1. Motion Graphs
Davey Krill
May 3, 2006

2. Overview: Project 2 MotionTestBed Framework
Motion Graph for 2 motion clips
Finding candidate transitions
Selecting transition points
Creating Transitions (linear blending)
Goal / Testing / Results
Project 3

3. Motion Framework
Skeleton contains all information about the motion clip
Frames indicate the orientation of joints and root position at that time
Joints are hierarchically related, defining their position relative to their parent joint and globally with the root joint
Poses can be adjusted with rigid transformations [quaternion rotation, (x,y,z) translation]

4. P2: Find Candidate Transitions
Goal: Find the distance between two frames
Method: Compute the minimal sum of squared distances between corresponding points within the point clouds of each frame pose
Compute this distance for every pair of frames in the motion set

5. P2: Select Transition Points
The 2D distance map can have several local minima
Need to select only those below a certain threshold
Good transitions vs. high graph connectivity trade-off
Finding ways to determine this threshold is one focus of Project 3
Sampled 2D error function
(Local minima are red dots)

6. P2: Creating Transitions
Align the second motion with the appropriate 2D transformation (the minimal Θ, x, z).
Create the transition frames between the ith frame of motion 1 and jth frame of motion 2. This is done by linearly blending the ith to ith+k-1 frames with the jth-k+1 to jth frames.
Use spherical linear interpolation on joint rotations, and linearly interpolate root positions

7. P2: Testing and Results
Goal of P2: Find transition points between two motions and generate linearly blended transitions at those points (i.e. create a 2-motion graph).
From this 2-motion graph, generate a new motion clip by manually selecting a single transition point.
Distance correctness: 2 identical motions, zero-diagonal on 2D distance function
Example: two kicking motions

8. P2: Two Kicking Motions
Empirically, any transition with a distance error <6.00 generated a “good” motion clip
Linear blending has been omitted to better illustrate the transition points
Clip72-47.bvh
Distance error of 5.11
Clip86-70.bvh
Distance error of 4.87
Clip bvh
Distance error of 31.66
Example of how linear blending wouldn’t help since the direction of momentum is different
Which brings us to…

9. Project 3 Full motion graph Transition point metrics
Handle arbitrary number of motions
Pruning the graph
Testing
Transition point metrics
Beyond point cloud matching
Evaluate physical state, momentum, footskate

10. P3: Full Motion Graph
Nodes are choice points connecting clips of motion
Arcs between nodes are clips of motion
Expands on 2-motion graph.
Each new motion added to the graph searches for transition points with the rest of the nodes, and creates new arcs appropriately.

11. P3: Pruning the Graph
Goal: Prune the graph such that it is possible to generate arbitrarily long streams of motion.
Remove any nodes with few or no outgoing edges.
How to handle transition points that are “close neighbors” yet still distinct local minima.
Example: (78, 57, 5.48) and (76, 51, 6.83) are very close transitions. How should these be handled? Eliminate one? Let both persist?

12. P3: Testing
Problem of generating arbitrary motion clips from the motion graph not generally addressed.
Testing by having advance knowledge of where the good transitions are and manually walking the graph.
In progress…

13. P3: Transition point metrics
Problem: Determining what local minima threshold to use when selecting transition points is somewhat of a hack.
As was seen from the earlier example, there are cases when using the point cloud distance is not a good enough metric for determining transition points.
Need to consider momentum, physical state (imagine a person jumping up and down)
Adaptive thresholds for:
Slow motions vs. fast motions
Familiar (walking) motions vs. strange motions
Context of motion determines whether you want a low or high threshold value

14. Work in Progress
Generate examples of an arbitrarily long motion graph walk
Develop better graph pruning
Evaluating threshold-finding techniques
Spacing out transition points
Adaptive threshold model

15. Questions?