## 4 Accuracy Assessment  
Convenient and precise fitting of the implant is necessary for an aesthetic and functional mandibular restoration. The accuracy of the implant fitting is invaluable, especially when a defect is present on facial features, such as the mandible. The implant fitting is indeed dependent on the reconstructed area obtained via mirroring and cavity-filled techniques. The restoration of the defective  
Figure 8: Fused deposition modeling (FDM) machine (**a**) with built resected mandible model, and (**b**) with support structures.  
Figure 9: FDM-fabricated polymer models: cavity-filled reconstructed model (**right**), resected original model (**center**), and mirror reconstructed model (**left**) after support removal.  
area for implant design requires several phases from data acquisition to eventual fabrication. Certainly, errors can occur at each step, and the final accuracy is the sum of all errors at each stage. Therefore, accuracy assessment is mandatory to enhance the placement of the implant and the overall aesthetics of the facial anatomy.  
The accuracy evaluation in this investigation was based on a comparison between the resected and the reconstructed mandible models. This analysis was conducted in two steps, to validate and corroborate the findings. Firstly, the STL files of the resected and recovered mandibles were compared, and the polymer-based prototypes were examined in a subsequent stage to achieve a precise fitting of the implants. The goal of this step was, therefore, to estimate the accuracy or precision of the defect reconstruction methods in partially edentulous patients by superimposing 3D digital (STL) files, as well as physical prototypes. The overall workflow for accuracy evaluation is shown in Figure 10.  
For assessment based on physical prototypes, the FDM-produced mirroring and cavity-filled models, as well as the resected model, were scanned using the FARO arm laser scanner (Faro, Lake Mary, FL, USA), as shown in Figure 11. The obtained files were imported into the Geomagics Control 2014 software (3D Systems, Rock Hill, SC, USA) for analysis. For STL-based analysis, the STL files of mirroring, cavity-filled, and resected models were directly imported into the Geomagics Control software from MIMICS. To analyze the deviation (or accuracy), the STL files of the resected mandible were superimposed one by one on both mirror and cavity-filled mandibles via perfect matching using the best-fit algorithm. The resected model was set as a reference, while the mirrored and cavity-filled models were set as test models to facilitate the accuracy assessment.  
The following 3D deviations were measured for accuracy analysis using Geomagics Control: root-mean square (RMS) and average deviation (AD). The AD required estimating the variations in the inside and outward directions between the test and the reference files. The RMS (Equation (1)) determined the average error magnitude between both datasets or models. It also quantified the overall accuracy of the models. The two statistics were considered to ascertain and substantiate the results.  
\[\text{RMS}=\ \frac{1}{\sqrt{n}}\sqrt{\sum\
olimits_{i=1}^{n}(X_{1,j}-X_{2,j}) ^{2}}, \tag{1}\]  
Figure 10: Evaluation of an implant design reconstruction technique using a comparison approach.  
where \(X_{1,i}\) is the \(i\)-th digitized point in the reference dataset, \(X_{2,i}\) is the \(i\)-th digitized point in the test dataset, and \(n\) represents the number of digitized points. The units of measurement considered for the RMS and AD were mm.