# Infrared Small Moving Target Detection via Saliency Histogram and Geometrical Invariability
## 3 Inter-Frame Detection Based on Geometrical Invariability
### Results of Inter-Frame Detection  
In this part, the binarized detection results of the consecutive frames are accumulated in the final frame. Figure 12 presents the cumulative results for each sequence in detail. Overall, our algorithm has the best performances in all sequences and nearly all of the false alarms remaining in the single frame detection are removed by the subsequent inter-frame detection effectively. Moreover, complete trajectories are drawn in the final resulting images, and the phenomenon of repeated trajectories for the same target is successfully avoided. By comparison, other methods have less satisfactory performances in this experiment. As is shown in the resulting images of Seq.1, Seq.3 and Seq.4, Max-Mean is easy to  
Figure 11: Schematic diagram of the parameters used for the measurement of detection accuracy.  
Figure 10: Binarized results of in-frame detection via [PERSON]’s method: (**a**) Raw IR images; (**b**) Max-Mean; (**c**) BHP; (**d**) Hat; (**e**) TDLMS.  
produce discontinuous trajectories, meaning that real targets are lost in certain frames. The trajectories generated by BHP are relatively complete, but regions with clutter edges contain large numbers of false alarms, which is especially outstanding in Seq.1 and Seq.3. Hat transformation suffers from missing detection seriously, and the trail of the dark IR small target is completely missed in Seq.3. However, this method can reduce the quantity of repeated trails to some extent when compared with the other three algorithms. Furthermore, it has a good anti-inference ability to clutter edges. In contrast, TDLMS tends to severely suffer from the repeated trails, and it is obvious that the trajectories produced by this method are thicker than others.  
Table 3 presents the \(\eta\) values of the five groups in detail. From the data provided by this table, we can clearly find that \(\eta\) values of our method are higher than 97% and are at least two times larger than other methods in all of the four sequences. Through further analyses for the source of false alarms produced by contrastive algorithms, we argue that the major sources contain two aspects: (1) the repeated trajectories increase the quantities of redundant and useless points to a great extent; (2) the false detection results of edges have been accumulated.  
The ROC (Receiving Operating Characteristic) curve [29] is an effective tool to describe the quality of detection methods. For an ROC curve, the abscissa and ordinate stand for the probability of false alarm rate (Pf) and detection rate (Pd), which are expressed as Equations (25) and (26), respectively:  
\[\mathrm{Pf}=\frac{\mathrm{N_{F}}}{\mathrm{N_{0}}} \tag{25}\]  
\[\mathrm{Pd}=\frac{\mathrm{N_{C}}}{\mathrm{N_{D}}} \tag{26}\]  
where \(\mathrm{N_{0}}\) denotes the total pixel number of the current frame. A good ROC means that the tested method is able to highlight the target and suppress the clutters at the same time. The ROC curves of the four experiments are drawn as Figure 13.  
Figure 12: Cumulative results of inter-frame detection.