1. Flexible Automatic Motion Blending with Registration Curves
Lucas Kovar
Michael Gleicher
University of Wisconsin-Madison

2. Motion Blending
Blending combines input motions according to time-varying weights.
Interpolation
Transitions
Continuous Control 1 1 1

3. Automatic Motion Blending
The success of blending depends on the information given about the input motions.
What if we’re 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)

4. Outline Overview Building Registration Curves
Blending with Registration Curves
Results

5. Outline Overview Building Registration Curves
Blending with Registration Curves
Results

6. What is a Registration Curve?
A data structure composed of three elements:
Timewarp Curve
Timing
Coordinate Frame (Root Blending)
Alignment Curve
Constraint Matches
Constraints

7. Registration Curves: Overview
“Straw man” algorithm: linear blending
ith blend frame combines ith frame of each input
Combine skeletal poses by averaging data values

8. Registration Curves: Overview

9. Outline Overview Building Registration Curves
Blending with Registration Curves
Results

10. Building a Registration Curve
A registration curve is composed of three elements, built in order:
Timewarp curve
Alignment curve
Constraint matches

11. Timewarp Curves Each point is a set of corresponding frames
Smooth and strictly increasing: a 1-1 mapping
Motion 2 Frame
Motion 1 Frame

12. 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

13. Dynamic Programming Details
Paths must be “reasonable”
valid
not strictly increasing
not continuous
degenerate
Can compute path incrementally for better efficiency

14. Fitting the Timewarp Curve
We now have discrete frame correspondenes.
Almost a timewarp curve, but not quite.
Solution: fit a strictly increasing spline

15. Building Timewarp Curves: More 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)

16. 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.

17. Frame Alignment: Example

18. 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.

19. Constraint Matches Each motion is labeled with constraints.
Constraint intervals
Motion 1
Motion 2
Motion 3
Goal: find sets of logically related constraints.

20. Finding Constraint Matches
Timewarp the constraint intervals
Group overlapping constraints, dropping or splitting constraints as needed

21. Outline Overview Building Registration Curves
Blending with Registration Curves
Results

22. 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

23. 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

24. Positioning and Orienting Frames
The alignment curve arranges frames into a coherent block that may be rigidly transformed.

25. Positioning and Orienting Frames
Each motion votes on a transformation based on the previous blend frame’s position/orientation + =
Intuitively, this is similar to blending root velocities relative to the local coordinate frame.

26. 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

27. 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.

28. Outline Overview Building Registration Curves
Blending with Registration Curves
Results

29. Results

30. 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)