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.

The Kinship Face in the Wild data sets, recently published in TPAMI, are currently used as a benchmark for the evaluation of kinship verification algorithms. We recommend that these data sets are no longer used in kinship verification research unless there is a compelling reason that takes into account the nature of the images. We note that most of the image kinship pairs are cropped from the same photographs. Exploiting this cropping information, competitive but biased performance can be obtained using a simple scoring approach, taking only into account the nature of the image pairs rather than any features about kin information. To illustrate our motives, we provide classification results utilizing a simple scoring method based on the image similarity of both images of a kinship pair. Using simply the distance of the chrominance averages of the images in the Lab color space without any training or using any specific kin features, we achieve performance comparable to state-of-the-art methods. We provide the source code to prove the validity of our claims and ensure the repeatability of our experiments.