Linear Combinations of Single Arm Motion

Yu Huang, Beckman Inst., UIUC

1. Represented by Displacement Eigenvectors.

=

(

) +

c1(

) +

c2(

) +

c3(

) +...

2. Add to the Mean Vector.

=

c1(

) +

c2(

) +

c3(

) +...

3. Illustration of Markers on the Right Arm.

4. Illustration of Singular Value Spectrum.

5. Add to the Mean Vector.

=

c1(

) +

c2(

) +

c3(

) +...

6. 3-D Illustration of the Mean Vector.

Notations: We attached 8 markers to the right arm for tracking by a commercial motion capture system (a six infrared-camera-system, Motion Analysis Corporation). Once the ground truth of 3-D position of each markers was captured, we started learning the motion model by PCA: : Sampling from original data, with the overlapped offset of 5 frames, we got 629 10-frame segments, each represented by 240 numbers (8 markers times 3 dimensions times 10 frames). After subtracting a mean vector we did SVD: X=USV', then columns of U are the basis functions (eigenvectors), diagonal elements of S are singluar values. The principal eigenvectors will be useful to synthesize a movement or analysis the true movement in the video.