A Tangible Solution for Hand Motion Tracking in Clinical Applications

Objective real-time assessment of hand motion is crucial in many clinical applications including technically-assisted physical rehabilitation of the upper extremity. We propose an inertial-sensor-based hand motion tracking system and a set of dual-quaternion-based methods for estimation of finger segment orientations and fingertip positions. The proposed system addresses the specific requirements of clinical applications in two ways: (1) In contrast to glove-based approaches, the proposed solution maintains the sense of touch. (2) In contrast to previous work, the proposed methods avoid the use of complex calibration procedures, which means that they are suitable for patients with severe motor impairment of the hand. To overcome the limited significance of validation in lab environments with homogeneous magnetic fields, we validate the proposed system using functional hand motions in the presence of severe magnetic disturbances as they appear in realistic clinical settings. We show that standard sensor fusion methods that rely on magnetometer readings may perform well in perfect laboratory environments but can lead to more than 15 cm root-mean-square error for the fingertip distances in realistic environments, while our advanced method yields root-mean-square errors below 2 cm for all performed motions.DFG, 414044773, Open Access Publizieren 2019 - 2020 / Technische Universität Berli

Optimality of uncertaintyprinciples for joint timefrequencyrepresentations

The study of joint time-frequency representations is a large field of mathematics and physics, especially signal analysis. Based on Heisenberg's cllassical uncertainty principle various inequalities for such time-frequency distributions have been studied. The objective of this thesis is to examine the role that Gaussian functions, including those with a chirp contribution, play in inequalities for the Short-Time Fourier transform and the Wigner distribution. We show that Gröchenig's uncertainty principles for the Short-Time Fourier transform are not optimal with regard to these functions. As for the Wigner distribution we show how an existing uncertainty principle by Janssen can be modied to reach optimality for Chirp Gaussians

Optimality of uncertaintyprinciples for joint timefrequencyrepresentations

The study of joint time-frequency representations is a large field of mathematics and physics, especially signal analysis. Based on Heisenberg's cllassical uncertainty principle various inequalities for such time-frequency distributions have been studied. The objective of this thesis is to examine the role that Gaussian functions, including those with a chirp contribution, play in inequalities for the Short-Time Fourier transform and the Wigner distribution. We show that Gröchenig's uncertainty principles for the Short-Time Fourier transform are not optimal with regard to these functions. As for the Wigner distribution we show how an existing uncertainty principle by Janssen can be modied to reach optimality for Chirp Gaussians