## 2 Materials and Methods  
The experiments were carried out on Norway spruce (_Picea abies_ (L.) [PERSON]). Wood was harvested from the Polana region in Slovakia. Cutting kerf was created by the cutting of tangential spruce lumber with dimensions of 8 mm x 100 mm x 1000 mm (tangential x radial x longitudinal), with a relative moisture content \(w=12\pm 1\%\) and average density \(\rho=428.4\pm 27.9\) kg\(\cdot\)m\({}^{-3}\). The moisture content of the samples was determined according to ISO 13061-1 [77]. The wood density was determined according to ISO 13061-2 [78]. The CO\({}_{2}\) laser LCS 400-1/W (TST Strojarne Piesok, Piesok, Slovakia) was used for cutting with a wavelength of 10.6 \(\upmu\)m operated at a continuous mode output power of 100 and 150 W. Three speeds of cutting were used, with values 3, 6, and 9 mm\(\cdot\)s\({}^{-1}\). A power of 150 W and speed of cutting of 9 mm\(\cdot\)s\({}^{-1}\) were used as a reference, since this combination is used in practice due to the speed of production. The focal length was 127 mm (5\"), beam diameter was 10 mm, and spot diameter was 0.3 mm. The focal point position of the laser beam was set to 1/2 of the sample thickness (measured from the upper surface of the board). The process gas was supplied via a laval contour nozzle with 0.25 MPa pressured air. All cuts were made parallel to the wood fibers in the tangential direction (Figure 1). The quality of the cut section of the wood was examined using Digital Microscopy (DM). The Response Surface Method (RSM) was used to prepare the experiment. The influence of three factors was investigated, namely, the effect of the laser power P, cutting speed V, and number of annual rings AR (Table 1) on the width of the cutting kerf WKU (width of the cutting kerf on the upper board's surface) and WKD (cutting kerf width on the board bottom), on their ratio WKR (ratio of the cutting kerf width on the upper and bottom board's surface), on the width of the heat-affected areas on the spruce board surface WHAZx (width of the heat-affected area on both sides of the cutting kerf is equal, and this applies to the upper board's surface, as well as to the bottom of the board), and on the degree of charring B. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Factor** & **Min. Value** & **Max. Value** & **Levels Number** & **Factor Levels** & **Unit** & **Type** \\ \hline AR & 3 & 11 & 9 & \(3,4,5,6,7,8,9,10,11\) & - & random \\ P & 100 & 150 & 2 & \(100,150\) & W & controlled \\ V & 3 & 9 & 3 & \(3,6,9\) & mm\(\cdot\)s\({}^{-1}\) & controlled \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental factors. Figure 1: Cutting scheme. Measuring of the cutting kerf width WKU, WKD, and WHAZx was observed by DM using the K-means clustering segmentation method [79]. The K-means clustering algorithm is an unsupervised algorithm and it clusters or partitions the given data into K-clusters based on the K-centroids. The algorithm is used when we have unlabeled data (without defined categories) and the objective is to minimize the sum of squared distances between all points and the cluster center. In our case, three different color-coded regions were searched in image processing software, namely, the area of the unaffected workpiece, the area of the heat-affected zone, and the area of the cutting kerf. The mean values of the width of the cutting kerf and especially the width of the heat-affected zones were determined from the segmented photos by applying the theorem on the mean value theorem for integrals (Figure 2). The measuring of the degree of charring consisted of an analysis of cutting kerf in a direction perpendicular to the surface and a subsequent analysis of the morphology (texture) of the examined surface. Surface charred areas are amorphous areas of cutting kerf without a visible texture with a damaged anatomical wood structure due to the thermal degradation of wood. The bimodal histogram was modeled as a mixture of two Gaussian density functions.