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We present a method for recovering fast and robustly the 3D shape of inextensible and smooth surfaces from a monocular image. We propose a weighted iterative least squares approach to minimize the reprojection error between 2D-3D point correspondences preserving the 3D lengths. In addition, a local 3D smoothness constraint for each mesh vertex is proposed to increase the robustness to noisy correspondences and occluded or poorly represented facets. Moreover, the proposed method updates automatically the relevance of each constraint in order to maximize the smoothness and minimize the reprojection error. Experimental results shown that our approach obtains accurate results and is faster than state-of-the-art algorithms using similar constraints.