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Generative 3D face models are a powerful tool in computer vision. They provide pose and illumination invariance by modeling the space of 3D faces and the imaging process. The power of these models comes at the cost of an expensive and tedious construction process, which has led the community to focus on more easily constructed but less powerful models. With this paper we publish a generative 3D shape and texture model, the Basel face model (BFM), and demonstrate its application to several face recognition task. We improve on previous models by offering higher shape and texture accuracy due to a better scanning device and less correspondence artifacts due to an improved registration algorithm. The same 3D face model can be fit to 2D or 3D images acquired under different situations and with different sensors using an analysis by synthesis method. The resulting model parameters separate pose, lighting, imaging and identity parameters, which facilitates invariant face recognition across sensors and data sets by comparing only the identity parameters. We hope that the availability of this registered face model will spur research in generative models. Together with the model we publish a set of detailed recognition and reconstruction results on standard databases to allow complete algorithm comparisons.