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Linear Combinations of Upper Body Motion
Yu Huang, Beckman Inst., UIUC
1. Represented by the Displacement Eigenvectors.
1. Represented by the Displacement Eigenvectors.
=
=
(
) +
c1(
) +
c2(
) +
c3(
) +
c4(
) + ....
2. Add to the Mean Vector.
2. Add to the Mean Vector.
=
=
c1(
) +
c2(
) +
c3(
) +
c4(
) + ....
3. Illustration of Markers on the Upper Body.
3. Illustration of Markers on the Upper Body.
4. Illustration of Singular Value Spectrum.
4. Illustration of Singular Value Spectrum.
5. Add to the Mean Vector.
5. Add to the Mean Vector.
=
=
c1(
) +
c2(
) +
c3(
) +
c4(
) + ....
6. 3-D Illustration of the Mean Vector.
6. 3-D Illustration of the Mean Vector.
Notations: We attached 13 markers to the upper human body (3 on the head, 4 for each arm, 2 on the torso) 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 390 numbers (13 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 singular values. The principal eigenvectors will be useful to synthesize a movement or analysis the true movement in the video.
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