State-of-the-art methods reconstruct three dimensional (3D) face shape from a single image either by fitting 3D face model to the input image or by warping to a reference shape. However, they are often difficult to apply in real-world applications due to expensive on-line optimization or to their unstable performance across poses and expressions. This letter approaches the 3D face reconstruction problem as a regression problem rather than a model fitting problem. Given an input face image along with annotated landmarks, a series of coarse-to-fine shape adjustments to the initial 3D face shape are computed through cascaded regressors based on the deviations between the input landmarks and the landmarks rendered from the reconstructed 3D faces. The cascaded regressors are off-line learned from a set of 3D faces and their corresponding 2D face images of various poses and expressions. By treating the landmarks that are invisible in large pose angles as missing data, the proposed method can handle arbitrary view face images in a unified way. Experiments on the BFM and BU3DFE databases demonstrate that the proposed method can reconstruct 3D faces more efficiently and more accurately than existing methods from 2D face images of arbitrary poses and expressions.
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