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

Parameterized 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 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

Outline 1.Finding example motions 2.Parameterizing blends 3.Results

Outline 1.Finding example motions 2.Parameterizing blends 3.Results

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

Related Work: Searching Time Series Databases (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 ≠ Numerically Similar!

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

Determining Numerical Similarity Segment 1 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: Intuitions Any subset of an optimal path is optimal. Optimal paths are redundant under endpoint perturbation. Motion 1 Motion 2

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

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

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 upputting back

Outline 1.Finding example motions 2.Parameterizing blends 3.Results

Natural Parameterizations parametersmotion 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 Weights blend weights blendparameters It is easy to map blend weights to parameters. But we want ! This has no closed-form representation.

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)

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

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.

Outline 1.Finding example motions 2.Parameterizing blends 3.Results

Results

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