Finger-vein biometrics has been extensively investigated for personal verification. Despite recent advances in finger-vein verification, current solutions completely depend on domain knowledge and still lack the robustness to extract finger-vein features from raw images. This paper proposes a deep learning model to extract and recover vein features using limited a priori knowledge. First, based on a combination of the known state-of-the-art handcrafted finger-vein image segmentation techniques, we automatically identify two regions: a clear region with high separability between finger-vein patterns and background, and an ambiguous region with low separability between them. The first is associated with pixels on which all the above-mentioned segmentation techniques assign the same segmentation label (either foreground or background), while the second corresponds to all the remaining pixels. This scheme is used to automatically discard the ambiguous region and to label the pixels of the clear region as foreground or background. A training data set is constructed based on the patches centered on the labeled pixels. Second, a convolutional neural network (CNN) is trained on the resulting data set to predict the probability of each pixel of being foreground (i.e., vein pixel), given a patch centered on it. The CNN learns what a finger-vein pattern is by learning the difference between vein patterns and background ones. The pixels in any region of a test image can then be classified effectively. Third, we propose another new and original contribution by developing and investigating a fully convolutional network to recover missing finger-vein patterns in the segmented image. The experimental results on two public finger-vein databases show a significant improvement in terms of finger-vein verification accuracy