Computer Graphics Lab.

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Coordinate-Invariant Methods ForMotion Analysis
and Synthesis

• Computer Graphics Lab.
• KAIST

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Contents

• 1. Issues in motion analysis and syntheis
• 2. Spatial filtering for motion data
• 3. Multiresolution motion analysis
• 4. Conclusion

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Character Animation

• Producing animation from available motion clips
• Requires specialized tools
• interactive editing, smoothing,
• enhancement, blending, stitching,
• Difficulties in handling motion data
• Singularity
• Inherent non-linearity of orientation space

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Motion Signal Processing

• Coordinate-invariance
• Independent of the choice of coordinate frames

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Overview

• Generalize conventional methods
• Spatial filters for orientation data
• Multiresolution analysis for rigid motion
• Requirements
• Coordinate-invariance
• Time-invariance

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Previous Work

• Filters for orientation data
• Euler angle parameterization Bodenheimer et al.
  (97)
• Re-normalization Azuma and Bishop (94)
• Exploit a local parameterization
• Lee and Shin (96), Welch and Bishop (97),
• Fang et al. (98), Hsieh et al. (98)
• Multiresolution analysis for rigid motion
• Image and signal processing Burt and Adelson
  (83)
• Texture analysis and synthesis, image editing,
  curve and surface manipulation, data compression,
  and so on
• Motion synthesis and editing
• Hierarchical spacetime control Liu, Gortler and
  Cohen (94)
• Motion signal processing Bruderlin and Williams
  (95)

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Spatial Filtering for Orientation Data

• Linear Time-Invariant filter
• Filter mask
• Vector-valued signal
• Not suitable for unit quaternion data
• Unit-length constraints

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Linear and Angular Displacement
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Transformation

• Transformation between linear and angular signals

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Filter Design

• Key idea
• Letting linear displacement caused by F be
  equivalent to the angular displacement caused by
  H
• Given spatial filter F
• Output spatial filter H for orientation data

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Examples
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Examples
Original
Angular acceleration
Filtered
Original Filtered
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Properties of Orientation Filters

• Coordinate-invariance
• Time-invariance
• Symmetry

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Multiresolution Analysis

• Representing a signal at multiple resolutions
• Facilitate a variety of signal processing tasks
• Give hierarchy of successively smoother signals

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Decomposition
Reduction
Expansion

• Expansion up-sampling followed by smoothing
• Reduction smoothing followed by down-sampling

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Decomposition and Reconstruction

• Decomposition
• Reconstruction

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Hierarchical Displacement Mapping
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Hierarchical Displacement Mapping

• A series of successively refined motions
• Coordinate-independence
• measured in a body-fixed coordinate frame
• Uniformity
• through a local parameterization

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Coordinate Frame-Invariance
Decomposition
Reconstruction
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Enhancement / Attenuation

• Level-wise scaling of coefficients

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Enhancement / Attenuation

• Level-wise scaling of coefficients

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Extrapolation
Walking
Turning
Limping
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Stitching

• Stitching motion clips seamlessly
• Merging coefficients level-by-level

stub a toe
limp
stitching
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Conclusion

• Spatial filters for orientation data
• Satisfy desired properties
• coordinate-invariance, time-invariance, symmetry
• Simple, efficient, easy to implement
• Multiresolution motion analysis
• Coherency in positions and orientations
• Coordinate-invariance and time-invariance