X-Tag: A Fiducial Tag for Flexible and Accurate Bundle Adjustment

Abstract

In this paper we design a novel planar 2D fiducial marker and develop fast detection algorithm aiming easy camera calibration and precise 3D reconstruction at the marker locations via the bundle adjustment. Even though an abundance of planar fiducial markers have been made and used in various tasks, none of them has properties necessary to solve the aforementioned tasks. Our marker, X-tag, enjoys a novel design, coupled with very efficient and robust detection scheme, resulting in a reduced number of false positives. This is achieved by constructing markers with random circular features in the image domain and encoding them using two true perspective invariants: cross-ratios and intersection preservation constraints. To detect the markers, we developed an effective search scheme, similar to Geometric Hashing and Hough Voting, in which the marker decoding is cast as a retrieval problem. We apply our system to the task of camera calibration and bundle adjustment. With qualitative and quantitative experiments, we demonstrate the robustness and accuracy of X-tag in spite of blur, noise, perspective and radial distortions, and showcase camera calibration, bundle adjustment and 3d fusion of depth data from precise extrinsic camera poses.