## 4 Dataset Development
### Depth Map Standardization
Our dataset, which allows for network training on a diverse range of scenarios, will be made publicly available to support future work in this domain. Figure 7: The image panels here are organized the same as in Figure 6, with the latent space (**left**) visualized from the first and second components of t-SNE, and the images (**right**) corresponding to the selected points in the latent space. The difference is that Figure 6 was trained on the entire dataset, whereas here it is trained exclusively on the deformation data. It is clear that images positioned closer in the latent space share more similarities in reflection shape, while those farther apart are less similar, even though they belong to the same overall category of deformation surfaces. This emphasizes the network’s capability to capture underlying similarities despite variations in surface characteristics within the same category. Experimental results demonstrate that VUDNet achieves incredible reconstruction accuracy from single-shot 2D images, with an RMSE error one-fourth as large (or better) and at reduced computational complexity in comparison to competing state-of-the-art methods. The integration of both MSE and TV regularization terms in the loss function promotes spatial smoothness and reduces noise, leading to visually coherent depth maps. The findings of this study set a new standard for single-shot deflectometry, showcasing the potential of deep learning in advancing optical metrology for specular surfaces. In future work, we plan to explore the application of VUDNet to other forms of surface measurement and extend our approach to dynamic and real-time scenarios. Additionally, we aim to investigate the integration of more advanced generative models to further improve the robustness of depth estimation in diverse and complex environments. Conceptualization, M.S., S.M. and P.F. ; Formal analysis, M.S. ; Funding acquisition, C.P., A.M.D.L. and P.F. ; Methodology, M.S., S.M. and A.N. ; Project administration, P.F. ; Resources, C.P. and A.M.D.L. ; Software, M.S. ; Supervision, P.F. ; Validation, M.S. ; Visualization, M.S. ; Writing--original draft, M.S. ; Writing--review and editing, S.M., A.N., C.P., A.M.D.L. and P.F. All authors have read and agreed to the published version of the manuscript. This work is financially supported by the MITACS Accelerate program. Not applicable. The raw data supporting the conclusions of this article will be made available by the authors on request. The authors gratefully acknowledge the financial support of the MITACS Accelerate program. Authors [PERSON], [PERSON] were employed by the company General Fusion Inc. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. ## References

* [PERSON] and [PERSON] (2023)Semiconductor multilayer nanometrology with machine learning. Nanomanufacturing Metrol.2023 (6), pp. 15. External Links: Document Cited by: SS1. * [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON] (2024)3D Vision and Intelligent On-line Inspection in SMT Microelectronic Packaging: A Review. IEEE J. Emerg. Sel. Top. Ind. Electron.2024 (5), pp. 779-789. External Links: Document Cited by: SS1. * [PERSON] and [PERSON] (2024)Comparative analysis of devices working on optical and spintronic based principle. J. Opt.2024 (53), pp. 1629-1649. External Links: Document Cited by: SS1. * [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], et al. (2024)Surface color estimation in 3D spatial coordinate remote sensing by a technical vision system. Opt. Quantum Electron.2024 (56), pp. 406. External Links: Document Cited by: SS1. * [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON] (2024)Machine Learning-Based 3D Scan Coverage Prediction for Smart-Control Applications. Comput.-Aided Des.2024 (7), pp. 103775. External Links: Document Cited by: SS1.