## 3 Experimental Analysis and Results
### Quantitative Analysis  
For image thresholding, the peak signal noise ratio (PSNR) [41] compares the image thresholding result of the methodology with that of the ground truth image. It reports the number of misclassified pixels of the image thresholding result of the methodology to the ground truth image:  
\[\text{PSNR}=20\log_{10}(L-1)-10\log_{10}\left(\frac{1}{\text{M}\times\text{N}} \sum_{i=0}^{M-1}\sum_{j=0}^{N-1}(B(x,y)-GT(x,y))\right) \tag{25}\]  
where \(L\) is the maximum gray level since we experimented on eight-bit images, the value of \(L\) is 256; \(M\times N\) is the size of the image; \(B(x,y)\) is the image thresholding result and \(GT(x,y)\) is the ground truth image. Sequences named as 'hiding', 'horse','mixed-distractors', and'saturated' in the LTIR dataset are the first four sequences and the image set in the Photovoltaic System Thermal Image Database is labeled as sequence 5. These five sequences are considered to evaluate the performance of the proposed method and the average peak signal noise ratio (PSNR) values obtained for each sequence are listed in Table 3. The performance comparison based on PSNR values obtained for the images in all sequences (total of 1249 images) is shown in Figure 6. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Sequence** & **Yen Method** & **[PERSON] et al.** & **[PERSON] et al.** & **[PERSON] et al.** & **Proposed** \\ \hline
**1** & 19.5227 & 18.9946 & 18.9830 & 21.2301 & **23.5662** \\
**2** & 28.1154 & 10.8097 & 20.7470 & 34.8999 & **35.0484** \\
**3** & 14.2475 & 14.4219 & 12.1629 & 15.0631 & **19.0519** \\
**4** & 4.7949 & 11.1707 & 19.7181 & 12.2039 & **21.1696** \\
**5** & 11.2230 & 27.4780 & 25.1709 & 17.2717 & **32.0171** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Average peak signal noise ratio (PSNR) (in dB) results for the five methods. Figure 5: Comparison results of the five methods for images (**i**–**v**): (**a**) original image; (**b**) ground truth image; thresholding results: (**c**) [PERSON] method; (**d**) [PERSON] et al. ; (**e**) [PERSON] et al. ; (**f**) [PERSON] et al. ; and (**g**) the proposed method. Sequence 1 and sequence 3 are recorded indoors to detect the human. Sequence 2 is recorded in a natural background to detect a horse. Sequence 4 offers very high-resolution images with a complex background and the purpose is to detect multi persons. Sequence 5 addresses solar energy applications where hotspots are to be detected for fault diagnosis. In order to check the detection capability through image segmentation, we considered all these sequences for evaluation. The Yen method works well for segmenting single objects in sequence 1 and sequence 2, however, this method fails to produce satisfactory single object segmentation for sequence 5. According to the PSNR metrics of the Yen method obtained for sequence 3 and sequence 4, this method is not suitable for the segmentation of multi-object infrared images. The [PERSON] et al. algorithm and Milad et al. algorithm work well for single object infrared image segmentation, meanwhile, they have provided poor performance for the segmentation of multi-object infrared images related to sequence 4. The performance of [PERSON] et al. is satisfactory for sequence 1, sequence 2, and sequence 3. However, this method produced a poor performance according to the PSNR metrics obtained for sequence 4 and sequence 5. The obtained metrics for PSNR in all sequences revealed that the proposed method can perform better segmentation for single-object infrared images and multi-object infrared images. To emphasize this fact, the finest performances were highlighted showing the best results between the comparisons. In order to assess the computational cost [42], the CPU times were measured for the images shown in Figure 5. A list of the CPU times for each method is provided in Table 4 and Figure 7. From this table, we can observe that the computational cost is high for the Yen method, [PERSON] et al. method, and the [PERSON] et al. method.