## 4 Results
### LED Brightness Mapping for Accurate Visualization  
Results of LEDs visualization presented in previous subchapter are not satisfying. To achieve more accurate visualization, a simple compensation function can be used to adjust virtual LED brightness. The function was proposed is in the following form:  
\[f_{map}(V)=1+a\cdot e^{-V\cdot b} \tag{5}\]  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Analyzed Feature** & **L6** & **L5** & **L4** & **L2** & **L1** & **L0** \\ \hline MKD-51 non-zero pixels ratio & 0.47 & 0.75 & 1 & 0.44 & 0.78 & 1 \\ MKD-51 SIM non-zero pixels ratio & 0.42 & 0.85 & 1 & 0.13 & 0.43 & 1 \\ \hline MKD-51 brightness mean & 0.48 & 0.62 & 0.63 & 0.41 & 0.73 & 0.8 \\ MKD-51 SIM brightness mean & 0.19 & 0.27 & 0.81 & 0.15 & 0.19 & 0.89 \\ \hline MKD-51 brightness median & 0.46 & 0.58 & 0.58 & 0.41 & 0.82 & 0.98 \\ MKD-51 SIM brightness median & 0.2 & 0.28 & 0.81 & 0.12 & 0.2 & 0.9 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of LED normalized images statistics.  
Figure 6: The LED bar of MKD-51 didactic system fed by different PWM duty cycles: (**a**) the real MKD-51 photo; (**b**) the real MKD-51 photo after normalization; (**c**) the MKD-51 SIM image; (**d**) the MKD-51 SIM image after normalization.  
where \(a\) and \(b\) coefficients were picked empirically as values of 4 and 5. The comparative results with the use of compensation formula and for different PWM duty cycle schemes are shown in Figure 7.  
The statistics of normalized images histograms for single LEDs were calculated using perceptual scale. The results are shown in Tables 3 and 4.  
\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Analyzed Statistics** & **L6** & **L5** & **L4** & **L2** & **L1** & **L0** \\ \hline MKD-51 non-zero pixels ratio & 0.65 & 0.9 & 1 & 0.73 & 0.95 & 1 \\ MKD-51 SIM non-zero pixels ratio W & 0.9 & 0.97 & 1 & 0.94 & 0.98 & 1 \\ MKD-51 SIM non-zero pixels ratio N & 0.85 & 0.95 & 1 & 0.43 & 0.96 & 1 \\ \hline MKD-51 brightness mean & 0.71 & 0.73 & 0.72 & 0.7 & 0.76 & 0.78 \\ MKD-51 SIM brightness mean W & 0.42 & 0.6 & 0.81 & 0.25 & 0.45 & 0.9 \\ MKD-51 SIM brightness mean N & 0.27 & 0.54 & 0.81 & 0.19 & 0.32 & 0.9 \\ \hline MKD-51 brightness median & 0.77 & 0.82 & 0.8 & 0.76 & 0.92 & 0.94 \\ MKD-51 SIM brightness median W & 0.44 & 0.59 & 0.81 & 0.25 & 0.44 & 0.9 \\ MKD-51 SIM brightness median N & 0.28 & 0.55 & 0.81 & 0.2 & 0.31 & 0.9 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of LED normalized images statistics with (W) and without (N) brightness compensation for 0%, 30%, 60%, and 100% duty cycle of PWM scheme for different photo exposure of the real MKD-51.  
\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Analyzed Feature** & **L6** & **L5** & **L4** & **L2** & **L1** & **L0** \\ \hline MKD-51 non-zero pixels ratio & 0.47 & 0.75 & 1 & 0.44 & 0.78 & 1 \\ MKD-51 SIM non-zero pixels ratio W & 0.73 & 0.9 & 1 & 0.28 & 0.94 & 1 \\ MKD-51 SIM non-zero pixels ratio N & 0.42 & 0.85 & 1 & 0.13 & 0.43 & 1 \\ \hline MKD-51 brightness mean & 0.48 & 0.62 & 0.63 & 0.41 & 0.73 & 0.8 \\ MKD-51 SIM brightness mean W & 0.22 & 0.42 & 0.81 & 0.17 & 0.25 & 0.9 \\ MKD-51 SIM brightness mean N & 0.19 & 0.27 & 0.81 & 0.15 & 0.19 & 0.9 \\ \hline MKD-51 brightness median & 0.46 & 0.58 & 0.58 & 0.41 & 0.82 & 0.98 \\ MKD-51 SIM brightness median W & 0.2 & 0.44 & 0.81 & 0.16 & 0.25 & 0.9 \\ MKD-51 SIM brightness median N & 0.2 & 0.28 & 0.81 & 0.12 & 0.2 & 0.9 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of LED normalized images statistics with (W) and without (N) brightness compensation for 0%, 10%, 30%, and 100% duty cycle of PWM scheme.  
Figure 7: The LED bars driven with different PWMs. **(a,b)** The real MKD-51 photos taken with two different exposures; **(c,d)** MKD-51 SIM with compensation formula; **(e,f)** MKD-51 SIM without compensation formula; **(a,c,e)** LEDs driven with 0%, 30%, 60%, and 100% of PWM duty cycle; **(b,d,f)** LEDs driven with 0%, 10%, 30%, and 100% of PWM duty cycle;