A Non-Iterative Solution to the Four-Point Three-Views Pose Problem in Case of Collinear Cameras

TL;DR

This paper presents a direct, non-iterative method for solving the four-point three-views pose problem specifically for collinear camera setups, using polynomial equations derived from epipolar constraints.

Contribution

It introduces a novel algebraic approach utilizing Cayley's representation to solve a specific multi-view geometry problem without iteration.

Findings

Method is robust on synthetic data

Effective in planar camera configurations

Provides exact solutions via polynomial roots

Abstract

We give a non-iterative solution to a particular case of the four-point three-views pose problem when three camera centers are collinear. Using the well-known Cayley representation of orthogonal matrices, we derive from the epipolar constraints a system of three polynomial equations in three variables. The eliminant of that system is a multiple of a 36th degree univariate polynomial. The true (unique) solution to the problem can be expressed in terms of one of real roots of that polynomial. Experiments on synthetic data confirm that our method is robust enough even in case of planar configurations.