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Quaternionic Upsampling: Hyperspherical Techniques for 6 DoF Pose Tracking

Fast real-time tracking is an integral component of modern 3D computer vision pipelines. Despite their advantages in accuracy and reliability, optical trackers suffer from limited acquisition rates depending either on intrinsic sensor capabilities or physical limitations such as exposure time. Moreover, data transmission and image processing produce latency in the pose stream. We introduce quaternionic upsampling to overcome these problems. The technique models the pose parameters as points on multidimensional hyperspheres in (dual) quaternion space. In order to upsample the pose stream, we present several methods to sample points on geodesics and piecewise continuous curves on these manifolds and compare them regarding accuracy and computation efficiency. With the unified approach of quaternionic upsampling, both interpolation and extrapolation in pose space can be done by continuous linear variation of only one sampling parameter. Since the method can be implemented rather efficiently, pose rates of over 4 kHz and future pose predictions with an accuracy of 128 μm and 0.5° are possible in real-time. The method does not depend on a special tracking algorithm and can thus be used for any arbitrary 3 DoF or 6 DoF rotation or pose tracking system.