## Optimal registration of 3D deformable models

2D-3D Non-rigid registration

Last November I presented a novel algorithm at ICIP 2009 in Egypt for registering 3D deformable models to images. This method was the result of the collaboration with João Xavier, Marko Stošić and Marija Dodig. We discovered an approach which can find the optimal solution for such problems using off the shelf convex optimization toolboxes. In such way we can solve for the following non-linear problem:
$\min_{R_i,l_{ik}} \left\| M_{i} - \left[l_{i1} R_i | \cdots | l_{iK} R_i \right] \right\|^2$
such that:
$R_i R_i^T = \left[ \begin{array}{cc} 1 & 0 \\ 0 & 1\end{array}\right]$
by forming a tight convex relaxation. The solution of the problem finds the camera parameters and the deformation coefficients given the 3D deformable model and the 2D image correspondences. This is one of the interesting hidden convex problem that it is possible to find when dealing with non-rigid Structure from Motion. More details can be found in our paper here:

• A. Del Bue, M. Stosic, M. Dodig, and J. Xavier, "2D-3D Registration Of Deformable Shapes With Manifold Projection," in International Conference on Image Processing (ICIP 2009), Cairo, Egypt, 2009.
@conference{DelBue:2009, title={2D-3D Registration Of Deformable Shapes With Manifold Projection},   author={A. {Del Bue} and M. Stosic and M. Dodig and J. Xavier},   booktitle = "International Conference on Image Processing (ICIP 2009), Cairo, Egypt", year={2009} }

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1. I want to study the face tracking, and I am glad to find your code page. thanks!