Lecture 10: From Rotations to Human Motion

by Mike Gleicher on February 15, 2013

Details of rotations that we didn’t get to last time

Quaternions

  • multiply
  • single axis
  • anti-podal equivalence
  • multiple different zeros

Log Map

  • the derivative of a unit quaternion is a vector in 3 space
  • S(3) –> R(3)
  • Local linearization

Interpolation

  • SLERP
  • NLERP
  • log map interpolation
  • Multi-Way averaging?
    • using the log map
    • how to pick the center?
    • iterate?
    • optimize?

Quaternion Splines

  • Construction by SLERP
    • Bezier construction
    • Doesn’t work (not commutative)
  • do in log map space?
    • need to be careful about choice of “center”

Filtering Quaternions Curves

  • Jehee Lee and Sung Yong Shin, General Construction of Time-Domain Filters for Orientation Data, IEEE Transactions on Visualization and Computer Graphics, volume 8, number 2, 119-128, 2002.
    PDF (214K)
  • find the deltas between steps (q^-1 (j) * q(j+1))
  • log map those (since they are velocities)
  • center of filter is the zero point
  • filter of the log map of the deltas gives how to change the center point
  • needs a little bit of redesign to the filters

Human Motion

  • Levels of Abstraction
  • Skeletons vs. Rigid Segments vs. Joint Clouds vs. Point Clouds
  • more anatomical joints
  • degrees of freedom per joint

Issues in skeletal structures

  • Describing hierarchies with offsets
  • zero poses
  • T-Pose vs. Frankenstein vs. Dress Pose vs. …
  • ZXY Euler angles

Motion

  • Representations
  • Ways to create
    • Artistic
    • Pure Hack (a form of artistry)
    • From Example (a different form of artistry)
    • From Physics / Control / Principles
  • Usefulness of motions in different settings
    • Usefulness with different skeletons
    • Different environments
  • Re-Targeting

Conceptual Math

  • Latent spaces
  • Pose space vs. “natural pose space”
  • Motion space
  • Metrics for pose space / Metrics for motion space
    • a little off the ground (is far)
    • just distance only works in some cases (and close by)
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