Aim: 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.

Materials and methods: Twenty crowns were generated for the study using 3D GAN. Their validation metrics, including IoU (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 (MEA), the deep emergence angle (DA), and the total contour angle (CA)—resulting in a total of 240 measured angles.

Results: The mean values of the angles were MEA=27.79°, DA=56.70°, and CA=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 IoU was 0.835, while the median precision, recall, and F1 score were 0.946, 0.942, and 0.91, respectively, across the 20 teeth.

Conclusion: The validation of AI 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 IoU, precision, recall, and F1 scores are not perfect (<1), clinically significant parameters such as MEA can still demonstrate an excellent mean value (27.79°), which is a predictive factor for peri-implant tissue health.

3D GAN, artificial intelligence, design, implant, validation

The integration of artificial intelligence (AI) into dental prosthetics has revolutionized the design and fabrication of implant-supported crowns, offering unprecedented precision and efficiency.^[1] Among the most promising tools in this domain are three-dimensional generative adversarial neural networks (3D GANs)^[2], which enable the automated generation of complex 3D prosthetic structures based on extensive training datasets. These AI-driven systems hold the potential to streamline workflows in prosthetic dental medicine, reducing human error and optimizing treatment timelines. However, the validation of these AI-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 AI-designed crowns when traditional validation metrics may not fully capture their real-world applicability?

In AI-driven design, validation typically relies on quantitative metrics such as the intersection over union (IoU) 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”^[3] 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 IoU 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.

The design of an implant crown involves multiple prosthetic parameters, such as those describing the emergence profile, which includes the contour of the crown^[4], and angles such as the mucosal emergence angle (MEA), deep emergence angle (DA), and total contour angle (CA). These parameters influence not only the crown’s fit and stability but also its biological integration and long-term prognosis.‌^[5] 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 AI system such as 3D GANs, 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 AI-designed crowns may depend less on achieving perfect metric scores and more on how prosthetic parameters align with real-world functionality.

This research paper explores the role of prosthetic parameters in validating AI-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 IoU 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 AI-driven prosthetics, emphasizing the synergy between computational design and practical application.

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.^[6] 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.

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.

Stage 1 – Generating and refining the voxelized data

The 3D GAN developed and trained by G. Kostadinov and A. Naydenov^[6] 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 (Fig. 1).

Figure 1.

The process of refining the raw GAN generated data in MeshMixer TM. A. The crown is still voxelized – raw data. B. Crown after selecting it and smoothing the outer surface by selecting the smoothing option with smoothing scale 4 and constraint rings 3. C. The surface that requires additional smoothing is highlighted in orange. The smoothing option was selected with smoothing scale 6 and constraint rings 1.

Stage 2 – Obtaining sectional view

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 (Fig. 2A, 2B).

Figure 2.

A and B shows the crown STL file uploaded in ExoCad ^TM simultaneously with the prosthetic field e.g., part of the GAN training set. A. Four red dots are visible. One red dot per each side: vestibular, lingual, medial, distal. B. Longitudinal cut view was observed corresponding to the yellow lines of A. For each crown 2 longitudinal cuts view were screenshotted (vestibulo-lingual and mesiodistal). C. 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 (MEA, DA, CA) were measured and visualized in green.

Stage 3 – Outlining and measuring

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.^[7]

Using green lines, the following angles were measured and illustrated: (1) deep angle (DA), 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 (MEA), 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 (CA), 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 (Figs 2C, 3). All results were measured in degrees and listed in Table 1. A total of 240 angles were measured (20 crowns × 4 surfaces × 3 angles).

Figure 3.

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.

Table 1.

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Degrees for three angles (MEA, DA, CA) per each surface (Vestibular -V; Lingial/Palatinal – L; Medial – M; Distal – D) were measured and presented for 20 cases (crowns). MEA: mucosal emergence angle, DA: deep angle, CA: total contour angle

S. Angle Crown No.	V			L			M			D
	DA	MEA	CA	DA	MEA	CA	DA	MEA	CA	DA	MEA	CA
1	66.69	45.85	56.94	93.55	57.69	81.10	64.61	36.90	12.35	46.58	32.16	15.94
2	32.26	28.66	46.76	68.10	62.30	66.69	42.94	22.56	30.79	60.19	14.69	41.86
3	83.01	44.09	83.01	71.62	44.69	62.41	67.93	9.65	48.04	34.05	7.32	17.00
4	60.85	35.77	56.07	56.38	34.95	44.80	51.94	3.71	28.74	56.73	26.78	43.83
5	71.60	31.52	58.69	58.14	36.01	47.77	52.04	17.37	35.57	47.04	19.97	36.97
6	58.73	39.27	53.58	49.22	28.07	40.86	49.39	16.11	36.10	52.14	21.40	40.90
7	54.35	37.97	59.77	54.25	30.36	47.29	43.60	37.53	30.53	50.20	00.00	22.77
8	76.59	48.77	68.15	64.58	20.39	50.25	70.68	15.39	48.24	58.75	16.92	39.12
9	61.66	53.73	59.32	55.87	24.50	46.08	51.13	3.83	24.18	46.22	12.70	38.08
10	59.72	22.50	47.69	69.79	44.74	64.70	49.75	24.10	36.05	57.59	10.51	31.47
11	70.92	2.41	35.00	76.04	68.78	73.17	63.83	17.06	39.63	80.63	52.80	72.75
12	56.27	44.14	52.82	55.14	34.13	48.36	40.72	11.09	32.77	54.56	29.80	41.52
13	78.94	27.42	60.26	62.08	19.70	43.25	63.60	3.25	36.66	55.44	4.98	32.08
14	56.66	27.61	47.55	63.44	52.65	61.10	47.83	28.09	41.47	47.28	13.58	29.59
15	72.20	47.90	63.50	63.28	41.25	53.86	65.19	30.20	52.44	58.26	10.90	30.86
16	51.65	2.88	28.49	52.08	12.03	30.36	61.44	19.22	43.94	56.87	52.01	66.82
17	32.79	32.79	42.41	59.76	44.27	54.94	46.34	1.76	28.87	50.23	2.75	32.43
18	34.50	33.23	26.50	31.67	27.10	26.87	56.87	63.81	76.98	27.51	39.23	26.72
19	55.25	24.24	45.13	69.07	33.90	57.54	48.09	8.05	21.15	45.22	27.96	38.61
20	57.06	40.48	52.04	61.13	42.83	52.50	45.06	2.10	29.47	46.39	13.82	33.18

For visual segmentation, the intersection over union (IoU) 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 (Fig. 4). This yielded 20 IoU values and 20 F1 scores (40 scores in total), which are presented in Table 2.

Table 2.

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The results for two different visual metrics are shown in the table: IoU and F1 score. Results for these metrics were obtained via the tool that we developed and visualized in Fig. 4

Visual Metrics Crown No.	IOU	F1 Score	Precision	Recall
1	0.80	0.89	0.97	0.82
2	0.81	0.89	0.87	0.92
3	0.85	0.92	0.93	0.92
4	0.80	0.89	0.98	0.82
5	0.77	0.87	0.97	0.79
6	0.86	0.93	0.95	0.91
7	0.86	0.92	0.96	0.89
8	0.84	0.91	0.88	0.96
9	0.89	0.94	0.91	0.98
10	0.80	0.91	0.82	0.97
11	0.81	0.90	0.96	0.84
12	0.84	0.91	0.92	0.90
13	0.90	0.95	0.96	0.93
14	0.90	0.95	0.94	0.95
15	0.79	0.89	0.83	0.96
16	0.86	0.93	0.97	0.89
17	0.85	0.92	0.95	0.89
18	0.79	0.88	0.97	0.85
19	0.83	0.90	0.85	0.92
20	0.79	0.88	0.83	0.94

Figure 4.

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: IoU, F1 score, Precision and Recall (results for which are visible in the box above every single superimposition. A – Newly generated crown and prosthetic field are visible; B – Prosthetic field is visible; C – Crown modeled by a specialist and the prosthetic field are visible; D – Prosthetic field, newly generated crown, and the crown modeled by a specialist are visible.

Stage 4 – Data Analysis

Calculation of median results for angular measurements (Figs 5, 6, 7).

To summarize the angular measurements, median values were computed for MEA, DA, and CA 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.

Figure 5.

Calculation of median for contour angle (CA) showing sorted 80 values with the median position (40th-41st) and actual median (43.54°).

Figure 6.

Calculation of median for deep angle (DA) showing sorted 80 values with the median position (40th-41st) and actual median (56.70°).

Figure 7.

Calculation of median for mucosal emergence angle (MEA) showing sorted 80 values with the median position (40th-41st) and actual median (27.79°).

Calculation of median results for visual metrics (Figs 8, 9, 10, 11, 12).

For the visual metrics, IoU 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 IoU were sorted in ascending order, and the median was determined as the average of the 10th and 11th values.

Figure 8.

Calculation of median for F1 score showing sorted 20 values with the median position (10th-11th) and actual median (0.91).

Figure 9.

Calculation of median for intersection over union (IoU) showing sorted 20 values with the median position (10th-11th) and actual median (0.835).

Figure 10.

Calculation of median for recall showing sorted 20 values with the median position (10th-11th) and actual median (0.910).

Figure 11.

Calculation of median for precision showing sorted 20 values with the median position (10th-11th) and actual median (0.945).

Figure 12.

Median results for visual metrics (IoU, F1 score, precision, and recall) with a perfect score threshold of 1.0.

Interpretation of visual metrics

A perfect IoU or F1 score of 1.0 indicates flawless segmentation – perfect score, though this is rarely achieved in practice. IoU 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 IoU and 0.7 for F1 are deemed low, indicating poor segmentation or classification accuracy unsuitable for clinical applications. In this study, IoU 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.^[8,9]

Interpretation of angular measurements

Value interpretation used for the analysis of the angles score was obtained from the previous publication^[7] regarding the odds ratio (OR) for developing peri-implantitis. MEA <30 is an “excellent” score; MEA ≥30°: OR=3.1 is a “very good” score; MEA ≥40°: OR=5.0 is a “satisfactory” score; MEA ≥50°: OR=7.5 is an “average” score; MEA ≥60°: OR=11.4 is a “below average” score; MEA ≥70°: OR=33.55 is a “poor” score.

Overall median scores: MEA: 27.79°, DA: 56.70°, CA: 43.54

Median scores per surface: MEA: vestibular: 34.50°, lingual/palatal: 35.48°, mesial: 16.59°, distal: 15.81°; DA: vestibular: 59.23°, lingual/palatal: 61.61°, mesial: 51.54°, distal: 53.35°; CA – vestibular: 53.20°, lingual/palatal: 51.38°, mesial: 36.08°, distal: 37.53°. Maximum values for MEA, DA, and CA are 68.78°, 93.55°, and 83.01°, and minimum values are -0.01°, 27.51°, and 12.35°.

For visual metrics, the overall median IoU 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 IoU, teeth with values ≥0.835 (n=11) had a median of 0.86, while those of <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 <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 <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 <0.91 (n=10) had a median of 0.84.

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.

The comparative analysis according to the values we used for interpretation shows that the MEA mean score is “excellent,” the CA mean score is “satisfactory,” the DA mean score is “average,” and the IoU, 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.

The integration of artificial intelligence (AI) 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^[10] highlights AI’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 (3D GANs)^[11], which enable the automated generation of complex three-dimensional prosthetic structures based on extensive training datasets. These AI-driven systems hold the potential to streamline workflows in prosthetic dental medicine, reducing human error and optimizing treatment timelines. However, the validation of these AI-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.^[12] support the need for robust validation beyond digital accuracy. This raises an essential question: how exactly do we assess the efficacy of AI-designed crowns when traditional validation metrics may not fully capture their real-world applicability?

Validating AI-designed crowns involves assessing 3D-generated files through neural network evaluations, often using metrics such as Intersection over Union (IoU) and F1 score. These metrics measure the similarity between the AI-generated design and a predefined ground truth.^[13] However, research suggests that these metrics may not fully capture clinical efficacy, as evidenced by Rohrer et al.^[14], who reported high F1 scores (97%), while clinical outcomes depend on more than digital accuracy.

The process of validation, as explored by Piedra-Cascón et al.^[15], involves comparing AI outputs against a reference model. However, this approach may overlook variability in clinical scenarios. Revilla-León et al.^[10] indicate that neural networks trained on a single ground truth may undervalue designs that deviate from this reference yet remain clinically viable.

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.^[5] reported that “Emergence Profile (EP), Emergence Angle (EA), and Cervical Margin (CM), 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.”

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.

The present findings indicate that commonly used visual metrics such as IoU 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 IoU and F1 scores show perfect results (=1).^[8,9] 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.^[3] 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 (MEA), demonstrated an excellent mean score, suggesting that the newly generated crowns may have excellent clinical applicability with respect to this parameter.

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.

In conclusion, while AI 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 IoU, F1 score, precision, and recall are not perfect (<1), clinically significant parameters such as MEA can still demonstrate excellent mean values (27.79°), which represent a predictive factor for peri-implant tissue health.

Ethical statement

• The authors declared that no clinical trials were used in the present study.
• 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.
• The authors declared that no informed consent was obtained from the humans, donors or donors’ representatives participating in the study.
• The authors declared that no experiments on animals were performed for the present study.
• The authors declared that no commercially available immortalized human and animal cell lines were used in the present study.

Conflict of interest

The authors have declared that no competing interests exist.

Artificial Intelligence (AI) use

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.

Funding

No funding was reported.

Author contributions

AN: wrote the manuscript and completed most of the digital dental work; GK: generated the AI 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.

Author ORCIDs

Aleksandar Naydenov https://orcid.org/0009-0007-6055-9438

Todor Uzunov https://orcid.org/0000-0002-8714-2778

Georgi Kostadinov https://orcid.org/0000-0002-3465-8797

Data availability

All of the data that support the findings of this study are available in the main text.