# Intra-oral 3D Scanning for the Digital Evaluation of Dental Arch Parameters
## 1 Introduction  
Dental arch analysis forms an essential tool in examination of stomatalogical disorders and their treatment. Plaster casts have been used for many years and are now often replaced by digital models [1, 2] that are constructed from magnetic resonance (MRI) records and intra-oral scanners [3, 4, 5, 6, 7]. Digital models introduced in late 1990s overcome several limitations of traditional plaster models that can be easily damaged, require time for model fabrication, and space for their storage [8].  
The use of different sensors is essential for acquisition of digital models to estimate dental arch parameters or to print separate three-dimensional (3D) objects using 3D printers [9]. This modern interdisciplinary approach assumes a combination of knowledge from dentistry [10], optics [11], engineering [12], biomechanics [13], information technologies [14, 15], and material sciences. Using digital technologies, orthodontists can more accurately analyze dental problems, their treatment, more precisely specify the refabrication tasks, and collaborate with further specialists as well.  
Main types of dental scanners are based upon the mechanical principle with a touch-probe or more preferred contactless light scanners [8]. Figure 1 presents an example of such intra-oral scanner [11; 16; 17; 18] that we used for data acquisition and for construction of a 3D digital model of the lower and upper dental arches. Each scanning device includes a handheld camera that is used to collect surface data inside the mouth region and a computer system to process, analyze and visualise the resulting 3D model. Either laser or white light is used for illumination of scanned area and its reflection is acquired by the sensor in the wand.  
Scanning technologies [19; 20] affect the measurement speed and accuracy [21]. The most common include [19] triangulation using laser light [22], parallel confocal imaging [23], or fringe interferometry [24] based upon projection of light patterns.  
Data acquired are processed by different imaging technologies [5; 19] and mathematical methods for object surface construction. The following analysis of digital dental models assumes the application of image processing methods, geometrical modelling [25], data denoising methods [26; 27], morphological operations, image registration and statistical evaluation of results. The analysis of different intra-oral scanners [2; 28] together with the application of mathematical methods for data processing, their visualization and evaluation contribute to their efficient use in stomatology [17].  
In the context of medical imaging, image registration allows comparison and analyses of images taken at different times (multimemporal analysis), from different viewpoints, with different image acquisition devices (multimodal analysis; e.g., MRI and CT) or with different patient positions. In medicine, registration is required to monitor tissue evolution in time, for treatment verification, in surgery, and so on. These methods are also very important in dentistry to compare images of dental arches taken at different times.  
The present paper is devoted to data acquisition recorded by an intra-oral scanner working on a contactless measurement basis and presented in Figure 1. A set of 20 records from one patient formed the database for the evaluation of dental arch parameters and for the estimation of their accuracy. To increase the reliability of the measurement, electronic dental arch models were rotated into the specific dental planes defined by the tops of individual teeth. This approach allowed a more precise comparison of dental arch changes [14] for separate scans.  
Figure 1: Principle of 3D intra-oral scanning (using a handheld camera and a computer system) device (Trios/3 shape) for data acquisition and for the 3D model construction: (**a**) 3D scanning; (**b**) Data processing steps.