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J Dent Res 82(6): 438-442, 2003
© 2003 International and American Associations for Dental Research

RESEARCH REPORT
Biomaterials & Bioengineering

Accuracy of a System for Creating 3D Computer Models of Dental Arches

R. DeLong1,*, M. Heinzen1, J.S. Hodges2, C.-C. Ko1, and W.H. Douglas1

1 Minnesota Dental Research Center for Biomaterials and Biomechanics, Department of Oral Science, University of Minnesota School of Dentistry, Moos Health Science Tower, 515 Delaware Street SE, Minneapolis, MN 55455; and
2 Division of Biostatistics and Oral Health Clinical Research Center, Department of Preventive Sciences, University of Minnesota;

*corresponding author, delon002{at}tc.umn.edu


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS & METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Three-dimensional imaging of dental tissues will have a major impact in dentistry if the images are accurate. The purpose of this study was to measure the accuracy and precision of a system for creating three-dimensional images of dental arches. Using vinyl polysiloxane impression materials and improved dental stone, we made 10 stone casts of a "dental" standard with known dimensions. The impressions and casts were scanned by means of a Comet 100 optical scanner. Custom software created three-dimensional images (computer models) from the scanned data. Accuracy was defined as the average of the absolute differences between the computer models and the standard. Precision was the standard deviation of accuracy over 10 repeated measures. Software processing improved the accuracy of the scanner data. Accuracy ± precision for the casts and impressions was 0.024 ± 0.002 mm and 0.013 ± 0.003 mm, respectively. The system produced computer models with sufficient accuracy for clinical application.

KEY WORDS: accuracy • precision • computers • three-dimensional • impressions • stone replicas


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS & METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Three-dimensional digital imaging will have a major impact on clinical dentistry in the near future. Interactive three-dimensional images of the soft and hard tissues of dental patients (Virtual Dental Patients) will provide quantitative evidence to aid dentists in diagnosis, treatment planning, and outcome assessment. Before this can occur, however, these images must be shown to be accurate representations of the patients. This study is a first step in measuring image accuracy by creating 3D computer models of simulated dental arches.

If these accuracies are not met, the clinical result is compromised; however, clinical accuracy requirements vary for different chairside and laboratory dental procedures. Possibly the most stringent accuracy requirements are for interocclusal contacts, because most dental patients are sensitive to 0.020-mm changes in their occlusal anatomy (Jacobs and van Steenberghe, 1994; Karlsson and Molin, 1995). Accuracy becomes a critical test when an image of a patient is rendered in a computer virtual environment, and it is what differentiates a Virtual Dental Patient from a cartoon image of a patient. Indeed, many graphical renditions of dental tissues, which appear realistic, would prove to be totally unreliable for prognosis and treatment planning.

Accuracy describes how well a measurement reproduces the "truth", which can be a calibrated standard. Creating computer images of dental tissues requires scanning the tissue surfaces or, more frequently, casts of the tissue surfaces. Scanner accuracy depends on the angle of the surface to the scanner (Hewlett et al., 1992). Therefore, determining the image accuracy for dental tissues requires a standard that provides oblique surfaces similar to those of the dental anatomy.

The purpose of this study was to measure the accuracy of hardware and software tools of the Virtual Dental Patient (VDP) at each step of the sequence from standard to image creation. If the VDP’s accuracy meets clinical requirements, then there is greater confidence that the VDP truly represents its clinical original.


   MATERIALS & METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS & METHODS
RESULTS
 DISCUSSION
 REFERENCES
 
The VDP system for creating three-dimensional computer images of dental arches has four steps: (1) Make impressions of the tissues, (2) make stone casts from the impressions, (3) scan the casts, and (4) process the scan data. Errors introduced at each step were measured against two standards: a "dental" steel standard and a quality stone cast of this standard. This follows traditional procedures, where the patient is the primary standard and the working cast is a secondary standard.

The steel standard was constructed with the use of 7 Grade 25 precision ball bearings (diameter 9.522 ± 0.001 mm) seated in a stainless steel arch (Fig. 1Go, upper left). Bearings 1, 4, and 7 defined an "occlusal" plane. The remaining 4 bearings were offset from this plane in steps of 0.025 mm. The stone standard replicated the steel standard. Both standards were calibrated with 95% confidence by a calibration service (QC Inspection Services, Inc., Burnsville, MN, USA) using a coordinate measuring machine (CMM). This was the only physical measurement made. It provided the center coordinates and radius of each sphere along with their associated errors. Because the geometry was closely controlled, mathematical models could be made of the two standards. The mathematical models provided point coordinates in a format that could be inserted into the VDP software for comparison with scanned images of the standards. From the CMM’s calibration errors and the law of propagation of errors (Mandel, 1964; Brunette, 1996), the errors of the steel and stone mathematical models were determined to be ± 0.008 mm and ± 0.009 mm, respectively (see Appendix, www.dentalresearch.org).



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  		Figure 1. Block diagram of the experimental method. Three-dimensional computer models were created in a clinically relevant four-step process: (1) make impression, (2) pour cast, (3) scan cast, and (4) process the scan data. Accuracy of the computer models and error introduced at each step were measured according to four physical models: a steel "dental" standard, impressions of the steel standard, and a stone standard and stone casts made from the impressions. The steel and stone standards were measured independently by means of a coordinate measuring machine (CMM). Mathematical computer models of the standards were created from the CMM measurements. Measurement parameters with dental relevance were also calculated from the CMM measurements. Computer models of the stone standard, impressions, and casts were created with custom software that processed data from an optical scanner. Model accuracy and errors introduced at each step in the model creation process were calculated by comparison of the impression, cast, and stone standard computer models with the mathematical computer models. Comparing VDP-calculated parameters with those calculated by the CMM measurements determined the accuracy of the VDP software measurement tools.

 
Eleven impressions of the steel standard were made with disposable impression trays (SmartPractice, Phoenix, AZ, USA), vinyl polysiloxane impression putty (Express STD, 3M ESPE, St. Paul, MN, USA), and an experimental scannable vinyl polysiloxane impression material (Digisil SBR #123948 113; 3M ESPE) in a two-step process. A single stone cast was made from each impression, with the use of white improved dental stone (FujiRock; GC Europe, Leuven, Belgium). The stone cast with the fewest imperfections was selected as the stone standard. The remaining 10 impressions and 10 casts were used to measure the accuracy and errors of Steps 1 and 2.

A Comet 100 optical digitizing system (Steinbichler Optical Technologies, Neubeuern, Germany) scanned the stone standard, casts and impressions. The Comet 100 has a point accuracy of ± 0.040 mm and a resolution (point-to-point distance) of 0.130 mm in X and Y and 0.005 mm in Z (parallel to the line-of-sight of the Comet). Objects were scanned from 20 different views that, when combined, defined the three-dimensional surface of the object. Total time to scan 20 views was 20 min. Because of its mirror-like surface, the steel standard could not be scanned directly; therefore, the stone standard was used to measure scanner (Step 3) and data processing (Step 4) accuracy and errors (Fig. 1Go).

Creating computer images (computer models) from scan data required filtering the data, aligning the individual views by means of PolyWorksTM (InnovMetric Software, Quebec, Canada), and merging the individual views into a single data file (DeLong et al., 2002). All computer models were rendered as three-dimensional surfaces and analyzed by means of the VDP software. (The filtering, merging, and VDP software were developed in the Minnesota Dental Research Center for Biomaterials and Biomechanics, Minneapolis, under NIH/NIDCR grant R01 DE12225. For more detail, see http://web.dent.umn.edu/vdp2002.)

Four basic computer model types were created: mathematical (steel and stone mathematical standards), stone standard (unprocessed and processed), impression, and cast. The unprocessed stone standard data were used to measure the scanner accuracy (Step 3). To measure effects of data processing on accuracy (Step 4), we processed the stone standard data in three ways: (1) merging only, (2) aligning plus merging, and (3) filtering, aligning, and merging. We measured error introduced by the object’s position in the scanner by scanning the stone standard in different mounting locations. Ten replicates were made for each computer model type. The impression computer models are positive replicas of the steel standard, where the computer "poured" the model.

Computer models are the working tools of the VDP software. Quantitative comparisons for accuracy can be determined for any point on the model’s surface, which provides the clinician with the ability to locate the sources of inaccuracies. Accuracies were determined relative to the standards for four parameters chosen for their dental relevance: (1) surface anatomical point, (2) distance from the "occlusal plane", (3) distance between two points on the surface (resembles tooth-to-tooth distance), and (4) absolute distance between two models.

Accuracy was defined as the average difference between the VDP measurement and the standard. Precision (error) was defined as the standard deviation of accuracy over repeated measures. The CMM sphere center coordinates and radii were used to compute coordinates for the point on each sphere closest to the plane defined by spheres 1, 4, and 7, the distances between the sphere centers, and the distances of the four offset spheres from the plane. Corresponding coordinates and distances were calculated for the stone standard, impression, and cast computer models, with the use of VDP software tools (see Appendix, www.dentalresearch.org). The computer and standard mathematical models were aligned to each other by means of the VDP surface registration algorithm (see Appendix, www.dentalresearch.org). The absolute distance from each point of the computer model to the mathematical model was calculated after the surfaces were aligned to each other.


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS & METHODS
 RESULTS
DISCUSSION
 REFERENCES
 
Mean differences between the computer models and the standards were the same order of magnitude as the standards’ intrinsic errors (Tables 1 and 2GoGo). Although this was very encouraging, it required that the errors of the standards be included in the final calculation of parameter accuracy, PAccuracy. This was done by calculating the mean squared error:

where PBias is the mean difference between the computer models and the standard for the parameter, {sigma}Standard is the standard parameter error calculated by the error propagation theorem (see Appendix, www.dentalresearch.org), and {sigma}Computer is the standard deviation of the differences between the computer model and the standard.


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  		Table 1. Absolute Difference between Computer Models and Mathematical Models (all values in mm)
 

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  		Table 2. Differences between Computer Models and Standards for Distance Measuring Parameters (all values are in mm)
 
Scanner accuracy for a single view was 0.018 ± 0.000 mm; for 20 combined views, it was 0.030 ± 0.001 mm (Table 1Go). Data processing actually improved the model accuracy to 0.013 ± 0.000 mm. The most dramatic improvement came from the alignment of the individual views (0.029 ± 0.002 mm to 0.012 ± 0.000 mm). Other processing steps had little or no effect on the accuracy. Processing standard deviations were all less than 0.002 mm, which showed that the model creation process was very reproducible. Accuracies of the impression models and cast models were 0.013 ± 0.003 mm and 0.024 ± 0.002 mm, respectively. Center-to-center, offset, and point coordinate parameters showed the same trends as the absolute distance parameter (Table 2Go).


   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS & METHODS
 RESULTS
 DISCUSSION
REFERENCES
 
Knowing the truth is difficult, especially when measuring complex surfaces. A standard was constructed with the use of precision steel ball bearings, round to within ± 0.0007 mm. A certified measuring company measured the ball bearing radii and center coordinates in a controlled environment with a calibrated coordinate-measuring machine. Even under these conditions, the accuracies of the steel and the stone standards’ center coordinates and radii could be certified only between ± 0.0019 mm to ± 0.0070 mm, respectively.

The parameters used in this study averaged multiple measures to produce a single value for the parameter. Artificially good results can occur when multiple values measured across a sample are averaged, especially if the sample is symmetric. The net effect is understated data variation. In these cases, ranges of values are helpful; however, ranges defined by the maximum and minimum values may be too severe a test. A smaller range that includes a large percent of the total individual measures will remove poorly scanned points and present a more realistic picture. The standard deviation of parameter values should still be provided as a measure of variation.

Absolute rather than signed distances between the computer and mathematical models were used to measure model accuracy, because surface registration makes the average signed distance between the two surfaces equal to zero. A similar problem occurred with the point coordinates, because the points were symmetrically distributed across the surface. The net effect was that signed coordinate differences averaged to near zero; therefore, absolute differences were used.

Accuracies of the four parameters used in this study are not independent; they are related through the law of propagation of errors. The accuracies of the coordinates of a point on the model surface and the distance from the point to a known reference depend on the accuracy of the computer model at that point. The accuracy of the distance from the point to a second point on the model surface depends on the accuracy of both points. Similar accuracies for the absolute difference, offset, and point coordinate parameters and the decreased accuracy of the center-to-center parameters of stone cast and impression models illustrate this relationship. Parameter ranges showed similar trends.

The best measure of differences between the computer models and the "truth" was the absolute difference between models. Its advantage was that differences were measured at thousands of points across the entire surface rather than at a few points. Because of the large number of measures, contour plots of the differences overlaid on the three-dimensional surface showed regions of high and low accuracy (Fig. 2AGo). Distortions or defects on the scanned surface were easily identified. Ideally, the distributions would be presented along with the mean absolute distance (Fig. 2BGo). If this is not practical, then the range of differences and the percent of total scanned points used to determine the range should be reported.




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  		Figure 2. Distributions of the absolute differences between computer and mathematical models. (A) Contour plots (Range, -0.100 mm to +0.100 mm) of the difference between a stone cast model and the steel mathematical model and the difference between an impression model and the steel mathematical model. Differences are displayed on the mathematical model. The contour plots show large distortions in the stone cast. (B) The absolute distance distribution is a plot of the percent of absolute distances between a computer model and the mathematical model that are less than or equal to a given absolute distance. For example, 90% of the absolute distances between the stone cast model and the steel mathematical model (Stone Cast) are less than or equal to 0.050 mm. The absolute distances between the impression models and steel mathematical model (Impressions) and the absolute distances between stone cast models and the stone mathematical model (Stone Standard) are nearly identical and lie below the Stone Cast curve. Ideally, the slope of the curve would be zero, indicating that the absolute distance between the two surfaces was the same across the entire surface, with a magnitude of zero. Distortions in the stone cast are apparent because its distribution curve compared with the steel mathematical standard lies above the analogous curve comparing it with the stone mathematical standard. The abrupt rise in the last 0.1% of distances represents scanner errors that should be excluded.

 
Accuracy of models created from unprocessed scanned data and multiple views was less than the single-view model accuracy, a result of errors in the angles of rotation used to align the views. After surface registration and data processing, the multi-view model accuracy was better than the single-view model accuracy. The improved accuracy is attributed to the removal of rotation errors and the averaging of data points in the overlapping regions of the different views. Filtering had a minor effect on accuracy because of the small number of points involved; however, it significantly improved the visual quality of the final image. Similarly, merging improved the accuracy only slightly. The primary benefits of merging are the creation of a single data file from multiple data files and a significant reduction in the number of data points, which improves computation speed.

Accuracy of the cast computer models was 0.024 ± 0.002 mm, with 99% of the absolute differences being less than 0.081 ± 0.007 mm. Model accuracy is close to the occlusal sensitivity of the average dental patient (0.02 mm), and is equivalent to the thickness of commonly used contact marking films (Schelb et al., 1985). Accuracy of the impression computer models was 0.013 ± 0.003 mm, with 99% of the absolute differences within 0.041 ± 0.011 mm, which equals the thickness of the shimstock (0.012 mm) used in the clinic to identify contacts. Analysis of these data implies that the accuracies of computer models, especially those made from impressions, are sufficient for clinical application.

In this study, impressions were made under ideal laboratory conditions. In the clinic, biological factors such as tooth movement and operator technique affect the quality of the impressions. Inclusion of biological factors will result in less accurate models with greater variability; however, the magnitude of the effect is not known.

The fact that the impression models were nearly twice as accurate as the stone models is surprising, because the setting expansion of the stone (0.08%) is about half that of addition silicones (-0.15%) (Craig, 1997). One explanation is that, in the two-step impression method, the setting contraction occurs over a relatively thin film of impression material, whereas the setting expansion of the stone affects the entire stone replica.

This study showed that common dental methods of duplicating dental tissues could produce computer models with accuracies equivalent to the measured occlusal sensitivity of patients. Thus, it may be possible to locate occlusal contacts as accurately on computer models as is done in the clinic. The significance of this is that three-dimensional models provide a permanent, quantitative record that can be viewed at any time in the future. Comparing sequential three-dimensional models could identify differences which, like laboratory medicine, could be used to quantify the dental health of the patient and identify problem areas.


   ACKNOWLEDGMENTS
 
This study was supported in part by USPHS Research Grant R01 DE-12225-05 from the National Institute of Dental and Craniofacial Research, National Institutes of Health, Bethesda, MD 20892, and by the Minnesota Dental Research Center for Biomaterials and Biomechanics.


   FOOTNOTES
 
A supplemental appendix to this article is published electronically only at http://www.dentalresearch.org.

Received August 20, 2002; Last revision February 3, 2003; Accepted February 17, 2003


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS & METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Brunette DM (1996). Critical thinking; understanding and evaluating dental research. Chicago: Quintessence Publishing Co, Inc.

Craig GC (1997). Restorative dental materials. 10th ed. St. Louis: Mosby-Year Book, Inc.

DeLong R, Ko CC, Olson I, Hodges JS, Douglas WH (2002). Helical axis errors affect computer-generated occlusal contacts. J Dent Res 81:338–343.[Abstract/Free Full Text]

Hewlett ER, Orro ME, Clark GT (1992). Accuracy testing of three-dimensional digitizing systems. Dent Mater 8:49–53.[Medline]

Jacobs R, van Steenberghe D (1994). Role of periodontal ligament receptors in the tactile function of teeth: a review. J Periodontal Res 29:153–167.[ISI][Medline]

Karlsson S, Molin M (1995). Effects of gold and bonded ceramic inlays on the ability to perceive occlusal thickness. J Oral Rehabil 22:9–13.[Medline]

Mandel J (1964). The statistical analysis of experimental data. Mineola, NY: Dover, pp. 72-77.

Schelb E, Kaiser DA, Brukl CE (1985). Thickness and marking characteristics of occlusal registration strips. J Prosthet Dent 54:122–126.[Medline]




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