Non-RigidShapeandMotionRecovery

Non-RigidShapeandMotionRecovery - where H satisfies:...

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
Non-Rigid Shape and Motion Recovery: Degenerate Deformations Jing Xiao and Takeo Kanade CVPR 2004
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Problem Addressed Ambiguity in non-rigid SFM if only Rotation Constraints used (ECCV 2004) SFM recovery in Degenerate Deformations
Background image of page 2
Basis Formulation for Non-Rigid Shape Shape at any time instant:
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 4
Degenerate cont’d First K3 triple columns of M correspond to non- degenerate basis and the rest to degenerate basis r j is a 3x1 eigen vector that corresponds to the degenerate basis shape Arises cause Bi (degenerate) can be factored as:
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Rotation Constraints Denote by Q i , 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
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 12
Background image of page 13
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: where H satisfies: Rotation cont is an arbitrary scalar and is a skew symmetric matrix The solution has degrees of freedom 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: Basis contd New constraints: Finally combining Rotation and Basis constraints: Constraints contd degrees of freedom and linear constraints. Therefore solution space has degrees of freedom. When N D is 0, there is a unique solution. Finding Qi If K2>0 then If K2=0, a unique solution exists using the constraints. Results Synthetic data: Results Real Data:...
View Full Document

Page1 / 13

Non-RigidShapeandMotionRecovery - where H satisfies:...

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online