale methods in RANSAC.

The method achieves competitive accuracy and stability.

Specialized solver for coplanar points is about 3x faster.

Abstract

We present gP4Pc, a new method for computing the absolute pose of a generalized camera with unknown internal scale from four corresponding 3D point-and-ray pairs. Unlike most pose-and-scale methods, gP4Pc is based on constraints arising from the congruence of shapes defined by two sets of four points related by an unknown similarity transformation. By choosing a novel parametrization for the problem, we derive a system of four quadratic equations in four scalar variables. The variables represent the distances of 3D points along the rays from the camera centers. After solving this system via Groebner basis-based automatic polynomial solvers, we compute the similarity transformation using an efficient 3D point-point alignment method. We also propose a specialized variant of our solver for the case of coplanar points, which is computationally very efficient and about 3x faster than the fastest existing solver. Our experiments on real and synthetic datasets, demonstrate that gP4Pc is among the fastest methods in terms of total running time when used within a RANSAC framework, while achieving competitive numerical stability, accuracy, and robustness to noise.