Flexible Automatic Motion Blending with Registration Curves

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Flexible Automatic Motion Blending with
Registration Curves

• Lucas Kovar
• Michael Gleicher
• University of Wisconsin-Madison

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Motion Blending

• Blending combines input motions according to
  time-varying weights.

Interpolation
Transitions
Continuous Control
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Automatic Motion Blending

• The success of blending depends on the
  information given about the input motions.

What if were not given any information?

• Registration Curves
• Encapsulate timing, coordinate frame, and
  constraint relationships
• Built automatically for arbitrarily many motions
  (compare with Rose et al. 98, Park et al. 02)

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Outline

1. Overview
2. Building Registration Curves
3. Blending with Registration Curves
4. Results

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Outline

1. Overview
2. Building Registration Curves
3. Blending with Registration Curves
4. Results

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What is a Registration Curve?

• A data structure composed of three elements

Timewarp Curve
Timing
Coordinate Frame (Root Blending)
Alignment Curve
Constraint Matches
Constraints
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Registration Curves Overview

• Straw man algorithm linear blending
• ith blend frame combines ith frame of each input
• Combine skeletal poses by averaging data values

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Registration Curves Overview
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Outline

1. Overview
2. Building Registration Curves
3. Blending with Registration Curves
4. Results

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Building a Registration Curve

• A registration curve is composed of three
  elements, built in order
• Timewarp curve
• Alignment curve
• Constraint matches

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Timewarp Curves

• Each point is a set of corresponding frames
• Smooth and strictly increasing a 1-1 mapping

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Building Timewarp Curves Two Motions

• Idea similar poses are more likely to correspond
• Use the same distance metric as before

Make grid of distances dynamic programming finds
minimal-cost path
Motion 2 frames
Motion 1 frames
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Dynamic Programming Details

• Paths must be reasonable

valid
not strictly increasing
not continuous
degenerate
Can compute path incrementally for better
efficiency
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Fitting the Timewarp Curve

• We now have discrete frame correspondenes.
• Almost a timewarp curve, but not quite.

Solution fit a strictly increasing spline
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Building Timewarp CurvesMore Than Two Motions

• Directly generalizing to more motions is costly.
• For k motions, dynamic timewarping is O(nk)

• Instead, create pairwise timewarp curves and
  merge into a single curve.
• O(k2)
• Storage is proportional to the number of input
  frames (not quadratic)

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Alignment Curves
Each point on the timewarp curve gives a set of
frames
The alignment curve gives transformations that
align these frames. Align bodies are centered
at the same point and face the same direction.
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Frame Alignment Example
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Building Alignment Curves

• Recall When computing the distance between two
  frames, we also found an aligning coordinate
  transformation.

Use these to build the alignment curve.
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Constraint Matches

• Each motion is labeled with constraints.

Constraint intervals
Motion 1
Motion 2
Motion 3
Goal find sets of logically related constraints.
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Finding Constraint Matches

• Timewarp the constraint intervals

Group overlapping constraints, dropping or
splitting constraints as needed
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Outline

1. Overview
2. Building Registration Curves
3. Blending with Registration Curves
4. Results

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Blending with Registration Curves

• To create a frame of a blend
• Select which input frames to combine
• Position and orient these frames
• Average skeletal parameters
• Determine constraints

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Choosing Frames to Combine
Blend frames are generated in order. For each, a
point is chosen on the timewarp curve.
Motion 2 Frame
Motion 1 Frame

• Each motion votes on how fast to travel
• Select speed so motion plays at natural rate
• Average votes based on blend weights

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Positioning and Orienting Frames

• The alignment curve arranges frames into a
  coherent block that may be rigidly transformed.

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Positioning and Orienting Frames

• Each motion votes on a transformation based on
  the previous blend frames position/orientation

Intuitively, this is similar to blending root
velocities relative to the local coordinate frame.
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Creating the Blend Frame

• 1. Merge skeleton poses
• Average skeletal parameters (averaging and
  normalizing quaternions works well in practice)

• 2. Find Constraints
• Average constraint intervals for each constraint
  match

Motion 2 frames
Motion 1 frames
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Results

• Building a registration curve for 18 motions (10s
  each 1800 frames total) took 3.3s.
• Storage is 1-2 of original data.
• Blends of 10 motions can be done at 1000fps.

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Outline

1. Overview
2. Building Registration Curves
3. Blending with Registration Curves
4. Results

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Results
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Discussion
Blending is a powerful and general method. It
usually works when motions are reasonably
similar, but no guarantees.

• Registration curves make it quick and easy to
  create and experiment with blends
• From original data to creating blends in a few
  seconds
• Essential for large data sets (see next topic)