Generic face detection algorithms do not perform well in the mobile domain due to significant presence of occluded and partially visible faces. One promising technique to handle the challenge of partial faces is to design face detectors based on facial segments. In this paper two different approaches of facial segment-based face detection are discussed, namely, proposal-based detection and detection by end-to-end regression. Methods that follow the first approach rely on generating face proposals that contain facial segment information. The three detectors following this approach, namely Facial Segment-based Face Detector (FSFD), SegFace and DeepSegFace, discussed in this paper, perform binary classification on each proposal based on features learned from facial segments. The process of proposal generation, however, needs to be handled separately, which can be very time consuming, and is not truly necessary given the nature of the active authentication problem. Hence a novel algorithm, Deep Regression-based User Image Detector (DRUID) is proposed, which shifts from the classification to the regression paradigm, thus obviating the need for proposal generation. DRUID has an unique network architecture with customized loss functions, is trained using a relatively small amount of data by utilizing a novel data augmentation scheme and is fast since it outputs the bounding boxes of a face and its segments in a single pass. Being robust to occlusion by design, the facial segment-based face detection methods, especially DRUID show superior performance over other state-of-the-art face detectors in terms of precision-recall and ROC curve on two mobile face datasets.