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Non-RigidShapeandMotionRecovery

# Non-RigidShapeandMotionRecovery - where H satisfies...

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

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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 Shape at any time instant:

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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
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:

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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

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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 cont’d 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:...
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Non-RigidShapeandMotionRecovery - where H satisfies...

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