Determining the point of minimum error for 6DOF pose uncertainty representation

D. Pustka, J. Willneff, Oliver G. Wenisch, Peter Lukewille, Kurt Achatz, P. Keitler, G. Klinker
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引用次数: 8

Abstract

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 6×6 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.
确定6DOF姿态不确定度表示的最小误差点
在许多增强现实应用中,特别是在医疗和工业领域,关于跟踪错误的知识很重要。目前大多数方法通过6×6协方差矩阵来描述跟踪误差,该矩阵描述了6DOF姿态的不确定性,其中旋转误差的中心位于目标坐标系的原点。假定这个原点与跟踪目标的几何质心重合。在本文中,我们证明了在多相机基准跟踪系统中,物体的几何质心不一定与最小误差点重合。后者不是固定在一个特定的位置,而是根据个人观察而移动。我们描述了如何在给定协方差矩阵的情况下计算这个最小误差点,并使用蒙特卡罗模拟在许多情况下验证了该方法的有效性。观察最小误差点的运动,我们发现它可以位于离预期位置很远的地方。通过实际摄像机系统的实验进一步验证了这一点。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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