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Two main classes of approaches have been studied to perform monocular nonrigid 3D reconstruction: Template-based methods and Non-rigid Structure from Motion techniques. While the first ones have been applied to reconstruct poorly-textured surfaces, they assume the availability of a 3D shape model prior to reconstruction. By contrast, the second ones do not require such a shape template, but, instead, rely on points being tracked throughout a video sequence, and are thus illsuited to handle poorly-textured surfaces. In this paper, we introduce a template-free approach to reconstructing a poorly-textured, deformable surface. To this end, we leverage surface isometry and formulate 3D reconstruction as the joint problem of non-rigid image registration and depth estimation. Our experiments demonstrate that our approach yields much more accurate 3D reconstructions than state-of-the-art techniques.