L. Wang, M. Springer, H. Heibel, N. Navab Floyd-Warshall All-Pair Shortest Path for Accurate Multi-Marker Calibration The 9th IEEE and ACM International Symposium on Mixed and Augmented Reality, Seoul, Korea, Oct. 13 - 16, 2010. (bib)
	Visual marker based tracking is one of the most widely used tracking techniques in Augmented Reality (AR) applications. Multiple square markers are generally needed to perform robust and accurate tracking, since a single marker cannot provide a stable and accurate enough pose estimation and has a limited viewing field to the camera. For this, relative poses of multiple markers which are fixed with respect to each other must be properly calibrated. A multi-image based method for calibrating relative marker poses was proposed by Baratoff et al. However, the calibration accuracy of their method relies on the order of the image sequence. Several studies have shown that the accuracy of pose estimation for an individual square marker depends on camera distance and viewing angle. We propose a novel method to compute the poses of multiple randomly positioned square markers in one consistent world coordinate frame, by taking each marker's pose accuracy into account. The problem of computing the ``best'' closed-form solution of the world pose of each marker is modeled as all-pair shortest path problem in graph theory. The computed world poses are further optimized by minimizing the geometric distances in images. Experimental results with three different setups show that incorporating the predicted accuracy of the pose estimation for each marker yields constant high quality calibration results independent of the order of image sequences compared to cases when this knowledge is not used.
	This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each authors copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.