Similarity metric learning for face verification using sigmoid decision function

In this paper, we consider the face verification problem, which is to determine whether two face images belong to the same subject or not. Although many research efforts have been focused on this problem, it still remains a challenging problem due to large intra-personal variations in imaging conditions, such as illumination, pose, expression, and occlusion. Our proposed method is based on the idea that we would like the similarity between positive pairs larger than negative pairs, and obtain a similarity estimation of two images. We construct our decision function by incorporating bilinear similarity and Mahalanobis distance to the sigmoid function. The constructed decision function makes our method discriminative for inter-personal differences and invariant to intra-personal variations such as pose/lighting/expression. What is more, our formulated objective function is convex, which guarantees global minimum. Our method belongs to nonlinear metric which is more robust to handle heterogeneous data than linear metric. We evaluate our proposed verification method on the challenging labeled faces in the wild (LFW) database. Experimental results demonstrate that the proposed method outperforms state-of-the-art methods such as Joint Bayesian under the unrestricted setting of LFW.