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Heterogeneous face recognition (HFR) aims at matching facial images acquired from different sensing modalities with mission-critical applications in forensics, security and commercial sectors. However, HFR presents more challenging issues than traditional face recognition because of the large intra-class variation among heterogeneous face images and the limited availability of training samples of cross-modality face image pairs. This paper proposes the novel Wasserstein convolutional neural network (WCNN) approach for learning invariant features between near-infrared (NIR) and visual (VIS) face images (i.e., NIR-VIS face recognition). The low-level layers of the WCNN are trained with widely available face images in the VIS spectrum, and the high-level layer is divided into three parts: the NIR layer, the VIS layer and the NIR-VIS shared layer. The first two layers aim at learning modality-specific features, and the NIR-VIS shared layer is designed to learn a modality-invariant feature subspace. The Wasserstein distance is introduced into the NIR-VIS shared layer to measure the dissimilarity between heterogeneous feature distributions. W-CNN learning is performed to minimize the Wasserstein distance between the NIR distribution and the VIS distribution for invariant deep feature representations of heterogeneous face images. To avoid the over-fitting problem on small-scale heterogeneous face data, a correlation prior is introduced on the fully-connected WCNN layers to reduce the size of the parameter space. This prior is implemented by a low-rank constraint in an end-to-end network. The joint formulation leads to an alternating minimization for deep feature representation at the training stage and an efficient computation for heterogeneous data at the testing stage. Extensive experiments using three challenging NIR-VIS face recognition databases demonstrate the superiority of the WCNN method over state-of-the-art methods.

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