## 2 Methodology  
The research methodology is depicted in Figure 1. The methodology for investigating the geometric characteristics of inhalable particles emitted from the process of grinding dental restorations consists of five steps:  
* Grinding of dental restorations;
* Sampling of emitted particles;
* Investigation--scanning electron microscope;
* Image analysis;
* Statistical processing of results. During the grinding process, air sampling for inhalable particle fractions was conducted. Personal sampling simulates the collection of particles that would be inhaled by a technician, who wears the sampling device. For particle sampling, the EGO PLUS TT (Zambelli, Milano, Italy) personal sampler with a display setting, with conical nozzle, and a filter made of a mixture of cellulose esters was used. The basic technical specifications of the sampler and filter were as follows: flow rate 3.5 L/min, sampled volume 420 L, normalised volume 407.9 L, filter diameter 25 mm, effective filter diameter 22 mm, effective filter area 380 mm\({}^{2}\), filter weight 0.022 g, and sampling time 30 min. The Jeol JSM--5610 LV (Jeol, Tokyo, Japan) scanning electron microscope with secondary electron image (SEI) and backscattered electron image (BEI) detectors and an EDS analyser (Jeol, Tokyo, Japan) was used. As part of the SEM analysis, sample conductivity preparation, elemental analysis (refractive index adjustment, contrast adjustment, particle classification), magnification adjustment, SEI, and BEI micrographs were carried out. In the first step, a quarter of the filter was cut with the collected particle mass, and the conductivity was prepared for analysis by SEM. Non-conductive samples required special preparation. Using the method of SEM, two types of micrographs, BEI and SEI, were obtained. BEI micrographs provided information about the topography of the sample. SEI micrographs were used to record surface irregularities (roughness). SEM was used to obtain a magnified image of an object by diffraction of high-energy electrons. The use of SEM in combination with the method of image analysis enabled a precise examination of the size and morphology of the particles, as well as the observation of the surface structure of the particles. As part of the image analysis, the micrographs obtained on the SEM were imported and pre-processed, and particle selection and particle image extraction were carried out. For image analysis, in order to obtain particle size distribution and their geometric characteristics from 2D SEM micrographs, it was necessary to implement certain steps in order to enable proper characterisation of the samples. In a specific investigation, it is necessary to create a set of specific steps to address various image processing stages and determine the workflow. Images based on different shades of grey are converted into binary images  
Figure 1: Methodology of research. by properly setting threshold values. Using the same threshold setting for all particles can lead to an increase in the so-called 'halo effect' around the particles and thus underestimate their dimensions. Therefore, a separate threshold adjustment procedure was examined and implemented for each particle. Subsequently, particles were separated from micrographs, and parameters determining their size and morphological characteristics were examined. Determination of particle geometry was conducted with the aim of their quantitative characterisation. The output from this phase was particle size parameters (Table 1) in accordance with standards [56; 57; 58]. Given the large number of obtained numerical parameters characterising particle geometry and the non-linear relationships between these parameters, the final step required statistical data processing. Correlation analysis, principal component analysis (PCA), and cluster analysis (CA) were used. Correlation analysis revealed the mutual connection between two variables, and the correlation coefficient was a measure of the connection between them.