1 / 13

Non-Rigid Shape and Motion Recovery: Degenerate Deformations

Non-Rigid Shape and Motion Recovery: Degenerate Deformations. Jing Xiao and Takeo Kanade CVPR 2004. Problem Addressed. Ambiguity in non-rigid SFM if only Rotation Constraints used (ECCV 2004) SFM recovery in Degenerate Deformations. Basis Formulation for Non-Rigid Shape.

saman
Download Presentation

Non-Rigid Shape and Motion Recovery: Degenerate Deformations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Non-Rigid Shape and Motion Recovery: Degenerate Deformations Jing Xiao and Takeo Kanade CVPR 2004

  2. Problem Addressed • Ambiguity in non-rigid SFM if only Rotation Constraints used (ECCV 2004) • SFM recovery in Degenerate Deformations

  3. Basis Formulation for Non-Rigid Shape • Shape at any time instant:

  4. With Degenerate Deformation • Of the K bases • K1 are rank 1 • K2 are rank 2 • K3 are rank 3 • Kd = K1 + 2xK2 + 3xK3 • W=MB is not a unique decomposition • Essentially the problem is to find G

  5. Degenerate cont’d • First K3 triple columns of M correspond to non-degenerate basis and the rest to degenerate basis • rj is a 3x1 eigen vector that corresponds to the degenerate basis shape • Arises cause Bi (degenerate) can be factored as:

  6. Rotation Constraints • Denote by Qi, we have: • Qi has unknowns, so given enough frames we can find a solution? • This is not true in general • Qi can be written as where H satisfies:

  7. Rotation cont • is an arbitrary scalar and is a skew symmetric matrix • The solution has degrees of freedom

  8. Basis Constraints • Ambiguity cause any non-singular transformation on the bases gives another valid set of bases. • To handle this choose the set of K3 frames that have smallest condition number (ECCV paper) • Denote the chosen frames as the first K3 frames • Coefficients will be:

  9. Basis contd • New constraints: • Finally combining Rotation and Basis constraints:

  10. Constraints cont’d • degrees of freedom and linear constraints. • Therefore solution space has degrees of freedom. • When ND is 0, there is a unique solution.

  11. Finding Qi • If K2>0 then • If K2=0, a unique solution exists using the constraints.

  12. Results • Synthetic data:

  13. Results • Real Data:

More Related