Evaluation of CBCT reconstructed tooth models at different thresholds and voxels and their accuracy in fusion with IOS data: an in vitro validation study

Abstract

Background

This study aims to evaluate the impact of different thresholds and voxel sizes on the accuracy of Cone-beam computed tomography (CBCT) tooth reconstruction and to assess the accuracy of fused CBCT and intraoral scanning (IOS) tooth models using curvature continuity algorithms under varying thresholds and voxel conditions.

Methods

Thirty-two isolated teeth were digitized using IOS and CBCT at two voxel sizes and five threshold settings. Crown-root fusion was performed using a curvature continuity algorithm. Volume, surface area, and crown width of tooth models were compared to laser scanning models, and RMS error was measured. Data were analyzed using Wilcoxon signed-rank test, paired t-test, and one-way ANOVA.

Results

Volume amplification errors of CBCT with 0.15 mm and 0.3 mm voxels ranged from 1.22 to 19.07%, surface area errors from 0.18 to 7.78%, crown linearity errors ranged from 2.47 to 7.69%, root linearity errors ranged from − 1.02 to 2.26% and RMS from 0.0691 mm to 0.2408 mm. Crown-root fusion of IOS and CBCT data reduced volume error to -0.90–5.10%, surface area error to -0.66–4.15%, and RMS to 0.0359 mm to 0.0945 mm.

Conclusions

Voxel size and threshold settings significantly affect the accuracy of CBCT reconstruction and crown-root fusion. Smaller voxel sizes yield higher reconstruction precision, and different voxel sizes and tooth regions correspond to distinct optimal segmentation thresholds. The validated semi-automated crown-root fusion algorithm significantly enhances overall model accuracy, offering new possibilities for clinical applications.

Background

Cone beam computed tomography (CBCT) is an advanced volumetric imaging technology that uses cone-shaped or pyramidal X-rays [1]. It offers low radiation doses, fast scanning speeds, and excellent isotropic spatial resolution, making it an ideal choice for dental imaging [2]. The three-dimensional digital models reconstructed from CBCT are widely used for observing root morphology and bone structure, and play a key role in orthodontic planning, implant placement, and root canal assessment [3]. However, the accuracy of these applications heavily depends on the precision of the three-dimensional surface models.

The process of digitizing CBCT tooth models includes two main steps: data acquisition and three-dimensional reconstruction. Errors in each step can accumulate, affecting the final model accuracy. In the data acquisition phase, scanning parameters such as tube current, voltage, and voxel size have a significant impact on model accuracy. After data acquisition, three-dimensional reconstruction is performed using medical image processing software, where factors such as data format and threshold settings also influence the final results. Most existing studies assess the impact of a single phase, overlooking the combined effects of voxel size and threshold during both the “data acquisition” and “reconstruction” stages. For example, van Leeuwen et al. [4]noted that low-resolution (large voxel) CBCT scans lead to increased measurement errors. Ye et al. [5] demonstrated that an increase in voxel size significantly increases errors in tooth crown volume. However, these studies have not addressed the impact of threshold settings during the reconstruction phase on tooth model accuracy, which could lead to biased results. In fact, threshold settings in dental tissue segmentation often rely on clinical experience. Improper threshold selection can lead to over- or underestimation of tissue structures, thereby affecting reconstruction accuracy [6]. Some studies have evaluated the impact of threshold selection on bone reconstruction accuracy. Research by van Eijnatten et al. shows that manually selected thresholds for CBCT cranial reconstruction result in errors ranging from − 2.3 mm to 4.8 mm when compared to optical scanning [7]. However, the combined effects of voxel size in the “data acquisition phase” and threshold settings in the “reconstruction phase” on tooth model accuracy have yet to be fully explored.

Given the limitations of CBCT, researchers have attempted to combine intraoral scanning (IOS) data with CBCT data to create more accurate multimodal three-dimensional models. IOS technology provides higher resolution tooth crown images, reducing errors during CBCT scanning and reconstruction [8–10]. This process involves initial alignment and subsequent fusion. The iterative closest point (ICP) algorithm is currently the most widely used registration method, aligning models by minimizing the average distance between two three-dimensional models [11, 12]. However, the post-registration fusion method and its accuracy assessment remain challenging. Due to differences in accuracy between CBCT and IOS, direct registration may lead to redundant information in overlapping areas, and removing this redundant data may result in the loss of anatomical details at the crown-root junction, affecting the natural transition and accuracy of the model [13]. Most studies currently focus on registration accuracy, with fewer addressing the accuracy of the fused model [14, 15] Additionally, in vivo studies are limited by the difficulty of obtaining high-precision crown-root reference models (e.g., laser scanning models or micro-CT models), and accuracy assessments often rely on manual segmentation rather than real “gold-standard” comparisons, which may overestimate the accuracy of fused models [16, 17].

This study aimed to address two research gaps: (1) investigating the impact of different voxel sizes and threshold settings on the accuracy of CBCT tooth reconstruction, and (2) evaluating the accuracy of fused CBCT and IOS tooth models using a curvature continuity algorithm. By comparing these models with laser-scanned models, we sought to provide a more objective foundation for clinical threshold selection. Additionally, this study validated a semi-automated multimodal crown-root fusion method, offering more reliable imaging data for clinical dental practice.

Materials and methods

This is an ex vivo study, approved by the Ethics Committee of Stomatological Hospital, Shandong University. The study flowchart is shown in Fig. 1.

Fig. 1.

Flow chart of the study design

Based on Ye N et al. [5], with magnification errors of 20% for 0.125 mm voxels and 40% for 0.3 mm voxels, G*power software (version 3.1, Heinrich Heine University Düsseldorf, Germany) calculated a minimum sample size of 21 teeth (power 80%, α = 5%). In this study, we collected 38 extracted teeth from cadaveric donors in the Department of Anatomy and Neurobiology, School of Basic Medical Sciences, Shandong University. Teeth with significant wear, caries, crown defects, root fractures, or restorations were excluded, resulting in 32 teeth being included in the study, comprising 10 central and lateral incisors, 6 canines, 11 premolars, and 5 molars.

Laser scanning

The surface of each tooth specimen was scanned using a 3Shape scanner (R700, 3Shape, Copenhagen, Denmark). The scanner can obtain a surface model in “point cloud” format with an accuracy of 20 microns. Following reverse engineering methods, the top and bottom parts of the teeth were scanned separately and then merged using Geomagic Wrap 2021 (Geomagic International, Research Triangle Park, NC), which automatically stitches the overlapping points of the two models. In this study, the laser-scanned models served as the reference standard.

CBCT tooth Model Reconstruction

A NewTom VG CBCT was used to scan a cup of water to calibrate the Hounsfield unit thresholds according to the manufacturer’s instructions. After calibration, all teeth were scanned twice under two voxel settings(Table 1).

Table 1.

CBCT scan parameters

	Voxel size (mm)	FOV (cm)	Tube voltage(kV)	Tube current(mA)	ST(s)
NewTom VG CBCT	0.3	8 × 8	110	0.58	3.6
	0.15	8 × 8	110	0.58	5.4

After scanning, each CBCT file was saved in DICOM format and subsequently imported into Mimics software(version 21.0; Materialise Dental, Leuven, Belgium) for 3D reconstruction. We set five thresholds of 800, 1000, 1200, 1400, and 1600 (two on each side of the recommended threshold) according to the minimum segmentation threshold of 1200 recommended by the Mimics software. The tooth pulp chamber were filled by the “cavity fill” tool in the Mimics software to obtain the intact volume.

Multimodal crown-root fusion

The tooth specimens were scanned in a Typodont model using an intraoral optical scanner (iTero Element, Align Technology, California, United States of America) to obtain 32 STL files. For crown-root fusion, we followed Zhao et al. [13], importing CBCT and IOS data into Geomagic Wrap. A curvature stitching algorithm was used for naturalistic shifting. The steps were as follows: (1) Align the oral scan and CBCT models using “point” and “ICP” alignment. (2) Create the “gingival margin line” on the oral scan model, delete data below the root side, and retain the high-resolution crown model. (3) Offset the line by 1 mm to the root side and project it onto the CBCT model, delete data above the crown side, and retain the CBCT root. (4) Use “Curvature Bridge” and “Curvature Filling” functions to automatically fill the gap between the crown and root, completing the crown-root fusion. In the last step, Geomagic wrap’s built-in curvature continuity algorithm calculates and analyzes curvature information, including curvature magnitude and direction, at and near the boundary points of the crown and root models to generate smooth, continuous transition surfaces or filler surfaces, which allow for smooth transitions at the crown-root junctions in the fusion model and the filling of missing areas (See Fig. 2).

Fig. 2.

Flowchart of IOS and CBCT crown-root fusion: A: CBCT and optical scanning model alignment; B: Optical scanning model cropping (retaining crown); C: CBCT model cropping (retaining root); and D: Integrated fusion of multimodal source crown and root

Accuracy measurements

Linearity deviation

The difference in crown width between CBCT reconstructions and laser scanned models assessed CBCT’s linear deviation. Multi -plane reconstruction positioning CBCT image steps are shown in Fig. 3.

Fig. 3.

CBCT image localization: A. In the horizontal cross-section, X and Y axes divided the labiolingual and proximo-lingual mesial diameters of the tooth’s cervical region. B. In the coronal section, the Y axis divided the proximo-longitudinal mesial diameters and passed through the tooth’s longitudinal axis. C. In the sagittal plane, the X axis intersected the labiolingual enamel-cementum junction, while the Y axis evenly divided the buccolingual diameter

Crown width and root length were measured in the coronal plane. The horizontal distance between the most protruding points of the proximal and distal surfaces was measured as the crown width. Root length was defined as the distance from the midpoint of the line connecting the proximal and distal midpoints of the cemento-enamel junction to the root apices of the teeth (Fig. 3B). The distance between the midpoint to the buccal root tip was measured for premolars and the distance between the midpoint to the proximal buccal root tip was measured for molars [18]. The direction determined in the first trial was saved and repeated for the 2nd time after an interval of 2 weeks, and the average of the two measurements was taken. All of these procedures are performed by an orthodontist with over five years of digital experience.

3D deviation and visualization

The CBCT tooth model/fused model and the laser scan model were imported into the Mimics software. The initial coarse registration of the measurement model with the laser scan was achieved using point registration, followed by precise alignment using the ICP algorithm. The 3-Matic Medical software (version 13.0; Materialise Dental, Leuven, Belgium) automation calculated the surface area and volume for each 3D model. Volume/surface area deviation = (CBCT/fusion model - laser model)/ laser model × 100%. For each pair of aligned models, the 3D geometric deviations were assessed by calculating the root mean square (RMS), which measures the distance difference between corresponding points on the two models. A smaller RMS value indicates a closer match between the reconstructed or fused model and the reference model. The aligned models were imported into the 3-Matic Medical software as STL files, where the “Create Comparative Analysis of Parts” tool was employed to conduct the RMS analysis. This also generated qualitative color maps to visualize regions of significant deviation between the models.

Statistical analysis

All statistical analyses were conducted using the Standard Statistical Package (version 25.0, SPSS Inc., Chicago, IL, USA). The Shapiro-Wilk test was applied to assess the normality of the data distribution. The Wilcoxon signed-rank test, paired t-test, and one-way analysis of variance (ANOVA) were employed for statistical analysis. Crown width and root length were reported as mean and standard deviation (SD), and interobserver reliability was evaluated using the intraclass correlation coefficient (ICC). The Wilcoxon signed-rank test was utilized for non-parametric data and paired observations, while the paired t-test was used for parametric comparisons between two related groups. One-way ANOVA was applied to compare the means among multiple groups to identify statistically significant differences influenced by voxel size and threshold settings. Bonferroni correction was used for multiple intra- and inter-group comparisons to control the type I error rate.

Results

The means and standard deviations of the HU thresholds for water and air are 56.84 ± 13.17 and − 990.19 ± 4.99, respectively, which are close to conventional CT values (water = 0 HU; air = -1000 HU). The volume and surface area of the laser-scanned tooth model were 502.21 mm³ and 416.90 mm², respectively. The measurements of the volume and surface area of the CBCT-reconstructed tooth under different voxel and threshold conditions are shown in Table 2, and the measurements after crown-root fusion are shown in Table 3.

Table 2.

Volume and surface area measurements for different CBCT voxel sizes with 5 thresholds compared to laser scanning

Voxel size (mm)	Thresholds (HU)	Volume				Surface Area
		Mean Vol ± SD(mm3)	Difference ± SD(mm3)	Deviation%(%)	P-value	Mean SA ± SD(mm2)	Difference ± SD(mm2)	Deviation%(%)	P-value
0.3 mm	800	593.52 ± 210.91	91.31 ± 22.94	19.07%	0.000	449.26 ± 113.71	32.36 ± 5.44	7.78%	0.000
	1000	578.29 ± 207.17	76.08 ± 19.37	15.88%	0.000	443.13 ± 112.91	26.23 ± 4.83	6.32%	0.000
	1200	563.48 ± 203.45	61.27 ± 16.07	12.78%	0.000	436.97 ± 112.03	20.07 ± 4.41	4.84%	0.000
	1400	548.71 ± 199.63	46.50 ± 13.26	9.70%	0.000	430.79 ± 110.93	13.83 ± 4.49	3.37%	0.000
	1600	533.69 ± 196.12	31.48 ± 11.55	6.54%	0.000	424.31 ± 110.33	7.42 ± 4.18	1.82%	0.000
0.15 mm	800	555.83 ± 201.18	53.62 ± 12.96	11.19%	0.000	436.44 ± 112.54	19.54 ± 3.39	4.70%	0.000
	1000	544.00 ± 198.19	41.79 ± 10.12	8.71%	0.000	431.51 ± 111.75	14.61 ± 2.96	3.52%	0.000
	1200	532.22 ± 195.14	30.02 ± 7.53	6.25%	0.000	426.58 ± 111.05	9.68 ± 2.68	2.34%	0.000
	1400	520.28 ± 191.97	18.07 ± 5.58	3.76%	0.000	421.53 ± 110.24	4.63 ± 2.80	1.13%	0.000
	1600	508.18 ± 188.99	5.97 ± 5.72	1.22%	0.000	416.08 ± 109.51	-0.82 ± 3.35	-0.18%	0.337
laser model		502.21 ± 188.75				416.90 ± 110.95

P-value: Mean CBCT model volume/surface area vs. mean laser model volume/surface area

Table 3.

Volume and surface area measurements after crown-root fusion with IOS and CBCT compared to laser scanning

Voxel size (mm)	Thresholds (HU)	Volume				Surface Area
		Mean Vol ± SD(mm3)	Difference ± SD(mm3)	Deviation%(%)	P-value	Mean SA ± SD(mm3)	Difference ± SD(mm2)	Deviation%(%)	P-value
0.3 mm	800	544.96 ± 202.20	42.82 ± 16.52	8.77%	0.000	433.42 ± 112.06	16.52 ± 4.90	4.15%	0.000
	1000	535.11 ± 198.25	32.90 ± 12.13	6.83%	0.000	429.53 ± 112.21	12.63 ± 4.11	3.16%	0.000
	1200	525.73 ± 195.56	23.52 ± 9.85	4.88%	0.000	425.11 ± 111.56	8.21 ± 3.92	2.07%	0.000
	1400	516.64 ± 193.10	14.43 ± 7.27	2.96%	0.000	420.90 ± 111.08	4.00 ± 3.95	1.01%	0.000
	1600	508.69 ± 190.92	6.48 ± 5.40	1.29%	0.000	417.38 ± 110.98	0.48 ± 3.68	0.12%	0.197
0.15 mm	800	527.17 ± 195.77	24.96 ± 7.67	5.10%	0.000	427.42 ± 112.24	10.53 ± 3.05	2.59%	0.000
	1000	519.54 ± 193.36	17.33 ± 5.62	3.54%	0.000	424.16 ± 111.63	7.26 ± 2.64	1.79%	0.000
	1200	512.91 ± 191.38	10.70 ± 4.13	2.17%	0.000	420.80 ± 111.01	3.90 ± 2.05	0.97%	0.000
	1400	505.64 ± 189.44	3.43 ± 3.41	0.67%	0.000	416.99 ± 110.17	0.10 ± 2.40	0.05%	0.513
	1600	498.05 ± 187.19	-4.15 ± 4.03	-0.90%	0.000	414.19 ± 110.01	-2.71 ± 2.26	-0.66%	0.000
laser model		502.21 ± 188.75				416.90 ± 110.95

P-value: Mean crown-root fusion model volume/surface area vs. mean laser model volume/surface area

As shown in Table 2, compared with the volume of the laser-scanned model, the CBCT reconstructed tooth models showed a volume difference of 5.97–91.31 mm³ (1.22–19.07%) and a surface area difference of -0.82-32.36 mm² (-0.18–7.78%). For the recommended tooth segmentation threshold “1200” in the Mimics software, its volume caused amplification errors of 6.25% and 12.78% at 0.15 mm voxels and 0.3 mm voxels, respectively, and the amplification errors in surface area were 2.34% and 4.84%, respectively. Table 3 shows the results of the crown-root fusion model. After the crown-root fusion of the CBCT and IOS models using the “curvature-based continuum algorithm”, the volume difference of all models was reduced to -4.15-42.82 mm³ (-0.90-8.77%), and the surface area difference was reduced to -2.71-16.52 mm² (-0.66-4.15%).

As shown in Fig. 4, in both the CBCT reconstruction and crown-root fusion groups, differences in volume and surface area increased with increasing voxel size and decreased with increasing threshold. However, the differences within the two groups were not consistent: under the same voxel conditions, the CBCT group showed a significant volume deviation for every 200 threshold increases (P < 0.05), whereas the crown-root fusion group showed a significant volume deviation for every 400 threshold increases, suggesting that the error associated with threshold selection was reduced. Under equivalent threshold conditions, volume differences in the CBCT reconstructions and crown-root fusion models were greater in the 0.3-mm voxel group compared to the 0.15-mm group (P < 0.05).

Fig. 4.

Differences in model volume and surface area for different thresholds, voxel CBCT reconstruction and crown-root fusion

When comparing intergroup differences between CBCT reconstructions and crown-root fusion groups, the volume difference (P = 0.07) and surface area difference (P = 1) were not statistically significant for the 0.15-mm voxel and 1600 threshold condition. For other voxel sizes and identical threshold parameters, model errors were smaller after crown-root fusion than in CBCT reconstructions (P < 0.05).

Linear measurement

The mean crown widths reconstructed by CBCT at voxel sizes of 0.3 mm and 0.15 mm were 7.87–8.11 mm and 7.73–7.91 mm, respectively, while the root lengths were 14.07–14.41 mm and 13.96–14.24 mm, respectively. Compared with laser-scanned models, the linear errors for the crowns reconstructed by CBCT at voxel sizes of 0.3 mm and 0.15 mm were 0.32–0.56 mm (4.42-7.69%) and 0.18–0.36 mm (2.47-4.97%), respectively; the linear errors for the roots were − 0.03–0.31 mm (-0.21-2.26%) and − 0.14–0.14 mm (-1.02-1.03%), respectively (Table 4). The errors in the 0.3 mm voxel group were significantly larger than those in the 0.15 mm voxel group (P < 0.05).

Table 4.

Crown width and root length measurements of CBCT reconstructed tooth models under different voxel and threshold conditions

Voxel size (mm)	Thresholds (HU)	Crown width				Root length
		Mean Width ± SD(mm)	Difference ± SD(mm)	Deviation(%)	P-value	Mean Width ± SD(mm)	Difference ± SD(mm)	Deviation(%)	P-value
0.3 mm	800	8.11 ± 1.49	0.56 ± 0.08	7.69%	0.000	14.41 ± 1.76	0.31 ± 0.09	2.26%	0.000
	1000	8.04 ± 1.49	0.49 ± 0.08	6.74%	0.000	14.32 ± 1.76	0.22 ± 0.07	1.58%	0.000
	1200	7.98 ± 1.49	0.43 ± 0.08	5.91%	0.000	14.25 ± 1.77	0.15 ± 0.07	1.08%	0.000
	1400	7.93 ± 1.49	0.38 ± 0.08	5.18%	0.000	14.15 ± 1.76	0.05 ± 0.08	0.39%	0.000
	1600	7.87 ± 1.47	0.32 ± 0.09	4.42%	0.000	14.07 ± 1.76	-0.03 ± 0.08	-0.21%	0.000
0.15 mm	800	7.91 ± 1.49	0.36 ± 0.07	4.97%	0.000	14.24 ± 1.76	0.14 ± 0.05	1.03%	0.000
	1000	7.87 ± 1.49	0.31 ± 0.06	4.32%	0.000	14.18 ± 1.76	0.08 ± 0.05	0.56%	0.000
	1200	7.82 ± 1.49	0.27 ± 0.06	3.66%	0.000	14.12 ± 1.77	0.02 ± 0.05	0.14%	0.000
	1400	7.78 ± 1.49	0.22 ± 0.06	3.06%	0.000	14.03 ± 1.76	-0.07 ± 0.07	-0.5%	0.000
	1600	7.73 ± 1.49	0.18 ± 0.06	2.47%	0.000	13.96 ± 1.76	-0.14 ± 0.09	-1.02%	0.000
laser model		7.55 ± 1.50				14.10 ± 1.76

P-value: Mean crown width/ root length of CBCT model vs. mean laser model

As shown in Fig. 5, for the same voxel size, the differences in linear magnification gradually decreased with increasing threshold values (every 400), demonstrating statistically significant differences among the groups (P < 0.05).

Fig. 5.

Linear measurement differences for different threshold, voxel CBCT reconstruction models

Geometric variation

As shown in Fig. 6, under identical threshold conditions, except for the fusion model, the RMS of the 0.3-mm voxel at the 1600 threshold did not differ significantly from that of the 0.15-mm voxel (P = 0.505). The RMS in the CBCT group and other fusion groups at the 0.15-mm voxel was smaller than in the 0.3-mm voxel group (P < 0.05). Within each group, there was a significant decrease in RMS with increasing segmentation threshold (P < 0.05). Furthermore, the RMS of models after crown-root fusion was significantly smaller than those of CBCT reconstruction models under identical voxel and threshold conditions (P < 0.05) (See Table 5).

Fig. 6.

Mean RMS for different thresholds, voxel CBCT reconstruction and crown-root fusion

Table 5.

RMS measurements of the CBCT model and crown-root fusion model compared to the laser model

Voxel size (mm)	Thresholds (HU)	Mean RMS ± SD(mm)
		CBCT model	Crown-root fusion model	P-value
0.3 mm	800	0.2408 ± 0.0210	0.0945 ± 0.0207	0.00
	1000	0.2091 ± 0.0227	0.0787 ± 0.0183	0.00
	1200	0.1781 ± 0.0156	0.0677 ± 0.0185	0.00
	1400	0.1502 ± 0.0132	0.0595 ± 0.0149	0.00
	1600	0.1269 ± 0.0125	0.0467 ± 0.0141	0.00
0.15 mm	800	0.1430 ± 0.0141	0.0749 ± 0.0130	0.00
	1000	0.1170 ± 0.0100	0.0610 ± 0.0097	0.00
	1200	0.0952 ± 0.0086	0.0471 ± 0.0101	0.00
	1400	0.0773 ± 0.0074	0.0407 ± 0.0092	0.00
	1600	0.0691 ± 0.008	0.0359 ± 0.009	0.00

(P-value: RMS of CBCT model vs. RMS of crown-root fusion model)

Figure 7A visualizes the error distribution of the tooth models reconstructed by CBCT under different conditions. As can be seen from the figure, the red part is more concentrated in the crown region, and the red area of the tooth model reconstructed with 0.15 mm voxel is significantly less than that of the 0.3 mm group. As the threshold increases, the red areas tend to decrease, and in the 0.15 mm voxel group, when the threshold increases to 1600, more blue areas appear on the root surface of the tooth, which produces a reduced error.

Fig. 7.

The colorimetric map of the tooth model with different voxels and threshold conditions after alignment with the laser scanning model: A and B show CBCT reconstruction models; C and D show crown-root fusion models

The tooth models resulting from the integrated fusion of intraoral scanner (IOS) crowns and CBCT roots using a curvature stitching algorithm with second-order derivative continuity exhibited smooth transitions at the crown and root junctions. The fused model predominantly displayed green in the crown region, with errors primarily occurring in the root region (Fig. 7B).

Discussion

This is an in vitro validation study in which we demonstrate the importance of voxel size and threshold selection on reconstruction accuracy and validate the accuracy of CBCT with IOS fusion models under various conditions by analyzing measured data from 32 isolated teeth under different scanning and reconstruction conditions. Increased voxel resolution significantly improves the accuracy of CBCT reconstruction models and crown-root fusion. Threshold selection also significantly affects model accuracy. Crown-root fusion reduces errors associated with voxel and threshold selection, enhancing overall model accuracy.

The voxel size is the smallest segmentation unit in 3D space. According to the partial volume effect theory, a voxel unit in 3D space can only display a single density value [19]. If there is only one object within a voxel, it will reflect the density of that object. However, if the voxel contains 2 objects with different densities (e.g., teeth and air/soft tissue), the voxel reflects the average of the densities of the two objects rather than the actual density of either. As a result, the edges of the CBCT-reconstructed tooth model will contain such artifacts, which may result in a larger tooth volume. Our study shows that smaller voxels (0.15 mm) provide higher spatial resolution, which improves the reconstruction accuracy of tooth models. This is consistent with previous findings. Ye et al. [5], using laser scanning as the gold standard, found that tooth volume measurements increased with larger voxel sizes during CBCT scanning. Ting Dong et al. evaluated different voxel sizes for the accuracy of CBCT in detecting alveolar bone defects and showed that the 0.2 mm voxel size had almost the same high diagnostic value as the 0.125 mm voxel size, but the 0.4 mm voxel size was not sufficiently clear to accurately detect the bone defects [20]. Van et al. reported that CBCT produced a magnification error of 7–9% in detecting buccal bone dehiscence in the mandibular anterior region, with the bias increasing as voxel size increased [4]. However, smaller voxels require higher radiation exposure and longer scanning times [21]. Thus, voxel size selection should balance CBCT scanning accuracy, clinically acceptable error levels, and radiation dose in clinical settings.

Threshold settings are likewise critical for CBCT reconstruction accuracy. Computed tomography uses Hu as its unit of measurement to indicate the X-ray absorption of tissue [22]. However, there are few studies on the relationship between threshold value and tooth reconstruction accuracy. Since HU values from CBCT systems vary among manufacturers, we first scanned water and air to obtain values close to those of conventional CT [23, 24], providing a reliable basis for setting tooth tissue thresholds. Mimics software, widely used for medical image processing, recommends segmentation thresholds based on tissue density, but its accuracy for teeth has not been evaluated. We tested five thresholds, including the recommended “1200,” for tooth model reconstruction. Our results indicate that CBCT reconstruction errors decrease as threshold values increase. Notably, we found that errors in the crown region were larger than those in the root region under the same threshold conditions, suggesting that the optimal segmentation threshold for crowns should be larger than that for roots. This may result from differences in partial volume effects due to the density variations between enamel and cementum. Our findings suggest that a global threshold is unsuitable for high-precision tooth models, and CBCT data should be optimized based on different tooth parts to achieve high-quality models. This is consistent with the study by Bing Fang et al., who demonstrated that threshold settings significantly affect mandibular reconstruction [25], and that each voxel size corresponds to a different optimal segmentation threshold. In Ye et al. ‘s study, they found that CBCT produces an amplification error of 18.27%- 43.92% by comparing CBCT with laser scanning model, which is larger than our measurements, probably because they used the same Hu threshold as water (lower threshold) for tooth segmentation and reconstruction, which amplified the actual error of CBCT [5] .

With the continuous development of artificial intelligence, CBCT tooth reconstruction has transitioned from a traditional digital process to an intelligent one. Convolutional neural networks (CNN) and other deep learning methods have been widely adopted in this field [26, 27]. However, due to the lack of large-scale in vivo CBCT datasets and corresponding real-world data (such as laser scanning or micro-CT), automated segmentation methods still rely on a significant amount of high-quality manually annotated data for training, with manual segmentation results serving as the reference standard for accuracy evaluation [16, 28, 29]. During the manual annotation process, clinicians typically select thresholds based on their personal experience for tooth reconstruction. However, there is often a discrepancy between the manually segmented results and the true values [17], which can lead to a potential overestimation of segmentation accuracy. Therefore, despite the advancements in artificial intelligence, evaluating the impact of threshold settings on CBCT tooth reconstruction remains crucial.

In this study, we used a curvature stitching algorithm based on second-order derivative continuum in Geomagic software. This approach constructs a naturally transitioning morphology in the junction zone after segmenting and clipping 3D crowns and roots from different data sources. In a previous study, Zhao et al. initially validated the feasibility of this method only by subjective scoring by senior dental clinicians [13]. In our study, by comparing with the laser scanning model, the results showed that this method significantly improved the overall model accuracy and reduces the errors caused by voxel size and threshold selection.

In this study, laser scanning was used as a reference standard. In previous studies microcomputed tomography and laser scanning in often used as reference standards. Although micro-computed tomography provides superior reproducibility [30], it was unable to fulfill the requirement of control variables in this study because it also requires selection of thresholds for model reconstruction. Laser scanning, on the other hand, requires less time while providing 20 mm accuracy. Lemos et al. assessed the reliability of measurements of digital casting models scanned in a 3Shape R700 scanner and found that laser scanning was reliable in generating digital versions of physical models [31]. Therefore, laser scanning rather than micro-computed tomography was used as a reference in this study.

For CBCT tooth segmentation and reconstruction, selecting a higher threshold than the 1200 HU recommended by Mimics software ensures greater overall model accuracy. In the case of crown-root fusion, considering that the crown of the CBCT is replaced after fusion, the selection of thresholds should be in favor of “root reconstruction”. Thresholds of “1600” for 0.3 mm voxels and “1400” for 0.15 mm voxels were found to be more suitable. If the recommended thresholds of the Mimics software are selected directly, a certain magnification error will be generated. In clinical practice, excessive magnification errors may lead to inappropriate restorations, biased guide fabrication, and inaccurate root reconstruction that may affect root canal treatment, as well as errors in arch crowding measurements and orthodontic root resorption measurements, which may affect clinical decision-making. It is worth mentioning that there is no consensus on the clinically acceptable accuracy limit, which may vary depending on the specific dental clinical application. Some researchers have reported that the error in restorative dentistry should be less than 120 microns [32]. Whereas, in orthodontic treatment, the American Board of Orthodontics states that a difference of up to 500 μm is acceptable [33]. This can be achieved through appropriate threshold selection or crown-root fusion, which helps reduce radiation dose to patients.

While this study yielded meaningful findings, certain limitations must be acknowledged. Firstly, CBCT image quality is influenced by various factors such as tube voltage, tube current, field of view (FOV), and metal artifacts. To control extraneous variables, the study was conducted under ideal in vitro conditions, which do not fully replicate clinical scenarios including patient movement and surrounding tissue interference [34]. However, in a clinical setting, soft tissues and bone would affect threshold selection and segmentation outcomes. Future in vivo studies are necessary to fully evaluate the influence of these structures on CBCT tooth reconstruction and segmentation accuracy. Secondly, although this study calibrated the thresholds and utilized various voxel and threshold settings, further validation across different CBCT device types is required for practical clinical applications. Caution should be exercised when adopting the threshold selections recommended by this study. The sample size, though statistically representative, requires further validation with a larger clinical sample. Finally, although the fusion method employed commercially available software for ease of use, the process still involved manual data processing, which is time-consuming. Future developments should aim for a fully automated fusion algorithm.

Conclusion

In this study, we systematically evaluated the impact of different voxel sizes and threshold settings on the accuracy of CBCT-reconstructed tooth models and explored the accuracy of models after fusion with IOS data. Comparison with the “gold standard” laser scan revealed that models reconstructed using the optimal tooth tissue segmentation threshold recommended by Mimics software still exhibited significant magnification errors. Our results suggest that using smaller voxel sizes or appropriate threshold settings can significantly enhance the accuracy of CBCT tooth reconstructions, providing a useful reference for manual segmentation. Furthermore, we validated a multimodal data fusion method based on curvature stitching algorithm, which achieved a seamless transition at the crown-root junction and significantly improved the overall model accuracy. Future studies should focus on optimizing automatic fusion algorithms and validating their effectiveness with larger clinical samples to advance the development of dental 3D imaging technology.

Abbreviations

CBCT

Cone-beam computed tomography

3D

Three-dimensional

IOS

Intraoral scanning

ICP

Iterative Closest Point

FOV

Field of view

HU

Hounsfield units

CNN

Convolutional Neural Networks

Author contributions

YS.Z led the primary study and drafted the manuscript. YX.L and TQ.L assisted in data acquisition. JH.Z and PY.L conducted data analysis, interpretation, and visualization. DX.L designed the main study framework and revised the manuscript. All authors read and approved the final manuscript.

Funding

This study was supported by the National Natural Science Foundation of China (81571010) and the Science and Technology Bureau of Jinan City (202228102).

Data availability

The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.

Declarations

Ethics approval and consent to participate

This study was approved by the Ethics Committee of Stomatological Hospital, Shandong University. Informed consent was waived by the ethics committee as the dental tissue samples used in this study were obtained from cadaveric donors. All related experiments were conducted in strict accordance with relevant guidelines and regulations.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.