Flexible Camera Calibration using a Collimator System

TL;DR

This work presents a collimator-based camera calibration framework that exploits angle invariance to enforce a spherical motion constraint, reducing relative motion to a 3DOF rotation. It introduces closed-form and minimal solvers for multi-image calibration and a fast single-image calibration using a reference image, followed by bundle adjustment to refine parameters. The method eliminates the need for directional measurement devices, offers a portable calibration target, and demonstrates superior robustness and accuracy in synthetic and real-data experiments, including structure-from-motion tasks and multi-focus cameras. Overall, the approach provides a flexible, fast, and accurate calibration solution suitable for challenging outdoor and long-range scenarios.

Abstract

Camera calibration is a crucial step in photogrammetry and 3D vision applications. This paper introduces a novel camera calibration method using a designed collimator system. Our collimator system provides a reliable and controllable calibration environment for the camera. Exploiting the unique optical geometry property of our collimator system, we introduce an angle invariance constraint and further prove that the relative motion between the calibration target and camera conforms to a spherical motion model. This constraint reduces the original 6DOF relative motion between target and camera to a 3DOF pure rotation motion. Using spherical motion constraint, a closed-form linear solver for multiple images and a minimal solver for two images are proposed for camera calibration. Furthermore, we propose a single collimator image calibration algorithm based on the angle invariance constraint. This algorithm eliminates the requirement for camera motion, providing a novel solution for flexible and fast calibration. The performance of our method is evaluated in both synthetic and real-world experiments, which verify the feasibility of calibration using the collimator system and demonstrate that our method is superior to existing baseline methods. Demo code is available at https://github.com/LiangSK98/CollimatorCalibration

Figures (19)

• Figure 1: Schematic diagram of our collimator-based calibration. The camera achieves precise calibration by capturing one or more images of the collimator system.
• Figure 2: Left: Schematic diagram of our collimator system. The geometric property of the collimator system leads to angle invariance of any point pair on the reticle; Right: Schematic diagram of spherical motion model. The angle invariance forces the relative motion between the calibration target and the camera to satisfy the spherical motion model.
• Figure 3: Schematic diagram of the camera capturing images with pure translation. Since the observation rays of $P$ are parallel, the angle between the optical axis and the observation ray is unchanged after the camera's pure translation ($\theta_1 = \theta_2 = \theta_3$). This motion does not generate new image points, resulting in degeneracy.
• Figure 4: Flowchart of the single-image calibration algorithm. The input includes only a single calibration image. A pre-constructed feature database is built using reference images, which captures the inherent angular information of our collimator system. The core constraint of our algorithm stems from the angle invariance of collimator system. The entire process involves consecutively solving three optimization problems.
• Figure 5: Comparison of calibration errors as noise level increases. The predefined virtual camera intrinsics are: $(f_x, f_y) = (1000, 1000)$ pixels, $(c_x, c_y)= (542, 478)$ pixels, $d_1 = 0.1$ and $d_2 = -0.2$. Our method consistently outperforms other methods across all noise levels.