Automated Construction of Automated Construction of Parameterized MotionsParameterized Motions

Lucas KovarLucas Kovar

Michael GleicherMichael Gleicher

University of Wisconsin-MadisonUniversity of Wisconsin-Madison

Parameterized MotionParameterized Motion

(Wiley and Hahn ’97; Rose et al. ’98,’01; Park et al.’02)

Blend (interpolate) captured motions to make new ones

Map blend weights to motion features for intuitive control

Adapting Parameterized Motion Adapting Parameterized Motion to Large Data Setsto 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

OutlineOutline

1. Finding example motions

2. Parameterizing blends

3. Results

OutlineOutline

1. Finding example motions

2. Parameterizing blends

3. Results

Finding MotionsFinding Motions

Example motions are buried in longer motions.

Strategy: search for motion segments similar to a query.

ready stance punch dodge punch

Related Work: Searching Time Series Related Work: Searching Time Series DatabasesDatabases

• (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

Goal: find data segments (“matches”) whose distance to query is < ε.

Confuses unrelated motions with distinct variants

Logically Similar Logically Similar ≠ ≠ Numerically Similar!Numerically Similar!

Our Search StrategyOur Search Strategy

Find “close” matches and use as new queries.

Precompute potential matches to gain efficiency.

Determining Numerical SimilarityDetermining Numerical Similarity

Segment 1S

egm

ent 1

Segment 2

,Segment 2

Time alignment

Factor out timing with a time alignment (just as with registration curves).

Compare average distance between corresponding frames with threshold.

Precomputing Matches: IntuitionsPrecomputing Matches: Intuitions

Any subset of an optimal path is optimal.

Optimal paths are redundant under endpoint perturbation.

Mot

ion

1

Motion 2

Match WebsMatch Webs

Compute a grid of frame distances and find long, locally optimal paths.

Motion 2

Mot

ion

1

Represents all possibly similar segments.

Searching With Match WebsSearching With Match Webs

At run time, intersect queries with the match web to find matches.

Motion 2

Mot

ion

1

Search ResultsSearch 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

OutlineOutline

1. Finding example motions

2. Parameterizing blends

3. Results

Natural ParameterizationsNatural Parameterizations

parameters

pM )(g

motion

Blend weights offer a poor parameterization.

We need more natural parameters.

reaching

turning

jumping

hand position at apex

change in hip orientation

max height of center of mass

From Parameters to Blend WeightsFrom Parameters to Blend Weights

)(f 1 pw

pMMw )()f( 11 nnwwg blend weights blend parameters

It is easy to map blend weights to parameters.

But we want !

This has no closed-form representation.

Building ParameterizationsBuilding Parameterizations

Can approximate from samples with scattered data interpolation (Rose et al ’98).

)(f 1 p ),( ii wp

Accuracy: create blends to generate new samples.

(see also: Rose et al ’01)

SamplingSampling

Require sampled weights to be “nearly convex”:

1iw1i iw and for 0

0 15.0

Sample blend weights only for subsets of nearby motions.

Scattered Data InterpolationScattered 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.

)1(O

)(nO

OutlineOutline

1. Finding example motions

2. Parameterizing blends

3. Results

ResultsResults

DiscussionDiscussion

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