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We present a novel algorithm aiming to estimate the 3D shape, the texture of a human face, along with the 3D pose and the light direction from a single photograph by recovering the parameters of a 3D Morphable Model. Generally, the algorithms tackling the problem of 3D shape estimation from image data use only the pixels intensity as input to drive the estimation process. This was previously achieved using either a simple model, such as the Lambertian reflectance model, leading to a linear fitting algorithm. Alternatively, this problem was addressed using a more precise model and minimizing a non-convex cost function with many local minima. One way to reduce the local minima problem is to use a stochastic optimization algorithm. However, the convergence properties (such as the radius of convergence) of such algorithms, are limited. Here, as well as the pixel intensity, we use various image features such as the edges or the location of the specular highlights. The 3D shape, texture and imaging parameters are then estimated by maximizing the posterior of the parameters given these image features. The overall cost function obtained is smoother and, hence, a stochastic optimization algorithm is not needed to avoid the local minima problem. This leads to the Multi-Features Fitting algorithm that has a wider radius of convergence and a higher level of precision. This is shown on some example photographs, and on a recognition experiment performed on the CMU-PIE image database.

In this article, we provide a detailed survey of 3D Morphable Face Models over the 20 years since they were first proposed. The challenges in building and applying these models, namely, capture, modeling, image formation, and image analysis, are still active research topics, and we review the state-of-the-art in each of these areas. We also look ahead, identifying unsolved challenges, proposing directions for future research, and highlighting the broad range of current and future applications.

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