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Biometric authentication is popular in authentication systems, and gesture as a carrier of behavior characteristics has the advantages of being difficult to imitate and containing abundant information. This research aims to use three-dimensional (3D) depth information of gesture movement to perform authentication with less user effort. We propose an approach based on depth cameras, which satisfies three requirements: Can authenticate from a single, customized gesture; achieves high accuracy without an excessive number of gestures for training; and continues learning the gesture during use of the system. To satisfy these requirements respectively: We use a sparse autoencoder to memorize the single gesture; we employ data augmentation technology to solve the problem of insufficient data; and we use incremental learning technology for allowing the system to memorize the gesture incrementally over time. An experiment has been performed on different gestures in different user situations that demonstrates the accuracy of one-class classification (OCC), and proves the effectiveness and reliability of the approach. Gesture authentication based on 3D depth cameras could be achieved with reduced user effort. [ABSTRACT FROM AUTHOR]