Geometric approach to multi-scale 3D gesture comparison

• Author / Creator

  Ochoa Mayorga, Victor Manuel

• 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.

• Subjects / Keywords

  • 3D trajectory smoothing
  • Curvature neighborhood
  • Arc-length parameterization
  • Frenet-Serret quaternion framework
  • Motion tracking
  • Motor skill transfer
  • Sequence comparison
  • 3D gesture comparison
  • Multiscale curvature
  • Finite difference methods
  • Curvature-torsion
  • Savitzky-Golay filter
  • Curvature signature correlations
  • Curvature signature
  • Quaternion metrics
  • Quaternion smoothing
  • Kinematics
  • Geodesic distance
  • Torsion signature
  • Child bearing simulator
  • Anisotropic kernel filter
  • Medical training
  • Quaternion projections
  • Nonlinear kernel filter
  • Medical manipulative gestures
  • Multilevel curvature analysis
  • Qualitative skill transfer measure
  • Complex trajectories
  • Curvature numerical stability
  • 3D electromagnetic trackers
  • Robotic simulator
  • Differential convolution filter
  • Nonlinear signatures
  • Differential geometry
  • Quaternion trajectories
  • Tensors
  • Least squares curve fitting

• Graduation date

  Fall 2010

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R3ZS40

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.