Extrinsic calibration of non-overlapping multi-camera system with high precision using circular encoded point ruler

In the field of visual metrology, achieving coordinate system unification among non-overlapping multi-camera systems in wide field-of-view scenarios poses significant challenges due to the absence of overlapping fields of view. This paper presents a novel calibration method for such multi-camera systems utilizing a ruler equipped with double-layer circular encoded landmarks. The fabrication of the ruler is simple, and its length covers the entire multi-camera measurement system, rendering the calibration process convenient. To calibrate the cameras, the ruler is positioned in front of the target cameras, and images of the ruler are captured by the multi-cameras. By establishing the initial transformation relationships between the non-overlapping cameras and the ruler's coordinate system, the proposed method efficiently determines the inter-camera transformations. Subsequently, by moving the ruler to different positions and capturing corresponding images, the distances between the encoded center points on the ruler and other encoded points, as captured by the non-overlapping cameras, are kept constant. An optimization-based objective function is formulated to minimize the three-dimensional distances between the measured encoded center points, thereby refining the initial transformation relationships. Combining the coplanarity constraint of the coding center points with the extrinsic results obtained through distance optimization, a secondary optimization was conducted to obtain the final transformation parameters. Experimental results demonstrate the simplicity and versatility of this method, which does not rely on complex constraints. Moreover, it exhibits high calibration accuracy, with maximum distance errors between ruler points and a fitting standard plane error both below 0.275 mm and 0.132 mm, respectively. Following multiple experimental iterations, the average disparity between the radius of the standard cylinder measured via line laser scanning and its true value was found to be 0.022 mm. The average maximum distance from the point cloud to the fitted cylinder surface was determined to be 0.281 mm, while the average distance, computed across multiple instances, was 0.048 mm. Consequently, the proposed approach proves effective for calibrating non-overlapping camera systems in various applications.