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 Chair for Computer Aided Medical Procedures & Augmented Reality Lehrstuhl für Informatikanwendungen in der Medizin & Augmented Reality

 D. Pustka, J. Willneff, O. Wenisch, P. Lükewille, K. Achatz, P. Keitler, G. Klinker Determining the Point of Minimum Error for 3DOF Pose Uncertainty Representation The Ninth IEEE and ACM International Symposium on Mixed and Augmented Reality, Seoul, Korea, Oct. 13 - 16, 2010, pp. 37-45. (bib) In many augmented reality applications, in particular in the medical and industrial domains, knowledge about tracking errors is important. Most current approaches characterize tracking errors by $6\times 6$ covariance matrices that describe the uncertainty of a 6DOF pose, where the center of rotational error lies in the origin of a target coordinate system. This origin is assumed to coincide with the geometric centroid of a tracking target. In this paper, we show that, in case of a multi-camera fiducial tracking system, the geometric centroid of a body does not necessarily coincide with the point of minimum error. The latter is not fixed to a particular location, but moves, depending on the individual observations. We describe how to compute this point of minimum error given a covariance matrix and verify the validity of the approach using Monte Carlo simulations on a number of scenarios. Looking at the movement of the point of minimum error, we find that it can be located surprisingly far away from its expected position. This is further validated by an experiment using a real camera system. 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.

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Lehrstuhl für Computer Aided Medical Procedures & Augmented Reality