Three-dimensional Face Reconstruction from a Single Image by a Coupled RBF Network

Reconstruction of a 3-D face model from a single 2-D face image is fundamentally important for face recognition and animation because the 3-D face model is invariant to changes of viewpoint, illumination, background clutter, and occlusions. Given a coupled training set that contains pairs of 2-D faces and the corresponding 3-D faces, we train a novel coupled radial basis function network (C-RBF) to recover the 3-D face model from a single 2-D face image. The C-RBF network explores: 1) the intrinsic representations of 3-D face models and those of 2-D face images; 2) mappings between a 3-D face model and its intrinsic representation; and 3) mappings between a 2-D face image and its intrinsic representation. Since a particular face can be reconstructed by its nearest neighbors, we can assume that the linear combination coefficients for a particular 2-D face image reconstruction are identical to those for the corresponding 3-D face model reconstruction. Therefore, we can reconstruct a 3-D face model by using a single 2-D face image based on the C-RBF network. Extensive experimental results on the BU3D database indicate the effectiveness of the proposed C-RBF network for recovering the 3-D face model from a single 2-D face image.