# Small Infrared Target Detection via a Mexican-Hat Distribution
## 4 Experimental Results and Analysis
### Comparison with Other Methods  
This experiment compares the proposed method with other nine popular small IR target detectors, i.e. Relative Local Contrast Measure (RLCM) [25], Patch-based Contrast Measure (PCM) [11], Variance difference (Var-diff) [15], Absolute Average Gray Difference (AAGD) [25], Laplacian of Gaussian (LoG) [26], Local Intensity and Gradient (LIG) [18], Max-median [27], Max-Mean [27] and the traditional Top-Hat filter. Some of them are traditional methods like LoG, Max-median, Max-Mean, and the traditional Top-Hat filter, and others are state-of-the-art methods like RLCM, PCM, Var-diff, AAGD, and LIG. Most parameters of the nine methods are the same as the original references, except the following parameters. The standard deviation of the Gaussian kernel is 0.5 in LoG, and the sliding window size of LIG is 19 \(\times\) 19. The patch sizes of Max-median and Max-Mean is 5. The structure element is a rectangle of 3 \(\times\) 3 in the Top-Hat filter. We determine these parameters to make the corresponding method perform best on both Seq.1 and Seq.2. Figures 10 and 11 visually illustrate the detection results corresponding to each method. The final detected target is circled in yellow. An image without any yellow circle means the method fails to detect any target. Here zoomed in images have been presented to see the target clearly. From the 3D intensity plots shown in Figures 10 and 11, we can see the target enhanced by our Mexican-hat distribution based method is more prominent than other compared methods, leading our method a satisfied detection performance. Particularly, RLCM can enhance the target successfully, but as shown in Figures 10 and 11, it cannot suppress the high bright backgrounds successfully. For the methods of LoG, Max-median, Max-mean, and Top-Hat, they sometimes fail in suppressing clutters, leading to a false detection or failing to detect any target. For PCM, Var-diff, AAGD, and LIG, they apt to fail to detect any target in the images with complex backgrounds. In fact, for the simple methods such as Max-median and Max-mean, they seem to be more effective on a synthetic target, because of the non-strict Gaussian distribution of real small IR targets as well as the low contrast between target and background. Figure 9: The twentieth image in Seq.2. Figure 10: The forty-ninth image in Seq.1. Besides visual comparisons, quantitative metrics have also been evaluated. We choose the Signal to Clutter Ratio Gain (SCRG) [28], Background Suppression Factor(BSF) [28], the true detection rate \(P_{d}\), the false detection rate \(P_{f}\)[29], and time cost as the quantitative metrics. The results are listed in Tables 1 and 2. Figure 11: The first image in Seq.2. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Method** & **Our Method** & **RLCM** & **PCM** & **Var-Diff** & **AAGD** & **LoG** & **LIG** & **Max-Median** & **Max-Mean** & **Top-Hat** \\ \hline \(P_{d}\) & 0.9900 & 0.0600 & 0 & 0.2600 & 0 & 0.3500 & 0.8100 & **1** & 0.9900 & 0.9000 \\ \(P_{f}\) & 0.0100 & 0.0500 & 0 & 0.1300 & 0 & 0.2300 & 0.0900 & **0** & 0 & 0.0400 \\ SCRG & **203.9131** & 0.3930 & 0.0025 & 0.4481 & 0.0055 & 0.0275 & 0.0275 & 0.3577 & 0.2193 & 0.1267 \\ BSF & **113.8130** & 0.0004 & 1.1872 & 0.2359 & 0.0703 & 0.0018 & 0.0018 & 0.00004 & 0.0001 & 0.0004 \\ Time (second) & 1.8572 & 40.3541 & 0.4709 & 0.1362 & 0.1537 & 0.1144 & 7.5586 & 6.8573 & 15.4546 & **0.1023** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Quantitative assessment on Seq.1 (time is the average per image processing time).