Motion Icon

Feng Liu

Advisor: Michael Gleicher

Computer Sciences Department

University of Wisconsin-Madison

Goal Motion Icon

Summarize a motion capture data into a single image

Application: motion database browsing

Solution Extract key frames

Pose clustering Extract key frames

Render key frames Re-position key frames Determine proper camera settings to

render them effectively

Feature dimension reduction Decomposing motion using Singular

Value Decomposition (SVD)

Select the q most significant singular values

Reconstruct new ‘motion’ M ‘

NNNTTTNT VSUM

qqqTqT SUM ''

qqS '

Only need 8~15/57 DOFs

to keep 90-95% singular values

Feature dimension reduction

first 3 new motion signals of M’Singular values from decomposing a walking motion using SVD

Pose clustering Unsupervised clustering method based

on Gaussian Mixture Models Estimate a GMM model for a motion using

Expectation-Maximization (EM) Initialize the clusters using the Gaussian

Mixture components Merge 2 closest clusters greedily until only 1

cluster is left Select the number of clusters with minimal

Rissanen cost

Rissanen cost A combination of fitting errors and the

number of clusters

)log()1)2

*)1(1((

2

1),|(log),( TN

NNNKKypKMDL y

fitting errors number of clusters

Clustering procedure

minimal cost with 4 clusters

Clustering examples

Extract key frames First frames of each cluster as key

frame

Shortest path from cluster graph containing all the clusters

First frame scheme

?

Shortest path scheme Shortest path from Cluster Graph

Containing all the clusters

C2 C0 C1

C3

Cluster graphC2 C0 C3 C1

Shortest path

Cluster sequence

Path-finding algorithm A variation of Hamiltonian path: NP-hard ! Greedy approximation

Construct cluster sequence Greedily shorten the cluster sequence

Find all sub-paths start and end with the same cluster, all the intermediate vertices exist in the other part

of the cluster sequence Select the shortest path, and reduce it

Eliminate redundant vertices at the beginning and the end of the path

Path-finding algorithm

C2 C0 C1 C0 C2 C0 C3 C1 C0 C2 C0 C3

C2 C0 C2 C0 C3 C1 C0 C2 C0 C3

C2 C0 C3 C1 C0 C2 C0 C3

C2 C0 C3 C1 C0 C3

C2 C0 C3 C1

Shortest path

Re-position key frames Along user-specified routes

Line Circle Grid ……

Lost motion trajectory info.

Re-position key frames Along the original motion trajectory

Scale the motion trajectory Evenly position the key frames

Proper camera setting selection Goal

Render key frames in a way with minimal key frame occlusion

At vector the center of the root trajectory

Up vector Interpolation btw [0 1 0] and the minor motion

axis Eye vector

Eye-At line perpendicular to the plane determined by the the Up vector and the major motion axis

Camera settings

Results

Motion icon

Walk containing 559 frames

Results

Motion icon

High-wire Walk containing 548 frames

Results

Motion icon

“Walk” containing 236 frames

Results

Motion icon

“Ballet” containing 1022 frames

Results

Motion icon

“Faint” containing 145 frames

More icons

Conclusion A complete framework for creating

motion icon SVD based feature reduction GMM based unsupervised pose clustering Cluster graph based key frame extraction Key frame reposition methods Motion trajectory based camera setting

determination

Thank You