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This paper proposes a novel algorithm to reconstruct a 3D surface from a calibrated set of images. In a first pass, it uses Scale Invariant Features Transform (SIFT) descriptor correspondences to drive the deformation of a mesh toward the true object surface. We introduce a method to handle the fact that these local descriptors are computed at positions that are not projections of mesh vertices in the images. In order to avoid projective deformations due to the large windows of interest of this descriptor, correspondences are only computed between images from the same viewpoint. This is used in a first pass to recover large concavities of the object. In a second pass, a one dimensional Lucas-Kanade tracker is used to recover small scale details. Using publicly available benchmarks, our algorithm obtains high accuracy while being among the fastest ones.