Self-Calibration of Cameras with Euclidean Image Plane in Case of Two Views and Known Relative Rotation Angle

TL;DR

This paper introduces a non-iterative self-calibration method for cameras with Euclidean image planes using two views, fixed but unknown focal length and principal point, requiring only a known relative rotation angle and multiple point correspondences.

Contribution

It presents a novel, stable, and robust self-calibration algorithm that works with minimal data and fixed internal parameters, extending existing calibration techniques.

Findings

The algorithm is correct and numerically stable.

It can handle real and synthetic data effectively.

The problem has six solutions in general.

Abstract

The internal calibration of a pinhole camera is given by five parameters that are combined into an upper-triangular $3\times 3$ calibration matrix. If the skew parameter is zero and the aspect ratio is equal to one, then the camera is said to have Euclidean image plane. In this paper, we propose a non-iterative self-calibration algorithm for a camera with Euclidean image plane in case the remaining three internal parameters --- the focal length and the principal point coordinates --- are fixed but unknown. The algorithm requires a set of $N \geq 7$ point correspondences in two views and also the measured relative rotation angle between the views. We show that the problem generically has six solutions (including complex ones). The algorithm has been implemented and tested both on synthetic data and on publicly available real dataset. The experiments demonstrate that the method is correct, numerically stable and robust.