# Estimation of Distances in 3D by Orthodontists Using Digital Models
## 4 Discussion  
The objective of our study was to find out if, for seven variables of interest, the estimation of distances carried out on numerical models was significantly different (or not) from the real distance (here, reduced to the value 0). For the variables whose estimates were significantly different from the real distance (comparison between the measurements carried out by the practitioners and the theoretical mean of 0), we also checked whether this difference between the estimates and the real value was greater than 1 cm (comparison between the measurements made by practitioners and the theoretical average of 1). Of the seven variables studied, three were associated with distances estimated to be significantly greater than the real distance, and for one variable, the difference was greater than 1 cm. These results question the reliability of the use of numerical models for decision-making, in particular in borderline cases. The relevant elements for this discussion are the difference in the estimation of distances between virtual and real models, the way in which our results can be discussed in the light of the work on the estimation of distances in virtual environments, and the perspectives of this study as part of further investigations. The results obtained in the study by [PERSON] et al. (2016) on real models revealed a statistically significant correlation between the objective measurements and the estimates made by orthodontists for all the variables (the same variables as those used in our study). Thus, with only the virtual model (i.e., other than a situation where the practitioner can manipulate real physical models), the estimate was less reliable for four of the seven variables, in particular the estimate of the mandibular crowding. The results of our study are in keeping with the various studies in the literature regarding the estimation of distances in a digital environment in terms of the presence of bias in the estimation of distances in a virtual environment ([PERSON] et al., 2016; [PERSON] et al., 2017; [PERSON] et al., 2018; [PERSON] et al., 2019; [PERSON] et al., 2019). In terms of crowding of the mandibular arch, which is the amount of space required for proper alignment of the teeth on the arch, this is the variable estimated in the least precise way. One of the explanations could be the difficulty for the practitioner to perform a three-dimensional mental reconstruction from the virtual model to estimate the space required for aligning the teeth from the malposed teeth. It is of particular interest to note that it was in case no. 5 that the accuracy was less good, that is to say, where the estimation of the crowding requires reconstitution of the shape of the arch based on the initial malpositions that were substantial before estimation of the lack of space for alignment of the teeth on the arch. For this particular case, the performance of the practitioners was particularly poor, with a relatively large standard deviation (\(\sigma=7.47\)), while the value of the variable was low (Table 2). The large standard deviation between the estimated value and the actual value in case no. 5 can be explained by the study by ([PERSON] et al., 2017), who showed the difficulty of maintaining attention and, therefore, the efficacy of the process beyond a certain degree of complexity of a 3D image. This appears to be illustrated by the difficulty of the estimation of the crowding. Future work should also study the role of calibration. This is a very important point. The contribution of calibration to visual perception in VR has been established by numerous works ([PERSON] et al., 2016; [PERSON] et al., 2017; [PERSON] et al., 2017). For example, Ref. ([PERSON] et al., 2017) showed the effects of calibration to visual and proprioceptive information on near filed distance judgments in 3D user interface. One method of calibration that could be experienced would allow viewing the error that they made on the different estimation of distance, and they allow the participant to correct the response.