# Using the Guided Fireworks Algorithm for Local Backlight Dimming
## 4 Simulation Results and Discussions  
To test the performance of our proposed method, we selected 20 different images as test samples. The resolution of the test images was 1920 x 1080. All test images were divided into 7 x 5 blocks for local dimming control. The simulation experiments were conducted with MATLAB R2016a. For each test image, the local dimming algorithm was run to calculate its corresponding backlight luminance. The displayed image when the backlight luminance is applied to the test image was then simulated, based on the simulation method mentioned in Section 2. Finally, the original test image was taken as the reference image and the MSSIM index (as shown in Equations (5) and (6)) was calculated to evaluate the quality of the displayed image. The higher the MSSIM index, the better the image quality. In this paper, the GFWA was compared with the LUT algorithm, which is a traditional parameter-based algorithm; the ISFLA, proposed in [12]; and the original FWA. To analyse the search ability of the four algorithms, they were used separately to process the 20 test images. The same constraint value of \(PC_{limit}\) was set for each of the four algorithms. Because the GFWA, ISFLA, and FWA are EC algorithms, they require termination conditions. In our experiments, each EC algorithm was terminated after 20,000 evaluations. The quality of the output solutions was evaluated by the objective function \(f(R)\), which is shown in Equation (7). The smaller the value of \(f(R)\), the better the quality of the output solution. We calculated the \(f(R)\) values that the four algorithms obtained when they were applied to process the 20 test images. The line charts drawn based on the \(f(R)\) values are shown in Figure 4, and, to better show the \(f(R)\) values of the four algorithms, some details of the line charts are enlarged in Figure 4.  
It can be seen from Figure 4 that for all 20 images, the \(f(\text{R})\) values of the GFWA were the smallest among the four algorithms, which means that the solutions obtained by the GFWA were of higher quality than the other three algorithms. The \(f(\text{R})\) values of the LUT algorithm were obviously larger than the other three algorithms, which proves that, compared with the parameter-based algorithm, the optimization methods effectively improved the solution quality. In most cases, the \(f(\text{R})\) values of the FWA were smaller than those of the ISFLA, which proves that the FWA had better performance in solving local dimming problem. We also calculated the MSSIM index values achieved by the four algorithms when they were applied to process the 20 test images. For the GFWA, the average MSSIM index value of the 20 test images was 0.9129, which is 0.0292 higher than the average MSSIM index value (0.8837) of the LUT algorithm, 0.0019 higher than the average MSSIM index value (0.9110) of the FWA, and 0.0044 higher than the average MSSIM index value (0.9085) of the ISFLA. All these results prove that the GFWA had the highest search ability. To further analyse the visual quality of the images processed by the four algorithms, we selected four images from the 20 test images. Among them, images 1 and 2 were low contrast ratio images, and images 3 and 4 were high contrast ratio images. The four selected test images are shown in Figure 5. They were also used as the reference images to evaluate the quality of the displayed images. The simulated displayed images of the four algorithms are shown in Figures 6-9. In order to better compare the visual differences of the four algorithms, the regions in the red circles of the displayed images are enlarged and shown next to the same regions in the reference images. In addition, the values of the MSSIM index and _PC_ of the four algorithms are given in Table 1.  
Figure 4: Comparison of the _f_(R) values of the four algorithms. LUT: Look-Up Table; ISFLA: Improved Shuffled Frog Leaping Algorithm. Figure 5: Test images 1, 2, 3, and 4. Images 1 and 2 are two low contrast ratio images, and Images 3 and 4 are two high contrast ratio images.