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1	Geometric approach to multi-scale 3D gesture comparison Ochoa Mayorga, Victor Manuel 11 1900 (has links) The present dissertation develops an invariant framework for 3D gesture comparison studies. 3D gesture comparison without Lagrangian models is challenging not only because of the lack of prediction provided by physics, but also because of a dual geometry representation, spatial dimensionality and non-linearity associated to 3D-kinematics. In 3D spaces, it is difficult to compare curves without an alignment operator since it is likely that discrete curves are not synchronized and do not share a common point in space. One has to assume that each and every single trajectory in the space is unique. The common answer is to assert the similitude between two or more trajectories as estimating an average distance error from the aligned curves, provided that the alignment operator is found. In order to avoid the alignment problem, the method uses differential geometry for position and orientation curves. Differential geometry not only reduces the spatial dimensionality but also achieves view invariance. However, the nonlinear signatures may be unbounded or singular. Yet, it is shown that pattern recognition between intrinsic signatures using correlations is robust for position and orientation alike. A new mapping for orientation sequences is introduced in order to treat quaternion and Euclidean intrinsic signatures alike. The new mapping projects a 4D-hyper-sphere for orientations onto a 3D-Euclidean volume. The projection uses the quaternion invariant distance to map rotation sequences into 3D-Euclidean curves. However, quaternion spaces are sectional discrete spaces. The significance is that continuous rotation functions can be only approximated for small angles. Rotation sequences with large angle variations can only be interpolated in discrete sections. The current dissertation introduces two multi-scale approaches that improve numerical stability and bound the signal energy content of the intrinsic signatures. The first is a multilevel least squares curve fitting method similar to Haar wavelet. The second is a geodesic distance anisotropic kernel filter. The methodology testing is carried out on 3D-gestures for obstetrics training. The study quantitatively assess the process of skill acquisition and transfer of manipulating obstetric forceps gestures. The results show that the multi-scale correlations with intrinsic signatures track and evaluate gesture differences between experts and trainees. 3D gesture comparison Multiscale curvature Curvature-torsion differential geometry complex trajectories quaternion trajectories quaternion projections quaternion metrics 3D trajectory smoothing curvature signature correlations qualitative skill transfer measure medical manipulative gestures nonlinear signatures anisotropic kernel filter curvature numerical stability quaternion smoothing kinematics motor skill transfer curvature signature torsion signature arc-length parameterization tensors Frenet-Serret quaternion framework nonlinear kernel filter geodesic distance finite difference methods differential convolution filter Savitzky-Golay filter least squares curve fitting curvature neighborhood multilevel curvature analysis medical training child bearing simulator robotic simulator motion tracking 3D electromagnetic trackers sequence comparison medical training
2	Geometric approach to multi-scale 3D gesture comparison Ochoa Mayorga, Victor Manuel Unknown Date No description available. 3D gesture comparison Multiscale curvature Curvature-torsion differential geometry complex trajectories quaternion trajectories quaternion projections quaternion metrics 3D trajectory smoothing curvature signature correlations qualitative skill transfer measure medical manipulative gestures nonlinear signatures anisotropic kernel filter curvature numerical stability quaternion smoothing kinematics motor skill transfer curvature signature torsion signature arc-length parameterization tensors Frenet-Serret quaternion framework nonlinear kernel filter geodesic distance finite difference methods differential convolution filter Savitzky-Golay filter least squares curve fitting curvature neighborhood multilevel curvature analysis medical training child bearing simulator robotic simulator motion tracking 3D electromagnetic trackers sequence comparison medical training

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Geometric approach to multi-scale 3D gesture comparison

Geometric approach to multi-scale 3D gesture comparison