# Estimation of Distances in 3D by Orthodontists Using Digital Models
### VR and the Evaluation of Distances  
Although the use of digital models has increased greatly, there are still a number of unresolved questions when it comes to comparisons with real-life models. In particular, to ensure that the applications developed in Virtual Reality are efficient, it is important that the spatial properties of the virtual environment are perceived with precision. This finding is even more important when the actions performed in VR are supposed to be transferred to the real world. If the actions carried out in VR require recalibration in the real environment, this will lead to an increase in training and cost [18].  
In this framework, research indicates that distance [19; 20; 21; 22; 23; 24; 25] and size [18; 26; 27; 28] are underperceived in VR, in contrast to relatively accurate perception in the real world. [PERSON] and [PERSON] [29] realized a review of 14 independent studies that examined distance estimation in immersive virtual environments [23; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41]. They showed that the estimation of distances in immersive VEs were, on average, only 71% \(\pm\) 8.2 of the modeled distance.  
As pointed out by [PERSON] and [PERSON] [29], although the causes of distance compression in immersive VEs were not fully understood [39; 42], several recent investigations documented experimental manipulations that can attenuate or alleviate it. These manipulations include (a) asking users to estimate distances in a known familiar environment [32];  
Figure 1: Plaster and 3D digital orthodontic working models.  
but see [23], (b) presenting the environment on a large projection screen instead of an HMD [35], (c) providing users with explicit feedback about their distance errors [36], and (d) providing users a brief period of interaction with the environment before having them make distance judgments [34; 43].  
Other authors show that the task used can eliminate this effect of compressing distances in VR. For example, [PERSON]. [44] used an affordance judgment task and observed conservative answers or overestimation in both real and virtual environments. The methodology used by these authors involves a verbal indication that a particular action can or cannot be performed in a viewed environment. The results show that this type of VR task, which consists in deciding whether elements present in the environment are relevant to carry out a given action, gives estimates much closer to reality than the simpler and more passive tasks of size or distance estimate.  
Indeed, in the study of [45], a task was carried out in two environments: a poor cue one with limited background cues and a rich cue one with textured background surfaces. The results show that the richness of the environment improves the estimation of distances and size of objects in a VR task.  
All these studies show that the estimation of distances in a virtual environment is a complex problem, which depends on many parameters such as the more or less immersive nature of the environment, the familiarity with the environment, the more or less realistic character of the presented objects, the type of task to be performed (passive or actually actions to be performed), etc.  
As we have indicated, in the medical field of orthodontics, distance estimation is at the center of the diagnosis and therapeutic follow-up of patients. The accuracy of these estimates is, therefore, a crucial issue from a quality-of-care perspective. [PERSON] et al. [46] published a study in which 69 orthodontists had to estimate, from 108 plaster molds, different variables, which included all the variables usually estimated by an orthodontist. The values were compared to the actual values measured with calipers. The results obtained revealed a statistically significant correlation between the objective measurements and the estimations carried out by the orthodontists. However, very few studies were carried out on virtual models, which are now widely used by professionals.