**4. Discussion**

This article presents a methodology for task-specific uncertainty assessment of 3D point clouds based on ISO 15530-3 and ISO 15530-4 technical specifications and the application of MBD-based post-processing for the automatic processing of point clouds.

It presents an uncertainty budget comprising three main uncertainty contributors according to ISO 15530-3 technical specifications. The three major uncertainty contributors are (a) measurement process variability (*up*)*,* (b) uncertainty of the CMM calibration (*ucal)*, and (c) uncertainty of the systematic error (*ub*). The uncertainty associated with the material and manufacturing variations, *uw*, is considered negligible.

The methodology presented here suggests an automatic 3D point cloud measurement and evaluation process, where the statistical analysis of multiple GD&T results is based on an MBD-based approach. From these data, the standard uncertainty associated with the measurement process variability (*up*) is automatically obtained. The standard uncertainty associated with the uncertainty of the MMC calibration (*ucal*) is obtained using the ZEISS VCMM™ tool, which assesses a task-specific uncertainty value for every calibrated feature according to ISO 15530-4 technical specifications. Finally, the standard uncertainty associated with the systematic error of the measurement process (*ub*) is obtained from the difference between the average value obtained during the measurement process variability and the indicated value of the CMM during the dummy part calibration process.

The experimental results show that the systematic error contribution (*ub*) is the main contributor to the uncertainty budget. While the CMM calibration uncertainty (*ucal*) contributor average value falls within 1 μm and the measurement process variability (*up*) average

value is less than 10 μm, the systematic error (*ub*) average value falls within 50 μm. Thus, the CMM calibration uncertainty (*ucal*) becomes negligible, which means that the main contributors to the task-specific uncertainty budget are the measurement process variability (*up*) and systematic error contributor (*ub*).

In summary, a reliable task-specific uncertainty method is developed and successfully implemented. In the absence of numerical simulation models for optical systems, which are not currently available, this methodology allows for the establishment of an uncertainty budget to understand the order of magnitude of the measurement uncertainty of 3D optical systems.

One of the limitations of the presented methodology is scalability to large components, where CMM reference values are hardly achievable by calibrating the existing dummy part. Hence, this methodology could be applied to the scanning of geometric parts approximately up to 1.5 ÷ 2 m and manufactured in serial production, since this is the most common working range for many applications such as automotive or the manufacturing of metallic components.

Finally, concerning the MBD-based metrology data processing strategy, the experimental approach presented in this article demonstrates that the nominal PMI-based method is appropriate for converting dense point cloud data into desired dimensional metrology results (GD&Ts). It enables an effective data processing approach in terms of accuracy, speed, and robustness which in turn allows a fully automatic geometric point cloud evaluation process to avoid errors during the result interpretation and procurement processes.

Further work will focus on analysing the deviations between the results of the 3D optical system and the reference values obtained with CMM. Because these measuring technologies differ considerably in terms of accuracy, number, and point distribution, deviations will remain, but they would help to understand the complex intrinsic performance of 3D scanning systems. These preliminary results and accuracy assessment methods could support the development of AI-based numerical methods that describe the optical performance of 3D scanners.

Regarding the VCMM approach, this study demonstrates that simulation-based metrology should be applied for task-specific assessment of reference values. This shows the applicability of digital twins within the metrology field in terms of a priori uncertainty estimation and a posteriori uncertainty assessment. Thus, the measurement procedure can be optimised based on those digital twin simulation results. Another interesting future research line within the VCMM field is to employ the simulation-based metrology concept to create nominal dense reference point clouds with known uncertainty values. Therefore, fast uncertainty assessment procedures should be developed for dense point cloud data.

**Author Contributions:** U.M. contributed to the state-of-the-art and uncertainty budget realisation. G.K. contributed to the development of the methodology for uncertainty budget realisation. B.A. contributed to the information related to technical specifications and uncertainty budget realisation. S.G. contributed to experimental realisation. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was carried out under a research program called ELKARTEK 2021–2022. The project called PRECITEK (grant number KK-2021/00039) is supported by The Basque Business Development Agency.

**Informed Consent Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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