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3--D detection and shape recovery of a non-rigid surface from video sequences require deformation models to effectively take advantage of potentially noisy image data. Here we introduce an approach to creating such models for deformable 3--D surfaces. We exploit the fact that the shape of an inextensible triangulated mesh can be parameterized in terms of a small subset of the angles between its facets. We use this set of angles to create a representative set of potential shapes, which we feed to a simple dimensionality reduction technique to produce low-dimensional 3--D deformation models. We show that these models can be used to accurately model a wide range of deforming 3--D surfaces from video sequences acquired under realistic conditions.