From anomaly detection to open set recognition: Bridging the gap

•We introduce novel methods that approximate the class acceptance regions with compact hypersphere models for anomaly detection and open set recognition.•In contrast to the other deep hypersphere classifiers, we treat the hypersphere centers as learnable parameters and update them based on the changing deep feature representations.•We propose novel loss terms that are more robust to the noisy labels within the outlier exposure and background datasets.•The experimental results show that the proposed methods typically outperform other state-of-the-art methods.