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A method for 3D shape reconstruction of deformable surfaces from consecutive frames was presented. In our method, the model of the surface is represented by a triangulated mesh. The constraints for the model, including keypoint correspondences and disallowing large changes of edge orientation between consecutive frames, are formulated as Linear Programming (LP) constraints. Therefore the deformable surface 3D tracking method turns into an LP problem that can be effectively solved. The robustness and efficiency of our approach are validated on synthetic and real data.