Novel Methods for Depth-Based Calibration of Multiple RGBD Cameras Using Four Mutually Equidistant Spheres

Abstract

This article presents novel calibration methods specifically tailored for multiple depth cameras, utilizing solely depth images. Traditional approaches often rely on infrared (IR) images of checkerboards, which, while feasible, fail to exploit the measured depth values, leading to calibration inaccuracies and 3-D misregistration errors. To overcome this limitation, we designed a 3-D tetrahedron object comprising four spheres placed at each corner. By employing an ellipse-fitting technique, we accurately identified the sphere centers in the depth images. Using these centers, we utilized 3-D reprojection errors and measured depths within a bundle adjustment framework to jointly determine the calibration parameters for four depth cameras. Our proposed methods significantly reduce error values compared with those obtained using IR images of checkerboards. The versatility of our techniques ensures their applicability to various types of depth cameras, independent of their underlying technologies. Here, we demonstrate that by integrating depth information directly into the calibration process, we achieve remarkable improvements. Our first method reduces the average system reconstruction error by 78.98%, while our second method, which introduces a novel cost function tailored to the tetrahedron object, achieves an even more substantial reduction of 82.32%. These results underscore the superiority of our depth-integrated calibration approach, particularly in the context of 3-D reconstruction involving multiple depth cameras.