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  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher-id">87</journal-id>
      <journal-id journal-id-type="index">urn:lsid:arphahub.com:pub:A116C711-4C18-5A38-8F1E-5E97753A8A64</journal-id>
      <journal-title-group>
        <journal-title xml:lang="en">Folia Medica</journal-title>
        <abbrev-journal-title xml:lang="en">FM</abbrev-journal-title>
      </journal-title-group>
      <issn pub-type="ppub">0204-8043</issn>
      <issn pub-type="epub">1314-2143</issn>
      <publisher>
        <publisher-name>Plovdiv Medical University</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.3897/folmed.68.e177266</article-id>
      <article-id pub-id-type="publisher-id">177266</article-id>
      <article-categories>
        <subj-group subj-group-type="heading">
          <subject>Research Article</subject>
        </subj-group>
        <subj-group subj-group-type="scientific_subject">
          <subject>Dental medicine</subject>
          <subject>Prosthetic dental medicine</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title>Role of prosthetic parameters for validating an AI designed crown</article-title>
      </title-group>
      <contrib-group content-type="authors">
        <contrib contrib-type="author" corresp="yes">
          <name name-style="western">
            <surname>Naydenov</surname>
            <given-names>Aleksandar V.</given-names>
          </name>
          <email xlink:type="simple">docnaidenov@gmail.com</email>
          <uri content-type="orcid">https://orcid.org/0009-0007-6055-9438</uri>
          <xref ref-type="aff" rid="A1">1</xref>
        </contrib>
        <contrib contrib-type="author" corresp="no">
          <name name-style="western">
            <surname>Uzunov</surname>
            <given-names>Todor T.</given-names>
          </name>
          <uri content-type="orcid">https://orcid.org/0000-0002-8714-2778</uri>
          <xref ref-type="aff" rid="A1">1</xref>
        </contrib>
        <contrib contrib-type="author" corresp="no">
          <name name-style="western">
            <surname>Kostadinov</surname>
            <given-names>Georgi</given-names>
          </name>
          <uri content-type="orcid">https://orcid.org/0000-0002-3465-8797</uri>
          <xref ref-type="aff" rid="A2">2</xref>
        </contrib>
      </contrib-group>
      <aff id="A1">
        <label>1</label>
        <addr-line content-type="verbatim">Faculty of Dental Medicine, Medical Univeristy of Sofia, Sofia, Bulgaria</addr-line>
        <institution>New Bulgarian University</institution>
        <addr-line content-type="city">Sofia</addr-line>
        <country>Bulgaria</country>
        <uri content-type="ror">https://ror.org/002qhr126</uri>
      </aff>
      <aff id="A2">
        <label>2</label>
        <addr-line content-type="verbatim">New Bulgarian University, Sofia, Bulgaria</addr-line>
        <institution>Faculty of Dental Medicine, Medical Univeristy of Sofia</institution>
        <addr-line content-type="city">Sofia</addr-line>
        <country>Bulgaria</country>
        <uri content-type="ror">https://ror.org/01n9zy652</uri>
      </aff>
      <author-notes>
        <fn fn-type="corresp">
          <p><bold>Corresponding author</bold>: Aleksandar Naydenov, Faculty of Dental Medicine, Medical Univeristy of Sofia, Sofia, Bulgaria; Email: <email xlink:type="simple">docnaidenov@gmail.com</email></p>
        </fn>
      </author-notes>
      <pub-date pub-type="collection">
        <year>2026</year>
      </pub-date>
      <pub-date pub-type="epub">
        <day>17</day>
        <month>06</month>
        <year>2026</year>
      </pub-date>
      <volume>68</volume>
      <issue>3</issue>
      <elocation-id>e177266</elocation-id>
      <uri content-type="arpha" xlink:href="http://openbiodiv.net/F6F2BD55-4F3B-5822-98FB-BD4B3966CD8A">F6F2BD55-4F3B-5822-98FB-BD4B3966CD8A</uri>
      <history>
        <date date-type="received">
          <day>06</day>
          <month>11</month>
          <year>2025</year>
        </date>
        <date date-type="accepted">
          <day>11</day>
          <month>02</month>
          <year>2026</year>
        </date>
      </history>
      <permissions>
        <copyright-statement>Aleksandar V. Naydenov, Todor T. Uzunov, Georgi Kostadinov</copyright-statement>
        <license license-type="creative-commons-attribution" xlink:href="http://creativecommons.org/licenses/by/4.0/" xlink:type="simple">
          <license-p>This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.</license-p>
        </license>
      </permissions>
      <abstract>
        <label>Abstract</label>
        <p><bold>Aim</bold>: To investigate the relationship between the angles describing the emergence profile of an implant crown and the metric data used to validate the digital design modeled via a 3D GAN.</p>
        <p><bold>Materials and methods</bold>: Twenty crowns were generated for the study using 3D GAN. Their validation metrics, including <abbrev xlink:title="intersection over union">IoU</abbrev> (intersection over union), F1 score, precision, and recall, were recorded. The initial voxelized files were processed with MeshMixer software, followed by the registration of longitudinal cuts using ExoCad software. CorelDRAW was used for outlining. Three angles were then measured for each examined surface—the mucosal emergence angle (<abbrev xlink:title="mucosal emergence angle">MEA</abbrev>), the deep emergence angle (<abbrev xlink:title="deep emergence angle">DA</abbrev>), and the total contour angle (<abbrev xlink:title="contour angle">CA</abbrev>)—resulting in a total of 240 measured angles.</p>
        <p><bold>Results</bold>: The mean values of the angles were <abbrev xlink:title="mucosal emergence angle">MEA</abbrev>=27.79°, <abbrev xlink:title="deep emergence angle">DA</abbrev>=56.70°, and <abbrev xlink:title="contour angle">CA</abbrev>=43.54°, with maximum values of 68.78°, 93.55°, and 83.01°, and minimum values of 0.01°, 27.51°, and 12.35°, respectively. The overall median <abbrev xlink:title="intersection over union">IoU</abbrev> was 0.835, while the median precision, recall, and F1 score were 0.946, 0.942, and 0.91, respectively, across the 20 teeth.</p>
        <p><bold>Conclusion</bold>: The validation of <abbrev xlink:title="artificial intelligence">AI</abbrev> must evolve to include clinical parameters beyond digital metrics. Visual parameters used to validate the design of implant crowns are not universal but rather supplementary measures for assessing the real clinical value of newly generated crowns. The present findings indicate that even in cases where the <abbrev xlink:title="intersection over union">IoU</abbrev>, precision, recall, and F1 scores are not perfect (&lt;1), clinically significant parameters such as <abbrev xlink:title="mucosal emergence angle">MEA</abbrev> can still demonstrate an excellent mean value (27.79°), which is a predictive factor for peri-implant tissue health.</p>
      </abstract>
      <kwd-group>
        <label>Keywords</label>
        <kwd>3D GAN</kwd>
        <kwd>artificial intelligence</kwd>
        <kwd>design</kwd>
        <kwd>implant</kwd>
        <kwd>validation</kwd>
      </kwd-group>
    </article-meta>
    <notes>
      <sec sec-type="Citation" id="sec1">
        <title>Citation</title>
        <p>Naydenov AV, Uzunov TT, Kostadinov G. Role of prosthetic parameters for validating an <abbrev xlink:title="artificial intelligence">AI</abbrev> designed crown. Folia Med (Plovdiv) 2026;68(3):е177266. <ext-link ext-link-type="doi" xlink:href="10.3897/folmed.68.e177266">doi: 10.3897/folmed.68.e177266</ext-link>.</p>
      </sec>
    </notes>
  </front>
  <body>
    <sec sec-type="Introduction" id="sec2">
      <title>Introduction</title>
      <p>The integration of artificial intelligence (<abbrev xlink:title="artificial intelligence">AI</abbrev>) into dental prosthetics has revolutionized the design and fabrication of implant-supported crowns, offering unprecedented precision and efficiency.<sup>[<xref ref-type="bibr" rid="B1">1</xref>]</sup> Among the most promising tools in this domain are three-dimensional generative adversarial neural networks (<abbrev xlink:title="three-dimensional generative adversarial neural networks">3D GANs</abbrev>)<sup>[<xref ref-type="bibr" rid="B2">2</xref>]</sup>, which enable the automated generation of complex 3D prosthetic structures based on extensive training datasets. These <abbrev xlink:title="artificial intelligence">AI</abbrev>-driven systems hold the potential to streamline workflows in prosthetic dental medicine, reducing human error and optimizing treatment timelines. However, the validation of these <abbrev xlink:title="artificial intelligence">AI</abbrev>-generated designs remains a critical challenge, as the success of a crown extends beyond its digital accuracy to its clinical performance in the human mouth. This raises an essential question: how do we assess the efficacy of <abbrev xlink:title="artificial intelligence">AI</abbrev>-designed crowns when traditional validation metrics may not fully capture their real-world applicability?</p>
      <p>In <abbrev xlink:title="artificial intelligence">AI</abbrev>-driven design, validation typically relies on quantitative metrics such as the intersection over union (<abbrev xlink:title="intersection over union">IoU</abbrev>) and F1 score, which measure the similarity between the generated 3D files and a predefined “ground truth”—a reference model used as training data and assumed to represent the ideal outcome. “Ground truth”<sup>[<xref ref-type="bibr" rid="B3">3</xref>]</sup> is usually a 3D model designed manually by a trained specialist with the aid of CAD software. The visual metrics evaluate how closely the neural network replicates the target design, with values approaching 1 indicating near-perfect alignment. Yet, the process of validating 3D-generated files in neural network assessments is inherently tied to this ground truth, which may not account for the variability inherent in clinical scenarios. For instance, a generated crown with a lower <abbrev xlink:title="intersection over union">IoU</abbrev> or F1 score—indicating deviation from the ground truth—might still yield a successful clinical outcome when applied in vivo. This discrepancy suggests that while these metrics are valuable for assessing algorithmic performance, they may not fully reflect the functional and aesthetic success of prosthetic restoration.</p>
      <p>The design of an implant crown involves multiple prosthetic parameters, such as those describing the emergence profile, which includes the contour of the crown<sup>[<xref ref-type="bibr" rid="B4">4</xref>]</sup>, and angles such as the mucosal emergence angle (<abbrev xlink:title="mucosal emergence angle">MEA</abbrev>), deep emergence angle (<abbrev xlink:title="deep emergence angle">DA</abbrev>), and total contour angle (<abbrev xlink:title="contour angle">CA</abbrev>). These parameters influence not only the crown’s fit and stability but also its biological integration and long-term prognosis.‌<sup>[<xref ref-type="bibr" rid="B5">5</xref>]</sup> In restoring a missing tooth, there is rarely a single “correct” design; rather, multiple configurations may achieve excellent clinical outcomes depending on patient-specific factors, such as occlusion, soft tissue architecture, and bone morphology. Thus, an <abbrev xlink:title="artificial intelligence">AI</abbrev> system such as <abbrev xlink:title="three-dimensional generative adversarial neural networks">3D GANs</abbrev>, trained to approximate a singular ground truth, might undervalue designs that deviate from this reference yet remain clinically viable. This highlights a key insight: the success of <abbrev xlink:title="artificial intelligence">AI</abbrev>-designed crowns may depend less on achieving perfect metric scores and more on how prosthetic parameters align with real-world functionality.</p>
    </sec>
    <sec sec-type="Aim" id="sec3">
      <title>Aim</title>
      <p>This research paper explores the role of prosthetic parameters in validating <abbrev xlink:title="artificial intelligence">AI</abbrev>-designed implant crowns, building on prior studies that correlate emergence angles with validation metrics. By examining how these parameters interact with neural network outputs, we aim to bridge the gap between digital precision and clinical efficacy. Our hypothesis posits that even crowns with suboptimal <abbrev xlink:title="intersection over union">IoU</abbrev> or F1 scores can achieve favorable outcomes in the human mouth if their prosthetic features meet critical clinical thresholds. This investigation seeks to redefine validation in <abbrev xlink:title="artificial intelligence">AI</abbrev>-driven prosthetics, emphasizing the synergy between computational design and practical application.</p>
    </sec>
    <sec sec-type="Materials" id="sec4">
      <title>Materials</title>
      <p>For the purposes of the study, a database of 200 training sets was created, each consisting of five 3D images, 20 of which were used as a control group. The 3D GAN developed and trained by G. Kostadinov and A. Naydenov was used to generate 20 screw-retained implant crowns replacing a missing tooth in position 36. The abutment used for all cases was Neodent GM.<sup>[<xref ref-type="bibr" rid="B6">6</xref>]</sup> The initial voxelized files of all 20 crowns were processed with the MeshMixer software, followed by the creation of medio-distal and vestibulo-lingual longitudinal cuts using the ExoCad software. For the emergence angle analysis, CorelDRAW was used. Grok, an artificial intelligence language model developed by xAI, was used to aid with the statistical calculations and graphics.</p>
    </sec>
    <sec sec-type="methods" id="sec5">
      <title>Methods</title>
      <p>This study comprised four sequential stages: first stage – refining the voxelized data; second stage – obtaining sectional views; third stage – outlining and measuring; fourth stage – analyzing the data.</p>
      <sec sec-type="Stage 1 – Generating and refining the voxelized data" id="sec6">
        <title>Stage 1 – Generating and refining the voxelized data</title>
        <p>The 3D GAN developed and trained by G. Kostadinov and A. Naydenov<sup>[<xref ref-type="bibr" rid="B6">6</xref>]</sup> was used to generate 20 screw-retained implant crowns replacing a missing tooth in position 36. The abutment used for all cases was Neodent GM. The initial output from the GAN consisted of rough, voxelized STL files. These files were uploaded into the MeshMixer™ software, and the following tuning operations were completed for all crowns: (1) smoothing scale adjusted to 4; (2) constraint rings adjusted to 3. After tuning, each crown was exported as an STL file for further processing <bold>(Fig. <xref ref-type="fig" rid="F1">1</xref>)</bold>.</p>
        <fig id="F1">
          <object-id content-type="arpha">F5C61CBE-E53C-56DA-9949-E2298E38789D</object-id>
          <label>Figure 1.</label>
          <caption>
            <p>The process of refining the raw GAN generated data in MeshMixer TM. <bold>A</bold>. The crown is still voxelized – raw data. <bold>B</bold>. Crown after selecting it and smoothing the outer surface by selecting the smoothing option with smoothing scale 4 and constraint rings 3. <bold>C</bold>. The surface that requires additional smoothing is highlighted in orange. The smoothing option was selected with smoothing scale 6 and constraint rings 1.</p>
          </caption>
          <graphic xlink:href="foliamedica-68-3-e177266-g001.jpg" id="oo_1682513.jpg">
            <uri content-type="original_file">https://binary.pensoft.net/fig/1682513</uri>
          </graphic>
        </fig>
      </sec>
      <sec sec-type="Stage 2 – Obtaining sectional view" id="sec7">
        <title>Stage 2 – Obtaining sectional view</title>
        <p>All 20 refined STL files were uploaded into the ExoCad™ software along with the digital models for the prosthetic field, e.g., adjacent teeth, gingival contour, and the abutment. After fitting the newly generated crown over the abutment, longitudinal cuts were obtained in two aspects—vestibulo-lingual and mesio-distal—and screenshots were taken for each. A total of 40 screenshots were saved <bold>(Fig. <xref ref-type="fig" rid="F2">2A</xref>, <xref ref-type="fig" rid="F2">2B</xref>)</bold>.</p>
        <fig id="F2">
          <object-id content-type="arpha">11A386F9-04BA-5849-ABB7-E05E061E8C34</object-id>
          <label>Figure 2.</label>
          <caption>
            <p><bold>A</bold> and <bold>B</bold> shows the crown STL file uploaded in ExoCad <sup>TM</sup> simultaneously with the prosthetic field e.g., part of the GAN training set. <bold>A</bold>. Four red dots are visible. One red dot per each side: vestibular, lingual, medial, distal. <bold>B</bold>. Longitudinal cut view was observed corresponding to the yellow lines of <bold>A</bold>. For each crown 2 longitudinal cuts view were screenshotted (vestibulo-lingual and mesiodistal). <bold>C</bold>. The screenshots were uploaded in CorelDRAW TM where outlining (with orange and red lines) was performed. Orange lines correspond to the axes of the abutment and the abutment collar. Red lines are drawn perpendicular to orange lines. Four yellow dots were drawn at the crown’s outer lines, and three different angles (<abbrev xlink:title="mucosal emergence angle">MEA</abbrev>, <abbrev xlink:title="deep emergence angle">DA</abbrev>, <abbrev xlink:title="contour angle">CA</abbrev>) were measured and visualized in green.</p>
          </caption>
          <graphic xlink:href="foliamedica-68-3-e177266-g002.jpg" id="oo_1682514.jpg">
            <uri content-type="original_file">https://binary.pensoft.net/fig/1682514</uri>
          </graphic>
        </fig>
      </sec>
      <sec sec-type="Stage 3 – Outlining and measuring" id="sec8">
        <title>Stage 3 – Outlining and measuring</title>
        <p>Each screenshot of the longitudinal cuts was imported into graphic software (CorelDRAW™). Outlining of the images was then performed. Two orange lines were drawn: a horizontal line corresponding to the platform of the abutment and a perpendicular line corresponding to the axis of the abutment. Red lines were drawn perpendicular to the orange lines to serve as hypotenuses for angle measurements. Four yellow dots (A, B, C, and D) were marked on all sides in the following positions: A – most coronal point of the soft tissue (mucosal margin); B – point of the prosthesis 0.5 mm apically to the mucosal margin (projected on the implant axis); C – point of the implant crown 1.5 mm apically to point A (projected on the implant axis); and D – point of the implant crown nearest to the implant platform. The positioning of these landmarks followed previously published clinical research.<sup>[<xref ref-type="bibr" rid="B7">7</xref>]</sup></p>
        <p>Using green lines, the following angles were measured and illustrated: (1) deep angle (<abbrev xlink:title="deep emergence angle">DA</abbrev>), defined as the angle of the abutment ascending directly from the implant platform and formed by the implant axis and the line connecting points D and C; (2) mucosal emergence angle (<abbrev xlink:title="mucosal emergence angle">MEA</abbrev>), defined as the angle of the prosthesis emerging through the soft tissue and formed by the implant axis and the line connecting points A and B; and (3) total contour angle (<abbrev xlink:title="contour angle">CA</abbrev>), defined as the angle of the overall contour of the prosthesis and formed by the implant axis and the line connecting points A and D <bold>(Figs <xref ref-type="fig" rid="F2">2C</xref>, <xref ref-type="fig" rid="F3">3</xref>)</bold>. All results were measured in degrees and listed in <bold>Table <xref ref-type="table" rid="T1">1</xref></bold>. A total of 240 angles were measured (20 crowns × 4 surfaces × 3 angles).</p>
        <fig id="F3">
          <object-id content-type="arpha">541AF8E7-C898-5C98-AF63-9D656F163A9A</object-id>
          <label>Figure 3.</label>
          <caption>
            <p>Outlining of the screenshots taken in ExoCad™ is performed with CorelDRAW™. The orange lines correspond to the axes of the abutment and abutment collar, which are perpendicular to each other. Red lines are drawn perpendicular to orange lines starting from the yellow dots, serving as tangents for measuring the angles. Yellow dots were positioned to correspond to the following: A – Most coronal point of soft tissue (mucosal margin), B – Point of prosthesis 0.5 mm apically of the mucosal margin (projected on the implant axis), C – Point of implant crown 1.5 mm apically of point A (projected on the implant axis); D – Point of implant crown nearest to the implant platform.</p>
          </caption>
          <graphic xlink:href="foliamedica-68-3-e177266-g003.jpg" id="oo_1682515.jpg">
            <uri content-type="original_file">https://binary.pensoft.net/fig/1682515</uri>
          </graphic>
        </fig>
        <table-wrap id="T1" position="float" orientation="portrait">
          <label>Table 1.</label>
          <caption>
            <p>Degrees for three angles (<abbrev xlink:title="mucosal emergence angle">MEA</abbrev>, <abbrev xlink:title="deep emergence angle">DA</abbrev>, <abbrev xlink:title="contour angle">CA</abbrev>) per each surface (Vestibular -V; Lingial/Palatinal – L; Medial – M; Distal – D) were measured and presented for 20 cases (crowns). <abbrev xlink:title="mucosal emergence angle">MEA</abbrev>: mucosal emergence angle, <abbrev xlink:title="deep emergence angle">DA</abbrev>: deep angle, <abbrev xlink:title="contour angle">CA</abbrev>: total contour angle</p>
          </caption>
          <table>
            <tbody>
              <tr>
                <td rowspan="2" colspan="1"><bold>S. Angle Crown No</bold>.</td>
                <td rowspan="1" colspan="3">
                  <bold>V</bold>
                </td>
                <td rowspan="1" colspan="3">
                  <bold>L</bold>
                </td>
                <td rowspan="1" colspan="3">
                  <bold>M</bold>
                </td>
                <td rowspan="1" colspan="3">
                  <bold>D</bold>
                </td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">
                  <bold>
                    <abbrev xlink:title="deep emergence angle">DA</abbrev>
                  </bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>
                    <abbrev xlink:title="mucosal emergence angle">MEA</abbrev>
                  </bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>
                    <abbrev xlink:title="contour angle">CA</abbrev>
                  </bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>
                    <abbrev xlink:title="deep emergence angle">DA</abbrev>
                  </bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>
                    <abbrev xlink:title="mucosal emergence angle">MEA</abbrev>
                  </bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>
                    <abbrev xlink:title="contour angle">CA</abbrev>
                  </bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>
                    <abbrev xlink:title="deep emergence angle">DA</abbrev>
                  </bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>
                    <abbrev xlink:title="mucosal emergence angle">MEA</abbrev>
                  </bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>
                    <abbrev xlink:title="contour angle">CA</abbrev>
                  </bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>
                    <abbrev xlink:title="deep emergence angle">DA</abbrev>
                  </bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>
                    <abbrev xlink:title="mucosal emergence angle">MEA</abbrev>
                  </bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>
                    <abbrev xlink:title="contour angle">CA</abbrev>
                  </bold>
                </td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">1</td>
                <td rowspan="1" colspan="1">66.69</td>
                <td rowspan="1" colspan="1">45.85</td>
                <td rowspan="1" colspan="1">56.94</td>
                <td rowspan="1" colspan="1">93.55</td>
                <td rowspan="1" colspan="1">57.69</td>
                <td rowspan="1" colspan="1">81.10</td>
                <td rowspan="1" colspan="1">64.61</td>
                <td rowspan="1" colspan="1">36.90</td>
                <td rowspan="1" colspan="1">12.35</td>
                <td rowspan="1" colspan="1">46.58</td>
                <td rowspan="1" colspan="1">32.16</td>
                <td rowspan="1" colspan="1">15.94</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">2</td>
                <td rowspan="1" colspan="1">32.26</td>
                <td rowspan="1" colspan="1">28.66</td>
                <td rowspan="1" colspan="1">46.76</td>
                <td rowspan="1" colspan="1">68.10</td>
                <td rowspan="1" colspan="1">62.30</td>
                <td rowspan="1" colspan="1">66.69</td>
                <td rowspan="1" colspan="1">42.94</td>
                <td rowspan="1" colspan="1">22.56</td>
                <td rowspan="1" colspan="1">30.79</td>
                <td rowspan="1" colspan="1">60.19</td>
                <td rowspan="1" colspan="1">14.69</td>
                <td rowspan="1" colspan="1">41.86</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">3</td>
                <td rowspan="1" colspan="1">83.01</td>
                <td rowspan="1" colspan="1">44.09</td>
                <td rowspan="1" colspan="1">83.01</td>
                <td rowspan="1" colspan="1">71.62</td>
                <td rowspan="1" colspan="1">44.69</td>
                <td rowspan="1" colspan="1">62.41</td>
                <td rowspan="1" colspan="1">67.93</td>
                <td rowspan="1" colspan="1">9.65</td>
                <td rowspan="1" colspan="1">48.04</td>
                <td rowspan="1" colspan="1">34.05</td>
                <td rowspan="1" colspan="1">7.32</td>
                <td rowspan="1" colspan="1">17.00</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">4</td>
                <td rowspan="1" colspan="1">60.85</td>
                <td rowspan="1" colspan="1">35.77</td>
                <td rowspan="1" colspan="1">56.07</td>
                <td rowspan="1" colspan="1">56.38</td>
                <td rowspan="1" colspan="1">34.95</td>
                <td rowspan="1" colspan="1">44.80</td>
                <td rowspan="1" colspan="1">51.94</td>
                <td rowspan="1" colspan="1">3.71</td>
                <td rowspan="1" colspan="1">28.74</td>
                <td rowspan="1" colspan="1">56.73</td>
                <td rowspan="1" colspan="1">26.78</td>
                <td rowspan="1" colspan="1">43.83</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">5</td>
                <td rowspan="1" colspan="1">71.60</td>
                <td rowspan="1" colspan="1">31.52</td>
                <td rowspan="1" colspan="1">58.69</td>
                <td rowspan="1" colspan="1">58.14</td>
                <td rowspan="1" colspan="1">36.01</td>
                <td rowspan="1" colspan="1">47.77</td>
                <td rowspan="1" colspan="1">52.04</td>
                <td rowspan="1" colspan="1">17.37</td>
                <td rowspan="1" colspan="1">35.57</td>
                <td rowspan="1" colspan="1">47.04</td>
                <td rowspan="1" colspan="1">19.97</td>
                <td rowspan="1" colspan="1">36.97</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">6</td>
                <td rowspan="1" colspan="1">58.73</td>
                <td rowspan="1" colspan="1">39.27</td>
                <td rowspan="1" colspan="1">53.58</td>
                <td rowspan="1" colspan="1">49.22</td>
                <td rowspan="1" colspan="1">28.07</td>
                <td rowspan="1" colspan="1">40.86</td>
                <td rowspan="1" colspan="1">49.39</td>
                <td rowspan="1" colspan="1">16.11</td>
                <td rowspan="1" colspan="1">36.10</td>
                <td rowspan="1" colspan="1">52.14</td>
                <td rowspan="1" colspan="1">21.40</td>
                <td rowspan="1" colspan="1">40.90</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">7</td>
                <td rowspan="1" colspan="1">54.35</td>
                <td rowspan="1" colspan="1">37.97</td>
                <td rowspan="1" colspan="1">59.77</td>
                <td rowspan="1" colspan="1">54.25</td>
                <td rowspan="1" colspan="1">30.36</td>
                <td rowspan="1" colspan="1">47.29</td>
                <td rowspan="1" colspan="1">43.60</td>
                <td rowspan="1" colspan="1">37.53</td>
                <td rowspan="1" colspan="1">30.53</td>
                <td rowspan="1" colspan="1">50.20</td>
                <td rowspan="1" colspan="1">00.00</td>
                <td rowspan="1" colspan="1">22.77</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">8</td>
                <td rowspan="1" colspan="1">76.59</td>
                <td rowspan="1" colspan="1">48.77</td>
                <td rowspan="1" colspan="1">68.15</td>
                <td rowspan="1" colspan="1">64.58</td>
                <td rowspan="1" colspan="1">20.39</td>
                <td rowspan="1" colspan="1">50.25</td>
                <td rowspan="1" colspan="1">70.68</td>
                <td rowspan="1" colspan="1">15.39</td>
                <td rowspan="1" colspan="1">48.24</td>
                <td rowspan="1" colspan="1">58.75</td>
                <td rowspan="1" colspan="1">16.92</td>
                <td rowspan="1" colspan="1">39.12</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">9</td>
                <td rowspan="1" colspan="1">61.66</td>
                <td rowspan="1" colspan="1">53.73</td>
                <td rowspan="1" colspan="1">59.32</td>
                <td rowspan="1" colspan="1">55.87</td>
                <td rowspan="1" colspan="1">24.50</td>
                <td rowspan="1" colspan="1">46.08</td>
                <td rowspan="1" colspan="1">51.13</td>
                <td rowspan="1" colspan="1">3.83</td>
                <td rowspan="1" colspan="1">24.18</td>
                <td rowspan="1" colspan="1">46.22</td>
                <td rowspan="1" colspan="1">12.70</td>
                <td rowspan="1" colspan="1">38.08</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">10</td>
                <td rowspan="1" colspan="1">59.72</td>
                <td rowspan="1" colspan="1">22.50</td>
                <td rowspan="1" colspan="1">47.69</td>
                <td rowspan="1" colspan="1">69.79</td>
                <td rowspan="1" colspan="1">44.74</td>
                <td rowspan="1" colspan="1">64.70</td>
                <td rowspan="1" colspan="1">49.75</td>
                <td rowspan="1" colspan="1">24.10</td>
                <td rowspan="1" colspan="1">36.05</td>
                <td rowspan="1" colspan="1">57.59</td>
                <td rowspan="1" colspan="1">10.51</td>
                <td rowspan="1" colspan="1">31.47</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">11</td>
                <td rowspan="1" colspan="1">70.92</td>
                <td rowspan="1" colspan="1">2.41</td>
                <td rowspan="1" colspan="1">35.00</td>
                <td rowspan="1" colspan="1">76.04</td>
                <td rowspan="1" colspan="1">68.78</td>
                <td rowspan="1" colspan="1">73.17</td>
                <td rowspan="1" colspan="1">63.83</td>
                <td rowspan="1" colspan="1">17.06</td>
                <td rowspan="1" colspan="1">39.63</td>
                <td rowspan="1" colspan="1">80.63</td>
                <td rowspan="1" colspan="1">52.80</td>
                <td rowspan="1" colspan="1">72.75</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">12</td>
                <td rowspan="1" colspan="1">56.27</td>
                <td rowspan="1" colspan="1">44.14</td>
                <td rowspan="1" colspan="1">52.82</td>
                <td rowspan="1" colspan="1">55.14</td>
                <td rowspan="1" colspan="1">34.13</td>
                <td rowspan="1" colspan="1">48.36</td>
                <td rowspan="1" colspan="1">40.72</td>
                <td rowspan="1" colspan="1">11.09</td>
                <td rowspan="1" colspan="1">32.77</td>
                <td rowspan="1" colspan="1">54.56</td>
                <td rowspan="1" colspan="1">29.80</td>
                <td rowspan="1" colspan="1">41.52</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">13</td>
                <td rowspan="1" colspan="1">78.94</td>
                <td rowspan="1" colspan="1">27.42</td>
                <td rowspan="1" colspan="1">60.26</td>
                <td rowspan="1" colspan="1">62.08</td>
                <td rowspan="1" colspan="1">19.70</td>
                <td rowspan="1" colspan="1">43.25</td>
                <td rowspan="1" colspan="1">63.60</td>
                <td rowspan="1" colspan="1">3.25</td>
                <td rowspan="1" colspan="1">36.66</td>
                <td rowspan="1" colspan="1">55.44</td>
                <td rowspan="1" colspan="1">4.98</td>
                <td rowspan="1" colspan="1">32.08</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">14</td>
                <td rowspan="1" colspan="1">56.66</td>
                <td rowspan="1" colspan="1">27.61</td>
                <td rowspan="1" colspan="1">47.55</td>
                <td rowspan="1" colspan="1">63.44</td>
                <td rowspan="1" colspan="1">52.65</td>
                <td rowspan="1" colspan="1">61.10</td>
                <td rowspan="1" colspan="1">47.83</td>
                <td rowspan="1" colspan="1">28.09</td>
                <td rowspan="1" colspan="1">41.47</td>
                <td rowspan="1" colspan="1">47.28</td>
                <td rowspan="1" colspan="1">13.58</td>
                <td rowspan="1" colspan="1">29.59</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">15</td>
                <td rowspan="1" colspan="1">72.20</td>
                <td rowspan="1" colspan="1">47.90</td>
                <td rowspan="1" colspan="1">63.50</td>
                <td rowspan="1" colspan="1">63.28</td>
                <td rowspan="1" colspan="1">41.25</td>
                <td rowspan="1" colspan="1">53.86</td>
                <td rowspan="1" colspan="1">65.19</td>
                <td rowspan="1" colspan="1">30.20</td>
                <td rowspan="1" colspan="1">52.44</td>
                <td rowspan="1" colspan="1">58.26</td>
                <td rowspan="1" colspan="1">10.90</td>
                <td rowspan="1" colspan="1">30.86</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">16</td>
                <td rowspan="1" colspan="1">51.65</td>
                <td rowspan="1" colspan="1">2.88</td>
                <td rowspan="1" colspan="1">28.49</td>
                <td rowspan="1" colspan="1">52.08</td>
                <td rowspan="1" colspan="1">12.03</td>
                <td rowspan="1" colspan="1">30.36</td>
                <td rowspan="1" colspan="1">61.44</td>
                <td rowspan="1" colspan="1">19.22</td>
                <td rowspan="1" colspan="1">43.94</td>
                <td rowspan="1" colspan="1">56.87</td>
                <td rowspan="1" colspan="1">52.01</td>
                <td rowspan="1" colspan="1">66.82</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">17</td>
                <td rowspan="1" colspan="1">32.79</td>
                <td rowspan="1" colspan="1">32.79</td>
                <td rowspan="1" colspan="1">42.41</td>
                <td rowspan="1" colspan="1">59.76</td>
                <td rowspan="1" colspan="1">44.27</td>
                <td rowspan="1" colspan="1">54.94</td>
                <td rowspan="1" colspan="1">46.34</td>
                <td rowspan="1" colspan="1">1.76</td>
                <td rowspan="1" colspan="1">28.87</td>
                <td rowspan="1" colspan="1">50.23</td>
                <td rowspan="1" colspan="1">2.75</td>
                <td rowspan="1" colspan="1">32.43</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">18</td>
                <td rowspan="1" colspan="1">34.50</td>
                <td rowspan="1" colspan="1">33.23</td>
                <td rowspan="1" colspan="1">26.50</td>
                <td rowspan="1" colspan="1">31.67</td>
                <td rowspan="1" colspan="1">27.10</td>
                <td rowspan="1" colspan="1">26.87</td>
                <td rowspan="1" colspan="1">56.87</td>
                <td rowspan="1" colspan="1">63.81</td>
                <td rowspan="1" colspan="1">76.98</td>
                <td rowspan="1" colspan="1">27.51</td>
                <td rowspan="1" colspan="1">39.23</td>
                <td rowspan="1" colspan="1">26.72</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">19</td>
                <td rowspan="1" colspan="1">55.25</td>
                <td rowspan="1" colspan="1">24.24</td>
                <td rowspan="1" colspan="1">45.13</td>
                <td rowspan="1" colspan="1">69.07</td>
                <td rowspan="1" colspan="1">33.90</td>
                <td rowspan="1" colspan="1">57.54</td>
                <td rowspan="1" colspan="1">48.09</td>
                <td rowspan="1" colspan="1">8.05</td>
                <td rowspan="1" colspan="1">21.15</td>
                <td rowspan="1" colspan="1">45.22</td>
                <td rowspan="1" colspan="1">27.96</td>
                <td rowspan="1" colspan="1">38.61</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">20</td>
                <td rowspan="1" colspan="1">57.06</td>
                <td rowspan="1" colspan="1">40.48</td>
                <td rowspan="1" colspan="1">52.04</td>
                <td rowspan="1" colspan="1">61.13</td>
                <td rowspan="1" colspan="1">42.83</td>
                <td rowspan="1" colspan="1">52.50</td>
                <td rowspan="1" colspan="1">45.06</td>
                <td rowspan="1" colspan="1">2.10</td>
                <td rowspan="1" colspan="1">29.47</td>
                <td rowspan="1" colspan="1">46.39</td>
                <td rowspan="1" colspan="1">13.82</td>
                <td rowspan="1" colspan="1">33.18</td>
              </tr>
            </tbody>
          </table>
        </table-wrap>
        <p>For visual segmentation, the intersection over union (<abbrev xlink:title="intersection over union">IoU</abbrev>) and F1 score were computed for all 20 crowns. Each generated crown was superimposed on a crown designed freehand by a dental specialist in ExoCad™ software for the same prosthetic field, also referred to as the ground truth <bold>(Fig. <xref ref-type="fig" rid="F4">4</xref>)</bold>. This yielded 20 <abbrev xlink:title="intersection over union">IoU</abbrev> values and 20 F1 scores (40 scores in total), which are presented in <bold>Table <xref ref-type="table" rid="T2">2</xref></bold>.</p>
        <table-wrap id="T2" position="float" orientation="portrait">
          <label>Table 2.</label>
          <caption>
            <p>The results for two different visual metrics are shown in the table: <abbrev xlink:title="intersection over union">IoU</abbrev> and F1 score. Results for these metrics were obtained via the tool that we developed and visualized in <bold>Fig. <xref ref-type="fig" rid="F4">4</xref></bold></p>
          </caption>
          <table>
            <tbody>
              <tr>
                <td rowspan="1" colspan="1"><bold>Visual Metrics Crown No</bold>.</td>
                <td rowspan="1" colspan="1">
                  <bold>IOU</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>F1 Score</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>Precision</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>Recall</bold>
                </td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">1</td>
                <td rowspan="1" colspan="1">0.80</td>
                <td rowspan="1" colspan="1">0.89</td>
                <td rowspan="1" colspan="1">0.97</td>
                <td rowspan="1" colspan="1">0.82</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">2</td>
                <td rowspan="1" colspan="1">0.81</td>
                <td rowspan="1" colspan="1">0.89</td>
                <td rowspan="1" colspan="1">0.87</td>
                <td rowspan="1" colspan="1">0.92</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">3</td>
                <td rowspan="1" colspan="1">0.85</td>
                <td rowspan="1" colspan="1">0.92</td>
                <td rowspan="1" colspan="1">0.93</td>
                <td rowspan="1" colspan="1">0.92</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">4</td>
                <td rowspan="1" colspan="1">0.80</td>
                <td rowspan="1" colspan="1">0.89</td>
                <td rowspan="1" colspan="1">0.98</td>
                <td rowspan="1" colspan="1">0.82</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">5</td>
                <td rowspan="1" colspan="1">0.77</td>
                <td rowspan="1" colspan="1">0.87</td>
                <td rowspan="1" colspan="1">0.97</td>
                <td rowspan="1" colspan="1">0.79</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">6</td>
                <td rowspan="1" colspan="1">0.86</td>
                <td rowspan="1" colspan="1">0.93</td>
                <td rowspan="1" colspan="1">0.95</td>
                <td rowspan="1" colspan="1">0.91</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">7</td>
                <td rowspan="1" colspan="1">0.86</td>
                <td rowspan="1" colspan="1">0.92</td>
                <td rowspan="1" colspan="1">0.96</td>
                <td rowspan="1" colspan="1">0.89</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">8</td>
                <td rowspan="1" colspan="1">0.84</td>
                <td rowspan="1" colspan="1">0.91</td>
                <td rowspan="1" colspan="1">0.88</td>
                <td rowspan="1" colspan="1">0.96</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">9</td>
                <td rowspan="1" colspan="1">0.89</td>
                <td rowspan="1" colspan="1">0.94</td>
                <td rowspan="1" colspan="1">0.91</td>
                <td rowspan="1" colspan="1">0.98</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">10</td>
                <td rowspan="1" colspan="1">0.80</td>
                <td rowspan="1" colspan="1">0.91</td>
                <td rowspan="1" colspan="1">0.82</td>
                <td rowspan="1" colspan="1">0.97</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">11</td>
                <td rowspan="1" colspan="1">0.81</td>
                <td rowspan="1" colspan="1">0.90</td>
                <td rowspan="1" colspan="1">0.96</td>
                <td rowspan="1" colspan="1">0.84</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">12</td>
                <td rowspan="1" colspan="1">0.84</td>
                <td rowspan="1" colspan="1">0.91</td>
                <td rowspan="1" colspan="1">0.92</td>
                <td rowspan="1" colspan="1">0.90</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">13</td>
                <td rowspan="1" colspan="1">0.90</td>
                <td rowspan="1" colspan="1">0.95</td>
                <td rowspan="1" colspan="1">0.96</td>
                <td rowspan="1" colspan="1">0.93</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">14</td>
                <td rowspan="1" colspan="1">0.90</td>
                <td rowspan="1" colspan="1">0.95</td>
                <td rowspan="1" colspan="1">0.94</td>
                <td rowspan="1" colspan="1">0.95</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">15</td>
                <td rowspan="1" colspan="1">0.79</td>
                <td rowspan="1" colspan="1">0.89</td>
                <td rowspan="1" colspan="1">0.83</td>
                <td rowspan="1" colspan="1">0.96</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">16</td>
                <td rowspan="1" colspan="1">0.86</td>
                <td rowspan="1" colspan="1">0.93</td>
                <td rowspan="1" colspan="1">0.97</td>
                <td rowspan="1" colspan="1">0.89</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">17</td>
                <td rowspan="1" colspan="1">0.85</td>
                <td rowspan="1" colspan="1">0.92</td>
                <td rowspan="1" colspan="1">0.95</td>
                <td rowspan="1" colspan="1">0.89</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">18</td>
                <td rowspan="1" colspan="1">0.79</td>
                <td rowspan="1" colspan="1">0.88</td>
                <td rowspan="1" colspan="1">0.97</td>
                <td rowspan="1" colspan="1">0.85</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">19</td>
                <td rowspan="1" colspan="1">0.83</td>
                <td rowspan="1" colspan="1">0.90</td>
                <td rowspan="1" colspan="1">0.85</td>
                <td rowspan="1" colspan="1">0.92</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">20</td>
                <td rowspan="1" colspan="1">0.79</td>
                <td rowspan="1" colspan="1">0.88</td>
                <td rowspan="1" colspan="1">0.83</td>
                <td rowspan="1" colspan="1">0.94</td>
              </tr>
            </tbody>
          </table>
        </table-wrap>
        <fig id="F4">
          <object-id content-type="arpha">D104B45D-EB51-5A64-B4F3-B28D346257C3</object-id>
          <label>Figure 4.</label>
          <caption>
            <p>Voxelized data used for training the GAN (prosthetic field – adjacent teeth, abutment and gingiva all shown in blue color ; modeled by a specialist crown in green color) and the newly generated by the GAN crown in red color, all are superimposed in online- based software to measure the following visual metrics: <abbrev xlink:title="intersection over union">IoU</abbrev>, F1 score, Precision and Recall (results for which are visible in the box above every single superimposition. <bold>A</bold> – Newly generated crown and prosthetic field are visible; <bold>B</bold> – Prosthetic field is visible; <bold>C</bold> – Crown modeled by a specialist and the prosthetic field are visible; <bold>D</bold> – Prosthetic field, newly generated crown, and the crown modeled by a specialist are visible.</p>
          </caption>
          <graphic xlink:href="foliamedica-68-3-e177266-g004.jpg" id="oo_1682516.jpg">
            <uri content-type="original_file">https://binary.pensoft.net/fig/1682516</uri>
          </graphic>
        </fig>
      </sec>
      <sec sec-type="Stage 4 – Data Analysis" id="sec9">
        <title>Stage 4 – Data Analysis</title>
        <sec sec-type="Calculation of median results for angular measurements (Figs 5, 6, 7)" id="sec10">
          <title><italic>Calculation of median results for angular measurements (Figs <xref ref-type="fig" rid="F5">5</xref>, <xref ref-type="fig" rid="F6">6</xref>, <xref ref-type="fig" rid="F7">7</xref>)</italic>.</title>
          <p>To summarize the angular measurements, median values were computed for <abbrev xlink:title="mucosal emergence angle">MEA</abbrev>, <abbrev xlink:title="deep emergence angle">DA</abbrev>, and <abbrev xlink:title="contour angle">CA</abbrev> across all 240 measurements per angle. For each angle, the 240 values (20 crowns ×4 surfaces × 3 angles ) were sorted in ascending order. The median was determined as the average of the 40th and 41st values in the sorted list, providing a robust central tendency measure that mitigates the influence of outliers.</p>
          <fig id="F5">
            <object-id content-type="arpha">30B14095-22D5-5544-933E-57852DB6D51F</object-id>
            <label>Figure 5.</label>
            <caption>
              <p>Calculation of median for contour angle (<abbrev xlink:title="contour angle">CA</abbrev>) showing sorted 80 values with the median position (40th-41st) and actual median (43.54°).</p>
            </caption>
            <graphic xlink:href="foliamedica-68-3-e177266-g005.jpg" id="oo_1682517.jpg">
              <uri content-type="original_file">https://binary.pensoft.net/fig/1682517</uri>
            </graphic>
          </fig>
          <fig id="F6">
            <object-id content-type="arpha">3B45EC3E-46E8-5D55-AC88-70BDB7CA90BE</object-id>
            <label>Figure 6.</label>
            <caption>
              <p>Calculation of median for deep angle (<abbrev xlink:title="deep emergence angle">DA</abbrev>) showing sorted 80 values with the median position (40th-41st) and actual median (56.70°).</p>
            </caption>
            <graphic xlink:href="foliamedica-68-3-e177266-g006.jpg" id="oo_1682518.jpg">
              <uri content-type="original_file">https://binary.pensoft.net/fig/1682518</uri>
            </graphic>
          </fig>
          <fig id="F7">
            <object-id content-type="arpha">309C69FC-B7FF-5BF8-A219-CE4F05D7FC7B</object-id>
            <label>Figure 7.</label>
            <caption>
              <p>Calculation of median for mucosal emergence angle (<abbrev xlink:title="mucosal emergence angle">MEA</abbrev>) showing sorted 80 values with the median position (40th-41st) and actual median (27.79°).</p>
            </caption>
            <graphic xlink:href="foliamedica-68-3-e177266-g007.jpg" id="oo_1682519.jpg">
              <uri content-type="original_file">https://binary.pensoft.net/fig/1682519</uri>
            </graphic>
          </fig>
        </sec>
        <sec sec-type="Calculation of median results for visual metrics (Figs 8, 9, 10, 11, 12)" id="sec11">
          <title><italic>Calculation of median results for visual metrics (Figs <xref ref-type="fig" rid="F8">8</xref>, <xref ref-type="fig" rid="F9">9</xref>, <xref ref-type="fig" rid="F10">10</xref>, <xref ref-type="fig" rid="F11">11</xref>, <xref ref-type="fig" rid="F12">12</xref>)</italic>.</title>
          <p>For the visual metrics, <abbrev xlink:title="intersection over union">IoU</abbrev> and F1 score were reported for each of the 20 crowns, resulting in 20 values per metric. To calculate the medians, the 20 values for <abbrev xlink:title="intersection over union">IoU</abbrev> were sorted in ascending order, and the median was determined as the average of the 10th and 11th values.</p>
          <fig id="F8">
            <object-id content-type="arpha">7CE132B8-92D3-5D29-BD65-36D4333AFF0F</object-id>
            <label>Figure 8.</label>
            <caption>
              <p>Calculation of median for F1 score showing sorted 20 values with the median position (10th-11th) and actual median (0.91).</p>
            </caption>
            <graphic xlink:href="foliamedica-68-3-e177266-g008.jpg" id="oo_1682520.jpg">
              <uri content-type="original_file">https://binary.pensoft.net/fig/1682520</uri>
            </graphic>
          </fig>
          <fig id="F9">
            <object-id content-type="arpha">F7DB3378-6027-5651-8B2B-A3CBDE4032CE</object-id>
            <label>Figure 9.</label>
            <caption>
              <p>Calculation of median for intersection over union (<abbrev xlink:title="intersection over union">IoU</abbrev>) showing sorted 20 values with the median position (10th-11th) and actual median (0.835).</p>
            </caption>
            <graphic xlink:href="foliamedica-68-3-e177266-g009.jpg" id="oo_1682521.jpg">
              <uri content-type="original_file">https://binary.pensoft.net/fig/1682521</uri>
            </graphic>
          </fig>
          <fig id="F10">
            <object-id content-type="arpha">0DE67A89-CC82-5458-A45B-D5BE1C4636E7</object-id>
            <label>Figure 10.</label>
            <caption>
              <p>Calculation of median for recall showing sorted 20 values with the median position (10th-11th) and actual median (0.910).</p>
            </caption>
            <graphic xlink:href="foliamedica-68-3-e177266-g010.jpg" id="oo_1682522.jpg">
              <uri content-type="original_file">https://binary.pensoft.net/fig/1682522</uri>
            </graphic>
          </fig>
          <fig id="F11">
            <object-id content-type="arpha">D8DEB5D1-104B-578E-BE2B-B5FFEDEF62D7</object-id>
            <label>Figure 11.</label>
            <caption>
              <p>Calculation of median for precision showing sorted 20 values with the median position (10th-11th) and actual median (0.945).</p>
            </caption>
            <graphic xlink:href="foliamedica-68-3-e177266-g011.jpg" id="oo_1682523.jpg">
              <uri content-type="original_file">https://binary.pensoft.net/fig/1682523</uri>
            </graphic>
          </fig>
          <fig id="F12">
            <object-id content-type="arpha">CCCA399F-6E5A-553B-8F91-86A9B3E306A0</object-id>
            <label>Figure 12.</label>
            <caption>
              <p>Median results for visual metrics (<abbrev xlink:title="intersection over union">IoU</abbrev>, F1 score, precision, and recall) with a perfect score threshold of 1.0.</p>
            </caption>
            <graphic xlink:href="foliamedica-68-3-e177266-g012.jpg" id="oo_1682524.jpg">
              <uri content-type="original_file">https://binary.pensoft.net/fig/1682524</uri>
            </graphic>
          </fig>
        </sec>
        <sec sec-type="Interpretation of visual metrics" id="sec12">
          <title>
            <italic>Interpretation of visual metrics</italic>
          </title>
          <p>A perfect <abbrev xlink:title="intersection over union">IoU</abbrev> or F1 score of 1.0 indicates flawless segmentation – perfect score, though this is rarely achieved in practice. <abbrev xlink:title="intersection over union">IoU</abbrev> values ≥0.7 and F1 scores ≥0.8 are generally considered appropriate for reliable performance in medical imaging tasks, including dental crown evaluation, reflecting substantial overlap and balanced precision-recall, respectively. Scores below 0.5 for <abbrev xlink:title="intersection over union">IoU</abbrev> and 0.7 for F1 are deemed low, indicating poor segmentation or classification accuracy unsuitable for clinical applications. In this study, <abbrev xlink:title="intersection over union">IoU</abbrev> values ranged from 0.77 to 0.90 (median: 0.84), and F1 scores ranged from 0.87 to 0.95 (median: 0.91), suggesting robust performance well above the thresholds for acceptable accuracy.<sup>[<xref ref-type="bibr" rid="B8">8</xref>,<xref ref-type="bibr" rid="B9">9</xref>]</sup></p>
        </sec>
        <sec sec-type="Interpretation of angular measurements" id="sec13">
          <title>
            <italic>Interpretation of angular measurements</italic>
          </title>
          <p>Value interpretation used for the analysis of the angles score was obtained from the previous publication<sup>[<xref ref-type="bibr" rid="B7">7</xref>]</sup> regarding the odds ratio (<abbrev xlink:title="odds ratio">OR</abbrev>) for developing peri-implantitis. <abbrev xlink:title="mucosal emergence angle">MEA</abbrev> &lt;30 is an “excellent” score; <abbrev xlink:title="mucosal emergence angle">MEA</abbrev> ≥30°: <abbrev xlink:title="odds ratio">OR</abbrev>=3.1 is a “very good” score; <abbrev xlink:title="mucosal emergence angle">MEA</abbrev> ≥40°: <abbrev xlink:title="odds ratio">OR</abbrev>=5.0 is a “satisfactory” score; <abbrev xlink:title="mucosal emergence angle">MEA</abbrev> ≥50°: <abbrev xlink:title="odds ratio">OR</abbrev>=7.5 is an “average” score; <abbrev xlink:title="mucosal emergence angle">MEA</abbrev> ≥60°: <abbrev xlink:title="odds ratio">OR</abbrev>=11.4 is a “below average” score; <abbrev xlink:title="mucosal emergence angle">MEA</abbrev> ≥70°: <abbrev xlink:title="odds ratio">OR</abbrev>=33.55 is a “poor” score.</p>
        </sec>
      </sec>
      <sec sec-type="Statistical analysis" id="sec14">
        <title>Statistical analysis</title>
        <p>No formal correlation analysis was performed due to the use of median values, which represent summary statistics rather than paired observations. Instead, a comparative analysis was conducted in conclusion by evaluating the medians against established clinical thresholds for the emergency angles. Statistical calculations were performed with the aid of Grok, an artificial intelligence language model developed by xAI.</p>
        <p>This approach focused on the clinical relevance of the findings, particularly the relationship between visual metrics and clinically relevant prosthetic parameters like <abbrev xlink:title="mucosal emergence angle">MEA</abbrev>, to assess the acceptability of the crown designs for real-world treatment.</p>
      </sec>
    </sec>
    <sec sec-type="Results" id="sec15">
      <title>Results</title>
      <p>Overall median scores: <abbrev xlink:title="mucosal emergence angle">MEA</abbrev>: 27.79°, <abbrev xlink:title="deep emergence angle">DA</abbrev>: 56.70°, <abbrev xlink:title="contour angle">CA</abbrev>: 43.54</p>
      <p>Median scores per surface: <abbrev xlink:title="mucosal emergence angle">MEA</abbrev>: vestibular: 34.50°, lingual/palatal: 35.48°, mesial: 16.59°, distal: 15.81°; <abbrev xlink:title="deep emergence angle">DA</abbrev>: vestibular: 59.23°, lingual/palatal: 61.61°, mesial: 51.54°, distal: 53.35°; <abbrev xlink:title="contour angle">CA</abbrev> – vestibular: 53.20°, lingual/palatal: 51.38°, mesial: 36.08°, distal: 37.53°. Maximum values for <abbrev xlink:title="mucosal emergence angle">MEA</abbrev>, <abbrev xlink:title="deep emergence angle">DA</abbrev>, and <abbrev xlink:title="contour angle">CA</abbrev> are 68.78°, 93.55°, and 83.01°, and minimum values are -0.01°, 27.51°, and 12.35°.</p>
      <p>For visual metrics, the overall median <abbrev xlink:title="intersection over union">IoU</abbrev> was 0.835, and the median F1 score was 0.91 across the 20 teeth. The median precision score was 0.945, and the median recall score was 0.91. To assess variability, teeth were grouped based on performance relative to the overall median. For <abbrev xlink:title="intersection over union">IoU</abbrev>, teeth with values ≥0.835 (n=11) had a median of 0.86, while those of &lt;0.835 (n=9) had a median of 0.80. For the F1 score, teeth with values ≥0.91 (n=11) had a median of 0.92, and those of &lt;0.91 (n=9) had a median of 0.89. For the precision score, teeth with values ≥0.945 (n=10) had a median of 0.96, while those of &lt;0.945 (n=10) had a median of 0.91. For recall, teeth with values ≥0.91 (n=10) had a median of 0.94, while those of &lt;0.91 (n=10) had a median of 0.84.</p>
      <p>The mean deviation from optimal values (equal to 1 for all visual metrics) is 0.165 for IOU, 0.055 for precision, 0.09 for recall, and 0.09 for the F1 score.</p>
      <p>The comparative analysis according to the values we used for interpretation shows that the <abbrev xlink:title="mucosal emergence angle">MEA</abbrev> mean score is “excellent,” the <abbrev xlink:title="contour angle">CA</abbrev> mean score is “satisfactory,” the <abbrev xlink:title="deep emergence angle">DA</abbrev> mean score is “average,” and the <abbrev xlink:title="intersection over union">IoU</abbrev>, F1 score, precision, and recall scores are not considered excellent – their mean score is less than 1.0, but it can be analyzed as appropriate.</p>
    </sec>
    <sec sec-type="Discussion" id="sec16">
      <title>Discussion</title>
      <p>The integration of artificial intelligence (<abbrev xlink:title="artificial intelligence">AI</abbrev>) in prosthetic dental medicine is transforming the design and fabrication of implant-supported crowns, offering enhanced precision and efficiency. A systematic review by Revilla-León<sup>[<xref ref-type="bibr" rid="B10">10</xref>]</sup> highlights <abbrev xlink:title="artificial intelligence">AI</abbrev>’s potential in diagnosis, treatment planning, and prosthesis design. Among the most promising tools in this domain are the three-dimensional generative adversarial neural networks (<abbrev xlink:title="three-dimensional generative adversarial neural networks">3D GANs</abbrev>)<sup>[<xref ref-type="bibr" rid="B11">11</xref>]</sup>, which enable the automated generation of complex three-dimensional prosthetic structures based on extensive training datasets. These <abbrev xlink:title="artificial intelligence">AI</abbrev>-driven systems hold the potential to streamline workflows in prosthetic dental medicine, reducing human error and optimizing treatment timelines. However, the validation of these <abbrev xlink:title="artificial intelligence">AI</abbrev>-generated designs remains a critical challenge, as the success of a crown extends beyond its digital accuracy to its clinical performance in the human mouth. Kong et al.<sup>[<xref ref-type="bibr" rid="B12">12</xref>]</sup> support the need for robust validation beyond digital accuracy. This raises an essential question: how exactly do we assess the efficacy of <abbrev xlink:title="artificial intelligence">AI</abbrev>-designed crowns when traditional validation metrics may not fully capture their real-world applicability?</p>
      <p>Validating <abbrev xlink:title="artificial intelligence">AI</abbrev>-designed crowns involves assessing 3D-generated files through neural network evaluations, often using metrics such as Intersection over Union (<abbrev xlink:title="intersection over union">IoU</abbrev>) and F1 score. These metrics measure the similarity between the <abbrev xlink:title="artificial intelligence">AI</abbrev>-generated design and a predefined ground truth.<sup>[<xref ref-type="bibr" rid="B13">13</xref>]</sup> However, research suggests that these metrics may not fully capture clinical efficacy, as evidenced by Rohrer et al.<sup>[<xref ref-type="bibr" rid="B14">14</xref>]</sup>, who reported high F1 scores (97%), while clinical outcomes depend on more than digital accuracy.</p>
      <p>The process of validation, as explored by Piedra-Cascón et al.<sup>[<xref ref-type="bibr" rid="B15">15</xref>]</sup>, involves comparing <abbrev xlink:title="artificial intelligence">AI</abbrev> outputs against a reference model. However, this approach may overlook variability in clinical scenarios. Revilla-León et al.<sup>[<xref ref-type="bibr" rid="B10">10</xref>]</sup> indicate that neural networks trained on a single ground truth may undervalue designs that deviate from this reference yet remain clinically viable.</p>
      <p>In prosthetic dental medicine, one of the most important predictors for successful treatment is the use of critical prosthetic parameters as guidelines in design. Mattheos et al.<sup>[<xref ref-type="bibr" rid="B5">5</xref>]</sup> reported that “Emergence Profile (<abbrev xlink:title="Emergence Profile">EP</abbrev>), Emergence Angle (<abbrev xlink:title="Emergence Angle">EA</abbrev>), and Cervical Margin (<abbrev xlink:title="Cervical Margin">CM</abbrev>), as well as the design of the implant–abutment and abutment–prosthesis junctions and their location in relation to the tissues of the implant supracrestal complex, can have a significant impact on the maintenance of stable and healthy peri-implant tissues in the long term.”</p>
      <p>Considering the evolution of implant crown design and the predictors for successful treatment, this study was conducted to investigate whether it is useful to assess the outcome of automated design by GAN networks using not only visual parameters but also clinical ones.</p>
      <p>The present findings indicate that commonly used visual metrics such as <abbrev xlink:title="intersection over union">IoU</abbrev> and F1 score are predictive factors for the quality of newly generated three-dimensional objects. However, it remains questionable whether a newly generated crown can be used in a real clinical situation even if <abbrev xlink:title="intersection over union">IoU</abbrev> and F1 scores show perfect results (=1).<sup>[<xref ref-type="bibr" rid="B8">8</xref>,<xref ref-type="bibr" rid="B9">9</xref>]</sup> This issue is related to the method used for training such GANs and the widely accepted approach to visual assessment. At present, the so-called ground truth is compared with newly generated 3D objects to assess inaccuracies.<sup>[<xref ref-type="bibr" rid="B3">3</xref>]</sup> Further investigations are needed to support this statement. Real clinical performance must be assessed using specific science-based parameters for prosthetic constructions, such as screw-retained implant crowns, among others. In this study, angles describing the emergence profile were measured as some of the most important clinically relevant parameters for successful prosthetic treatment. It was observed that one of the most important predictors, the mucosal emergence angle (<abbrev xlink:title="mucosal emergence angle">MEA</abbrev>), demonstrated an excellent mean score, suggesting that the newly generated crowns may have excellent clinical applicability with respect to this parameter.</p>
      <p>It is suggested that further investigations should include additional clinically and prosthetically relevant parameters, as well as their relationship to the visual metric scores used for validation. A standardized protocol incorporating all clinically relevant parameters and visual metrics should be adopted to improve the assessment of newly generated crowns and enhance their translation into clinical practice.</p>
    </sec>
    <sec sec-type="Conclusion" id="sec17">
      <title>Conclusion</title>
      <p>In conclusion, while <abbrev xlink:title="artificial intelligence">AI</abbrev> offers immense potential, validation must evolve to include clinical parameters beyond digital metrics. Visual parameters used to validate the design of implant crowns are not universal but rather serve as supplementary measures for assessing the real clinical value of newly generated crowns. The present findings demonstrate that even in cases where <abbrev xlink:title="intersection over union">IoU</abbrev>, F1 score, precision, and recall are not perfect (&lt;1), clinically significant parameters such as <abbrev xlink:title="mucosal emergence angle">MEA</abbrev> can still demonstrate excellent mean values (27.79°), which represent a predictive factor for peri-implant tissue health.</p>
    </sec>
  </body>
  <back>
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    <sec sec-type="Additional information" id="sec18">
      <title>Additional information</title>
      <p>
        <bold>Ethical statement</bold>
      </p>
      <list list-type="bullet">
        <list-item>
          <p>The authors declared that no clinical trials were used in the present study.
</p>
        </list-item>
        <list-item>
          <p>The authors declared that no experiments on humans or human tissues were performed for the present study. This is an in-vitro study using digital models only.
</p>
        </list-item>
        <list-item>
          <p>The authors declared that no informed consent was obtained from the humans, donors or donors’ representatives participating in the study.
</p>
        </list-item>
        <list-item>
          <p>The authors declared that no experiments on animals were performed for the present study.
</p>
        </list-item>
        <list-item>
          <p>The authors declared that no commercially available immortalized human and animal cell lines were used in the present study.
</p>
        </list-item>
      </list>
      <p>
        <bold>Conflict of interest</bold>
      </p>
      <p>The authors have declared that no competing interests exist.</p>
      <p>
        <bold>Artificial Intelligence (<abbrev xlink:title="artificial intelligence">AI</abbrev>) use</bold>
      </p>
      <p>The authors accept full responsibility for the content of the manuscript, including the disclosure of any use of Al. Regarding the use of Al in the preparation of this manuscript, the authors declare the following: Grok, an artificial intelligence language model developed by xAI, was used to help with statistical calculations and graphics.</p>
      <p>
        <bold>Funding</bold>
      </p>
      <p>No funding was reported.</p>
      <p>
        <bold>Author contributions</bold>
      </p>
      <p>AN: wrote the manuscript and completed most of the digital dental work; GK: generated the <abbrev xlink:title="artificial intelligence">AI</abbrev> crowns and found the visual metrics describing them; TU: revised the whole work and corrections where necessary. The work is original, not previously published, and not under consideration elsewhere. All authors have approved the final version and agree with the submission to Folia Medica.</p>
      <p>
        <bold>Author ORCIDs</bold>
      </p>
      <p>Aleksandar Naydenov <ext-link xlink:href="https://orcid.org/0009-0007-6055-9438" ext-link-type="uri">https://orcid.org/0009-0007-6055-9438</ext-link></p>
      <p>Todor Uzunov <ext-link xlink:href="https://orcid.org/0000-0002-8714-2778" ext-link-type="uri">https://orcid.org/0000-0002-8714-2778</ext-link></p>
      <p>Georgi Kostadinov <ext-link xlink:href="https://orcid.org/0000-0002-3465-8797" ext-link-type="uri">https://orcid.org/0000-0002-3465-8797</ext-link></p>
      <p>
        <bold>Data availability</bold>
      </p>
      <p>All of the data that support the findings of this study are available in the main text.</p>
    </sec>
  </back>
</article>
