# 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
Figure 7: In-frame detection results of Seq.3 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 9 presents the original processing results using the state-of-the-art algorithms, and Figure 10 further shows their binarized results via thresholds calculated by [PERSON]'s method. For Max-Mean, it has poor performances when dealing with the cloud and sea backgrounds, indicating that it cannot remove the strong interferences caused by edges. BHP has the same drawbacks when addressing the edges, which can be seen from Figure 10b, because this algorithm is sensitive to frequency characteristics and large numbers of false alarms would appear, if the cutting-off frequency is chosen inappropriately. In addition, according to Figure 10c, an obvious phenomenon of Hat transformation is found that if there are both bright and dark targets in the image, it is inevitable that at least one kind of target would be lost because we cannot use Top-hat transformation and Bottom-hat transformation simultaneously. Finally, TDLMS has a stronger ability to suppress edges when compared to others, but it is easy to generate large quantities of candidate points for the same target region and this would cause repeated trajectories in inter-frame detections remarkably. In order to discuss the performances more convincingly, two widely-accepted metrics called precision rate P and recall rate R [27] are selected to measure the detection results quantitatively. As is illustrated in Figure 11, an assumption is made that \(\rm{N_{T}}\) is the pixel number of true targets existing in the current frame; \(\rm{N_{D}}\) is the pixel number of targets detected by the tested algorithm, and \(\rm{N_{C}}=\rm{N_{T}}\cap\rm{N_{D}}\) is the pixel number of targets detected correctly. In this case, precision rate P and recall rate R can be thus defined as  
\[\rm{P}=\frac{\rm{N_{C}}}{\rm{N_{D}}}\times 100\% \tag{22}\]  
\[\rm{R}=\frac{\rm{N_{C}}}{\rm{N_{T}}}\times 100\% \tag{23}\]  
Furthermore, a comprehensive evaluation index \(\rm{\eta}\) representing the detecting precision of each algorithm [28] can be expressed as  
\[\rm{\eta}=\frac{(1+\lambda^{2})\cdot P\cdot R}{\lambda^{2}\cdot P+R}\times 100\% \tag{24}\]  
Figure 8: In-frame detection results of Seq.4 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. where \(\lambda\) is harmonic coefficient, and we set this coefficient as \(\lambda=1\) in this paper. \(\eta=1\) indicates that there are no false alarms and all of the real targets are discovered, while \(\eta=0\) means that none of the real targets are found out. Hence, the larger \(\eta\) is, the more satisfactory the result is. Table 2 reveals the statistical data of \(\eta\) for the in-frame detections at length. Clearly, the result presented by Table 2 matches the qualitative analyses made above. Our method achieves the largest \(\eta\) in all sequences, but the accuracies are not at a high level as a whole. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Methods** & **Seq.1** & **Seq.2** & **Seq.3** & **Seq.4** \\ \hline
**Max-Mean** & 1.05 & 5.00 & 12.90 & 2.23 \\
**BHP** & 4.24 & 3.39 & 9.52 & 10.00 \\
**Hat** & 13.33 & 0 & 26.67 & 0.31 \\
**TDLMS** & 4.44 & 3.08 & 14.29 & 0.30 \\
**Ours** & 57.14 & 40.00 & 50.00 & 40.00 \\ \hline \hline \end{tabular} BHP means Butterworth high-pass and TDLMS means two-dimensional least mean square.  
\end{table} 
Table 2: Statistical results of \(\eta\)(%) for the in-frame detection. Figure 9: Original results of in-frame detection generated by four state-of-the-art algorithms: (**a**) Raw IR images; (**b**) Max-mean; (**c**) Butterworth high-pass (BHP) (**d**) Hat; (**e**) Two-dimensional least mean square (TDLMS).