Automated Construction of Parameterized Motions

1. Automated Construction of Parameterized Motions Lucas Kovar Michael Gleicher University of Wisconsin-Madison

2. Parameterized Motion Blend (interpolate) captured motions to make new ones Map blend weights to motion features for intuitive control (Wiley and Hahn ’97; Rose et al. ’98,’01; Park et al.’02)

3. Adapting Parameterized Motion to Large Data Sets Previous work used manual blending methods on small, contrived data sets. We introduce automated tools that simplify working with larger, more general data sets • Automatically locate examples • Automatic blending (discussed previously) • Accurate, efficient, and “stable” parameterization Inputs: one example + feature of interest

4. Outline • Finding example motions • Parameterizing blends • Results

5. Outline • Finding example motions • Parameterizing blends • Results

6. Finding Motions Example motions are buried in longer motions. ready stance punch dodge punch Strategy: search for motion segments similar to a query.

7. Related Work: Searching Time Series Databases Goal: find data segments (“matches”) whose distance to query is < ε. • (Faloutsos et al. ’94): place low-dimensional approximation in spatial hierarchy • (Cardle et al. ’03, Liu et al. ’03; Keogh et al. ‘04): motion data Confuses unrelated motions with distinct variants

8. Logically Similar ≠ Numerically Similar!

9. Our Search Strategy Find “close” matches and use as new queries. Precompute potential matches to gain efficiency.

10. Determining Numerical Similarity Factor out timing with atime alignment (just as with registration curves). Time alignment Segment 1 , Segment 1 Segment 2 Segment 2 Compare average distance between corresponding frames with threshold.

11. Precomputing Matches: Intuitions Any subset of an optimal path is optimal. Motion 1 Motion 2 Optimal paths are redundant under endpoint perturbation.

12. Match Webs Compute a grid of frame distances and find long, locally optimal paths. Motion 1 Represents all possibly similar segments. Motion 2

13. Searching With Match Webs At run time, intersect queries with the match web to find matches. Motion 1 Motion 2

14. Search Results • 37,000 frame data set with ~10 kinds of motion. • 50 min. to create match web, 21MB on disk • All searches (up to 97 queries) in ≤ 0.5s • Manual verification of accuracy • Can not discern meaning of motions! picking up putting back

15. Outline • Finding example motions • Parameterizing blends • Results

16. Natural Parameterizations Blend weights offer a poor parameterization. We need more natural parameters. motion parameters reaching hand position at apex turning change in hip orientation jumping max height of center of mass

17. From Parameters to Blend Weights It is easy to map blend weights to parameters. blend weights blend parameters But we want ! This has no closed-form representation.

18. Building Parameterizations Can approximate from samples with scattered data interpolation (Rose et al ’98). Accuracy: create blends to generate new samples. (see also: Rose et al ’01)

19. Sampling Require sampled weights to be “nearly convex”: and for Sample blend weights only for subsets of nearby motions.

20. Scattered Data Interpolation Previous work uses an RBF interpolation method that does not constrain blend weights. • (Rose et al ’98,’01); (Park et al. ’02) K-nearest-neighbor interpolation is (almost) and ensures blend weights are nearly convex.

21. Outline • Finding example motions • Parameterizing blends • Results

22. Results

23. Discussion Parameterized motions make it easy to synthesize and edit motion. We want lots of them, so we need tools that simplify their construction • Automated extraction of examples • Efficient and accurate parameterization that respects boundaries implied by data