**6. Conclusions**

Machine learning, especially deep learning, has made significant progress in many research areas and applications such as visual recognition, image classification and image processing, etc. However, to the best of our knowledge, no deep learning approaches have been successfully applied to RDH schemes which require images to be completely restored and secret information to be extracted. This motivates us to apply such approaches to RDH. In this paper, we propose a reversible data hiding scheme based on three-dimensional prediction-error histogram modification and MLP networks. We utilize a trained MLP neural network to predict pixel values and combining with PEE to achieve RDH. In addition, the proposed method of modifying the three-dimensional prediction-error histogram can better utilize the space in the three-dimensional coordinates for data embedding. Evaluation of the quality and embedding capacity of the stego-images shows that the proposed method still maintains a good PSNR and increases the maximum embedding capacity which is 1.9–9.8 times of previous methods. Nevertheless, the proposed method still has its disadvantages. Specifically, training the neural network and predicting pixels bit-by-bit are both time-consuming. Developing methods to enhance the efficiency of the proposed method, such as reducing the training time and predicting multiple bits at once, deserves to be further investigated in future works. Moreover, this work focused on proposing a novel reversible data hiding scheme which trains multilayer perceptrons by utilizing the correlation between image pixel values and their adjacent pixels so that the accurate pixel predictions can be achieved. There should be a trade-off between the performance and the fragility. For a future research direction, it is worthy to discuss the impact of fragility caused by transmission errors.

**Author Contributions:** Conceptualization, H.-C.W.; methodology, H.-C.W., C.-C.H. and C.-W.L.; software, C.-W.L.; validation, C.-C.H., C.-C.L., H.-C.W. and C.-W.L.; formal analysis, C.-C.L. and C.-W.L.; investigation, C.-C.L. and C.-W.L.; resources, H.-C.W.; data curation, C.-W.L.; writing— original draft preparation, C.-C.H. and C.-W.L.; writing—review and editing, C.-C.H. and C.-C.L.; supervision, H.-C.W.; project administration, H.-C.W.; funding acquisition, C.-C.H. and H.-C.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research is supported by the Taiwan Ministry of Science and Technology under gran<sup>t</sup> no. MOST 110-2221-E-005 -045, no. MOST 110-2222-E-032-002-MY2, and no. MOST 110-2221-E-167-002.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data is contained within the article.

**Conflicts of Interest:** The authors declare no conflicting interest regarding the publication of this work.
