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Non-linear optimization for non-rigid structure from motion recovery |
We use bundle adjustment to estimate the structure, motion and
deformation of our model by minimizing a meaningful geometric cost
function based on the BHB [1] non-rigid model:
The initialization of the minimization method is given by the factorization of the measurement matrix W with an approach essentially similar to the Brand method (See [2] for an accurate description and this page for a general introduction on factorization) |
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A video (avi,
10.3MB) shows the subject face performing rigid motion and a
set of face deformations. The video presents 2 views (front and
side) of the reconstructed face, the image point tracks used to
create the measurement matrix and 3 axes representing the object
relative orientation.
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The following plots
represent the parameters (configuration weights and rotation
angles) extracted with the factorization method used as
initialization for the non-linear optimization step. Note the
extremely noisy behavior of the parameters.
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The parameters behavior after the bundle adjustment optimization
are shown in the following
figure. The parameters values reflects the real deformation
and motion components of the non-rigid object.
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References on non-rigid factorization |
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[1] C. Bregler, A. Hertzmann, H.Biermann. Recovering Non-Rigid 3D Shape from Image Streams.
IEEE International Conference on Computer Vision and Pattern Recognition (CVPR), June 2000. [2] M. E. Brand. Morphable 3D Models from Video. IEEE Computer Vision and Pattern Recognition (CVPR), December 2001. |
| Updated Feb 2005 by Alessio Del Bue |