Photogrammetry based space analysis measurements in orthodontic diagnosis

Summary Introduction Lundstrom segmental analysis is often used analysis in orthodontic diagnosis. It includes measurements of available and needed space in the arch in order to determine whether there is a lack or excess of space for proper teeth alignment. Measurements are traditionally performed on plaster study models, but with recent developments of computer-based systems, there is an increase in use of digital models in measuring process. The aim of this study was to present a photogrammetry based measurement approach that requires no specialized and expensive hardware and compare results with ones obtained on 3D scanned models. Material and method On 50 plaster study models measurements of 24 teeth, widths of 12 segments and Lundstrom segmental analysis were performed. 3D scanned study models were analyzed in the photogrammetry software Ortho-Photo4D on the set of four photographs of the study model in custom made measurement apparatus. The software corrects for finite distance of the camera and corrects errors due to perspective distortion. Results Statistical analysis performed on obtained measurements provided Bland-Altman plots that strongly suggested high degree of correspondence between the two measurements methods. Discrepancies for maxilla for individual segments were under 0.25 mm with standard deviation of up to 0.16 mm, and less than 1 mm and deviation of up to 0.4 mm for complete arch. For mandible the differences were up to 0.27 mm for segments with 0.15 mm deviation and 0.6 mm for complete arch with up to 0.24 mm deviation. Correlation coefficient was over 0.985 in all cases. Conclusions Both analyzed methods can be equally used in clinical practice.


INTRODUCTION
Orthodontic study models have multiple uses and represent an invaluable part of orthodontic documentation. Aside from clinical examinations, intraoral and extraoral radiographic images, plaster study models represent an irreplaceable diagnostic tool in orthodontic diagnosis. Direct measurements on the study models have advantages, however there are several limiting factors such as: ideal positioning of the measurement tools on the models requires significant time, errors due to involuntary movements of the hand produce errors in results, complicated use of measurement instruments, for example calipers in Korkhaus analysis, as well as issues related to storing, durability and mobility of plaster models [1,2].
In order to determine correct orthodontic and dentofacial diagnosis and plan the treatment, radiological images and functional analyses are used. The aim of these techniques is to correctly replicate or describe anatomical and physiological facts and properly show the 3D anatomy with precision. Photography is one of auxiliary diagnostic methods. Orthodontists routinely use 2D techniques in order to record craniofacial anatomy. Depth of the structure cannot be obtained and localized from 2D images and that is one of their limits. Development of information technologies and widespread use of generating 2D and 3D models that appropriately depict real world objects has lead to using aforementioned technologies in dentistry and orthodontic practice [3,4].
3D modeling is gaining more popularity in orthodontics and in definition of certain orthodontic parameters [5]. Contemporary technologies and more frequent use of computers in orthodontics enabled simulations of orthodontic and surgical interventions that helped patients preparing for surgical procedures [6,7]. A number of diagnostic methods for visualization of face and teeth structures were developed. Currently, most commonly used methods of 3D recording are computerized tomography (CT), cone beam computerized tomography (CBCT), 3D laser and 3D face morphology (3DFM). 3D techniques provide detailed information even in difficult cases in soft and hard tissues [8][9][10][11][12]. Digital models have numerous advantages, from simpler storage, over more efficient exchange of data to automation of certain processes. How-ever, question often raised is whether these models truthfully depict study models orthodontic therapy is based on. Aside from this, real world obstacle to wider use is also the cost of high quality 3D scanners and software packages required for quality work [13,14,15].
Other than 3D scanning, during the measurement process, it is possible to use digital photographs through the process called photogrammetry. Today, photogrammetry implies modeling based on a set of photographs, although the term itself is derived from "measuring from photographs" [16]. Modeling based on photographs through the use of photogrammetry is considered one of the most advanced techniques of image processing that provides accurate data and detailed 3D information. This method allows precision and reliability of data tied to the image and control points (CP) that represent locations of corresponding points in two or more digital images and can be used to connect images. Therefore, there is a requirement of at least two images in order to recreate 3D information through the use of projection and perspective geometry [17]. In order for a set of photographs to be a basis for photogrammetry, there needs to be an overlap between the images. This means that each geometric element that we want to locate must be present in at least two photographs [16,17].
The aim of this paper was to describe an alternative approach in measuring process during space analysis based on the use of photogrammetry in custom developed Or-thoPhoto4D software. This program calculates and corrects errors due to perspective distortion.

MATERIAL AND METHODS
Fifty sets of plaster study models were used in the study. All study models were with permanent dentition, without caries lesions with adequate restorations. In the first phase, the study models were scanned with Steinbichler L3D 5M industrial scanner. We created the software package OP4D shown in Figure 1. The main characteristic of this program is that it is Internet based and as such requires no additional software to be installed, except any Internet browser (Google Chrome, Mozilla Firefox, etc). It is based on 3DHOP package and supports working with digital models in PLY (Polygon File Format / Stanford Triangle Format) and NXS (Nexus) formats [18,19]. The measurement process requires choosing the object we want to measure as well as the type of measurement we want to perform. The system allows an arbitrary number of measurements of the same or different types on any of the objects. Performing different types of measurements enables carrying out multiple analyses, while repeating the same type of measurement allows future studies, such as reliability or repeatability studies. After the measuring is completed, the data were saved to database and stored in JSON format [20]. This format enabled significant flexibility as it had dynamic structure and support presenting data as scalars, vectors, maps and other hierarchical data structures. In the second phase of the study, plaster study models were photographed from the front, left, right and upper side in measurement apparatus that enables simple positioning of the model in required orientations. The camera was mounted on the firm and sturdy tripod and was triggered by a wireless remote in order to minimize accidental movement of the camera during operation. In order to provide sufficient field depth, aperture was set to f/22 and lens was set to focal length of 200 mm. Lighting was provided by 30 × 30 cm white LED source positioned on the left and matte reflecting surface on the opposing side. Light sources were positioned in such way to provide soft and sufficiently uniform lighting of the object while providing enough shadow to detect the details of the model. Additional problems in using photographs in measurements are related to perspective distortion as well as issues with measuring distances not parallel to the imaging plane.
In order to increase the accuracy of measurements, we designed a measurement apparatus that consists of a stand and a model mount, while the measurements were made on the set of four photographs for each model. The stand was permanently fixed to the stable surface and could not be moved relatively to the camera during pho-tographing. It consisted of base plate, back plate and front plate. The base plate was made in such way to allow the operator to position the back and front plates in required locations and facilitate simple placing of the model mount in all four required states. The apparatus contained central marker lines in order to ease proper positioning of the camera. Models were fixed by a screw with rubber top in order to minimize damages to models. Model mount also contained QR codes that denoted the side of the model currently being photographed: T for top, F for front, R for right and L for left. Models were also marked by QR codes that help identifying the model and automating the procedure.
After the model or multiple models have been photographed, the photographs were analyzed and camera parameters derived from photographs in OrthoPhoto4D software. This process consisted of five major steps: 1. Converting photographs to grayscale representation and eliminating chromatic aberrations by using green channel as a base. 2. Identifying QR codes and processing their contents by the Zbar library [21]. This step provides information on distances between markers, photographed side and identification of the model.  For each measurement, the operator has to select corresponding measurement button and one of the two end points, for example 14-13 segment and 14 point. The operator can translate and enlarge the views that are automatically synchronized, in order to select the point in at least two views. As an example, the operator can select the location of the point in "top" and "left" views. This requirement is mandatory in order to locate the point in 3D space and there is insufficient information in location in just one projection. The first selected point is used to calculate two coordinates while the second location is used only for the third coordinate (Z axis in this case). Once the operator locates both ends of the measured length the program will calculate the length in 3D space and display the value  in the value field section. Each completed measurement is denoted by green background color with measurements in progress being red or orange depending on the current phase of measurement. Measurement values obtained on 3D models and photographs were subsequently statistically processed and the mean values and standard deviations were calculated, as well as correlation coefficients and paired t-test. Table 1 contains the results of statistical analysis of the maxilla measurements. Mean value of difference for individual segments was under 0.25 mm with standard deviation of under 0.16 mm while the mean difference for the whole arch was under 1 mm and deviation under 0.4 mm. Correlation coefficient was over 0.98 for each segment and over 0.99 for the arch, while p values of t-test were under required 0.05 in all cases (p<0.0001). Table 2 contains the results of statistical analysis of the mandible measurements. In this case, the mean value of difference for individual segments was under 0.27 mm with standard deviation under 0.15 mm while the mean difference for the whole arch was under 0.6 mm and deviation was under 0.24 mm. Correlation coefficient was over 0.98 for each segment and over 0.99 for the whole arch. Except in the case of 43-44 segment, the p value of t-test were under required 0.05, while in the case of 43-44 segment the recorded mean difference was under 0.1 mm and clinically insignificant. Images 3 to 6 show Bland-Altman plots for values obtained by both analysed methods [23]. Mean of each pair of measurements is presented on X axis while the difference is plotted on Y-axis. Black line represents mean difference for all samples, while red lines denote two standard deviations above and below the mean. Interval containing 95% of samples is 1.96 standard deviations above and below the mean.

RESULTS
Majority of measurements is concentrated around the mean and falls within the red line interval, regardless of the measured value. Such Bland-Altman plot suggests the high level of correlation between the two measurements methods.

DISCUSSION
Due to the advantages of digitization of the study models, in the recent years the increase of the computer use in dentistry can be observed. In several papers authors present the comparisons of mesiodistal widths of teeth and segments between the plaster study models and digital representations. Two of the most widely used digital representations are 3D scanned models and digital photographs of the models. Available literature contains studies comparing measurements and analyses on study models and their digital surrogates, but there is a notable lack of analyses on indirect values calculated from the measurements. One of such analyses is Lundstrom segment analysis that was presented in this paper. As a set of three individual measurements for each two-teeth segment, width of the each tooth and segment were used, it was required to analyze both individual measurements as well as indirectly calculated values. This is especially significant when working with complete arch since we used a set of 18 individual measurements.
The aim of the study done by Quimby et al. was to determine accuracy, repeatability and efficacy of the measurements made on digital models. Dentoform and plaster models were used as a "gold standard. " Measured parameters were divided into the seven groups, two of which were available and needed width of the segment. They used digital callipers for plaster model measurements and a standard computer mouse to select points on digital models. Measurements were repeated after two weeks. Repeatability was high for both measurements on plaster models as well as on digital models. Efficacy was also similar regardless of the method of measurement. Recorded differences for arch were 0.54 mm for available and 2.23 mm for needed space in maxilla and 2.88 mm for available and 0.21 mm for needed space in mandible. Statistically significant difference was found only in the case of needed space in mandible. Conclusion of the study was that digital models could be used as clinically acceptable alternative to plaster models [24]. Although the authors did not analyze the difference between needed and available space, from the published results one can see that the method presented in our paper has comparable or significantly lower differences and we did not find any statistically significant differences when analyzing complete arches. In the study performed by Leifert et al., the authors compared the measurements done by two orthodontists on mesiodistal widths of the teeth and arch lengths on plaster study models and 3D virtual models. Difference in measurements for missing space in maxilla was 0.424 mm and 0.384 mm in mandible. Paired t-test showed statistically significant differences in measurements in maxilla. It is worth noting that differences between the two orthodontists were up to 0.408 mm and were comparable to differences between the two measurements methods, therefore the study concluded that differences between methods are acceptable in clinical practice [25]. In our case our method has comparable or lower differences with absence of statistically significant difference on analyzed values. Recorded differences for segments of under 0.3 mm are not clinically significant, while discrepancies of under 0.8 mm on the level of arch are also clinically insignificant.
Yoon et al. examined usability of intraoral scanners by comparing measurements obtained on plaster study models and 3D scanned study models. Results were statistically analyzed using paired t-test. One of the observed measurements was the missing space for the whole arch and they obtained differences between plaster and 3D scanned models of up to 0.58 mm for maxilla with statistically significant differences and up to 0.63 mm for mandible also with statistically significant difference. Differences between plaster and intraorally scanned models were up to 0.86 mm for maxilla and 0.55 mm for mandible with statistically significant differences. Authors concluded that recorded differences are not clinically significant and that all three methods can be used in practice, regardless of the severity of crowding [26]. Comparison of these results and results presented in our paper indicates that recorded discrepancies between methods are comparable, with the note of no statistically significant difference being present in our results for complete arches.
Liang et al. examined usability of 3Shape TM D800 scanner in clinical practice by comparing the measurements on digital model and plaster study models. Models were divided into the three groups based on the severity of crowding. Presented results strongly suggested that the use of 3D scanned models in clinical practice is justified since the measurement differences for available and needed space were under 0.3 mm with no significant statistical difference found. Statistically significant difference was found when authors analyzed the results by severity of crowding [27]. Aforementioned conclusions of the authors are in accordance with our findings as our measurements differences for segments fall within the same intervals, while the differences for the whole arch are somewhat larger but still acceptable in clinical practice.

CONCLUSIONS
Measurements performed by presented photogrammetry method are comparable to measurements made on 3D scanned plaster study models. Recorded measurement differences fall within the intervals acceptable in clinical practice with a very high coefficient of correlation and with no statistically significant differences found in Lundstrom analysis for arches. Presented results strongly suggest that the use of the presented method is justified in the diagnosis of orthodontic irregularities.