# Infrared Small Moving Target Detection via Saliency Histogram and Geometrical Invariability
## 3 Inter-Frame Detection Based on Geometrical Invariability
### Experimental Results of In-Frame Detection  
First of all, this section is organized to show the processing results by our algorithm and the four other conventional algorithms. Then, several metrics are applied to make a quantitative comparison. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dataset** & **Background** & **Image Size** & **Frame Number** & \
\begin{tabular}{c} **Number of** \\ **Bright Targets** \\ \end{tabular} &
\begin{tabular}{c} **Number of** \\ **Dark Targets** \\ \end{tabular} \\ \hline Seq.1 & sky-cloud & \(512\times 512\) & \(100\) & \(192\) & \(0\) \\ Seq.2 & ground & \(493\times 309\) & \(50\) & \(0\) & \(47\) \\ Seq.3 & sea & \(313\times 236\) & \(150\) & \(150\) & \(145\) \\ Seq.4 & cloud & \(320\times 256\) & \(200\) & \(192\) & \(0\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Detailed information of our datasets. Figure 4: First frames of the tested infrared (IR) sequences: (**a**) Seq.1; (**b**) Seq.2; (**c**) Seq.3; (**d**) Seq.4. We choose the four groups of IR images shown in Figure 4 as the tested samples to perform the experiment. Meanwhile, four state-of-the-art algorithms: Max-Mean, Butterworth high-pass (BHP), Hat transformation (including Top-hat and Bottom-hat transformations) and two-dimensional least mean square (TDLMS) are selected to compare with our method. For Max-Mean, the raw IR image is filtered by a max-mean filter, and the filtered output is subtracted from the original image to enhance the IR small target. Furthermore, specific frequency components belonging to IR targets are extracted by setting a specific cut-off frequency of the Butterworth high-pass filter in the BHP method. Hat transformation denotes the pixel-wise difference between the raw image and the resulting image processed by morphological opening or closing operation. It should be noted that Top-hat transformation is designed for detecting bright targets while Bottom-hat transformation is designed for dark targets. As a result, Bottom-hat transformation is implemented in Seq.2 while Top-hat transformation is implemented in other sequences. Lastly, TDLMS detects small targets in the way of calculating the difference between the original image and the background estimation. Figures 5-8 show the significant intermediate results and the output results of Eqs. (1-4) produced by our method, respectively. Note that real targets are marked with red circles and false alarms are marked with yellow ones. These figures demonstrate the following five points clearly:  
1. While intensity histogram only discloses the pixel number of each gray level, the peaks of the proposed saliency histogram are only located in gray levels corresponding to salient regions, i.e., saliency histogram reveals the saliency distribution of each gray level;
2. The thresholds calculated via [PERSON]'s method can suppress the bins with small bin values in the raw saliency histogram well and only few bins are preserved in the modified saliency histograms;
3. The saliency maps obtained by tuning amplitude spectra can roughly highlight the IR target no matter whether it is bright or dark, but the edges of sea waves and clouds with large gradient values are also preserved in the map;
4. Each candidate region in the binarized image is represented by a single centroid point in the final output, although few false alarms still exist;
5. The main sources of our false alarms are edges, dead pixels and still bright points. Figure 5: In-frame detection results of Seq.1 generated by our method: (**a**) intensity histogram; (**b**) original saliency histogram; (**c**) modified saliency histogram; (**d**) saliency map; (**e**) binarized image; (**f**) in-frame detection result. Figure 6: In-frame detection results of Seq.2 generated by our method: (**a**) intensity histogram; (**b**) original saliency histogram; (**c**) modified saliency histogram; (**d**) saliency map; (**e**) binarized image; (**f**) in-frame detection result.