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Geometric approach to multi-scale 3D gesture comparison Open Access


Other title
nonlinear kernel filter
curvature signature
medical training
arc-length parameterization
nonlinear signatures
curvature signature correlations
3D gesture comparison
medical manipulative gestures
finite difference methods
curvature neighborhood
sequence comparison
least squares curve fitting
differential geometry
differential convolution filter
multilevel curvature analysis
complex trajectories
robotic simulator
motor skill transfer
qualitative skill transfer measure
anisotropic kernel filter
Frenet-Serret quaternion framework
Multiscale curvature
3D electromagnetic trackers
3D trajectory smoothing
quaternion metrics
quaternion trajectories
Savitzky-Golay filter
torsion signature
motion tracking
child bearing simulator
quaternion projections
geodesic distance
curvature numerical stability
quaternion smoothing
Type of item
Degree grantor
University of Alberta
Author or creator
Ochoa Mayorga, Victor Manuel
Supervisor and department
Pierre Boulanger (Computing Science)
Examining committee member and department
Brian Maraj (Physical Education & Recreation)
Herb Yang (Computing Science)
Dale Schuurmans (Computing Science)
Roy Eagleson (Electrical & Computer Engineering University of Western Ontario)
Department of Computing Science

Date accepted
Graduation date
Doctor of Philosophy
Degree level
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.
License granted by Victor Manuel Ochoa Mayorga ( on 2010-09-29T19:24:33Z (GMT): Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of the above terms. The author reserves all other publication and other rights in association with the copyright in the thesis, and except as herein provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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