## 3 Results
### Application to Rectangular Current Power Supply Operated in Burst Mode
The gray-levels histograms of the last row in Figure 18 present the result of a statistical analysis, which presents good matching with the discharge appearance and offers a quantification solution to translate the visual effect into a number. This analysis was proposed by [13] and is achieved as previously on the only central part of the image (red frame); it is carried out after the translation of the image into gray levels and its geometrical transformation (before the segmentation): the horizontal axis of the histogram presents the gray level (from 0 to 255), and the vertical axis presents the frequency of pixels for each level. Based on the histogram results, statistical measures as the mean gray level and the standard deviation are used to characterize the discharge. Below, the parameters of this analysis are commented:  
* Mean Gray Level (\(\upmu\)gray): It is the mean of the gray-level value (in the central discharge area). This indicates the mean brightness of the discharge. In order to be able to compare the discharges obtained under different operating conditions, care must be taken to deactivate all automatic settings of the camera. * Gray Level Intensity: It is the sum of the gray-level values of the pixels in the area of interest. * Discharge Intensity/mm\({}^{2}\): It is the Gray Level Intensity divided by the area covered by the discharge. * Standard Deviation (SD): the SD measures the dispersion of the data from its mean value, and it is a crucial parameter to determine the discharge uniformity quantitatively [27]. In an ideal uniform discharge, all the reactor pixels should have the same gray-level value; thus, the SD is zero in this case. The SD value will rise if the gray level takes increasingly different values on the surface. In general, the lower the standard deviation, the data points tend to be closer to their mean, meaning a more uniform discharge. The value of SD is calculated considering each pixel of the image, as defined in [27]. Table 1 presents the resulting parameters of the image processing for both cases shown in Figure 18.  
As can be seen, the SD of the case obtained with the rectangular current source is significantly higher than cases with the sine voltage. Despite the fact that cases worked with similar electrical power, the intensity of the first case is higher than for the second. Accordingly, the discharges obtained by the sinusoidal voltage source are more uniform, diffuse, and weak than the discharges obtained by the square current source. This observation has been verified with a set of different operating points in a wide range of the \(\beta\) parameter. The Manley figures of both supply conditions showed that DBD works in a filamentary mode, even if diffuse and uniform discharges appeared with the sinusoidal voltage source. One can notice that the image (a) is much more luminous than the (b) one--this is confirmed by the difference of the values of the Gray level Intensity/mm\({}^{2}\). Nevertheless, the [PERSON]'s algorithm has been clearly able to differentiate the background and the area covered by the discharge. In this way, the discharge segmentation process is validated under different image conditions. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Pict.** & \(\beta\) **[\%]** & **Discharge** & **Mean Gray** & **Gray Level** & **Gray Level** & **Standard** \\  & **Area [mm\({}^{2}\)]** & **Level—ugray** & **Intensity** & **Intensity/mm\({}^{2}\)** & **Deviation—SD** \\ \hline Rectangular & & & & & & \\ current—column (a) & 80 & 1659 & 52.73 & 1,787,099 & 1077 & 10.12 \\ \hline Sinusoidal & & & & & & \\ voltage—column (b) & 85 & 1762 & 15.83 & 576,172 & 327 & 3.88 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Grayscale images statistical properties (electrical waveforms presented on Figure 3 and images in Figure 18).