# Learning Motion Constraint-Based Spatio-Temporal Networks for Infrared Dim Target Detections
## 1 Introduction  
The Infrared Search and Tracking (IRST) system based on the thermal radiation principle has superiority in terms of favorable concealment and night monitoring. With the fast-growing development of unmanned aerial vehicles (UAVs), the remote monitoring and early warning of the IRST have drawn substantial attention. Due to the long-range distance, the UAV's image appears with very few pixels and fuzzy texture in the infrared image [1]. Worse still, the complicated background may introduce random noise. The detection of robust infrared dim targets, therefore, is still a challenging task. Researchers developed various algorithms to solve the problem. Specifically, the involved methods can be divided into two types: traditional methods and deep learning methods. _A. Traditional methods_  
Traditional methods can be further classified into those that are single-frame-based and multiple-frame-based. Single-frame-based methods are mainly based on the edge gradient between the background and the target. Many effective algorithms have been proposed in recent years. When considering morphological filtering, [PERSON] et al. [2] adopted omnidirectional morphological filters to detect small targets. However, the method cannot avoid the disadvantage of the fixed parameter. Inspired by the mathematical theory, [PERSON] et al. [3] improved the popular infrared patch-tensor (IPT) model with a non-convex tensor rank surrogate merging tensor nuclear norm (TNN) and the Laplace function. The method requires complex iterative computation, which makes it difficult for real-timedetection. [PERSON] et al. [4] figured out that the adjacent region of a dim target holds a Mexican hat distribution. Their experiments indicate that direct detection would degrade performances when the background becomes complicated. Moreover, there are many ways to consider the Human Visual System (HVS). According to the HVS, [PERSON] et al. [5] proposed a weighted local coefficient of variation (WLCV) for small target detection. [PERSON] et al. [6] computed the diagonal grey-level difference to suppress the background. [PERSON] et al. [7] used a fixed-size sliding window to detect different target sizes, which is called the Double-Neighborhood Gradient Method (DNGM). Nevertheless, the above-discussed algorithms are based on the hypothesis of the local maximum. They become very poor when the SNR decreases rapidly. The traditional multiple-frame-based algorithms are designed to capture the motion trajectory to detect the target. They depend on rigorous mathematical theories. [PERSON] et al. [8] improved the mixture of the Gaussian (MoG) model to describe the noise and select the target via the difference between the target and background in a modified flux density (MFD) method. The method is strictly based on low-rank assumptions leading to impracticability in real applications. [PERSON] et al. [9] used two optical flow methods (TV-L1 and Brox) with contrast enhancement kernels to detect the moving small target. They consume more computational time to achieve better accuracies. [PERSON] et al. [10] considered using background movement to suppress the background and enhance the foreground. They utilized [PERSON]'s correlation coefficient and the regional gray level (RGL). [PERSON] et al. [11] addressed the target maneuver by using a general measurement-directed (MD) strategy. Online learning of the target from the observations was achieved. However, the high detection rate depends on the hypothesis of the gray-level distribution. Most multiple-frame methods suppose that the background is uniform, and the motion is slow. They need more computational resources to adapt to the inconsistency of the background and target motion. As analyzed above, the traditional methods mainly rely on the edge gradient between the background and the target. Typical single-frame methods perform well when the background is relatively unitary. However, the result is very sensitive to the bad points, which are blamed for the production defect of the infrared sensors.