Efficient Tensor-Based 2D+3D Face Verification

We propose a novel approach for face verification by encoding 2D and 3D face images as a high order tensor. To perform tensor dimensionality reduction for both the unsupervised and supervised cases, we propose multilinear whitened principal component analysis (MWPCA) and tensor exponential discriminant analysis (TEDA), respectively. MWPCA is utilized to solve the small sample size problem in the high-dimensional space and to improve the discrimination power achieved by classical MPCA. In the supervised case, we extend multilinear discriminant analysis to TEDA in order to emphasize the discriminant data included in the null space of the within-class scatter matrix of each tensor's mode. Additionally, TEDA enlarges the margin between samples belonging to different classes via distance diffusion mappings. Our proposed approach can be seen as a novel data fusion method based on tensor representation. Indeed, the histograms of different local descriptors extracted from both 2D and 3D face modalities are combined through different tensor modes. The extensive experimental evaluation carried out on FRGC v2.0, Bosphorus, and CASIA 2D and 3D face databases indicates that the proposed approach performs significantly better than the state-of-the-art approaches.