## 3 Methodology
### Binary-Channel Verification Model  
A binary-channel verification model is proposed to improve the quality of the state estimation as function of each object. For each object in frame \(t\), a function \(SOT_{k}\) is learned to separate the object itself from the background information by assigning a high score to it, while returning low scores for the background. The parameter \(\dashv_{k,j}^{t}\) is set to choose the best correlated spatial location \(d_{j}^{t}\) from \(D^{t}\) on object \(k\) exclusively to one object only referring to scores from all objects. Regarding different states of incoming tracks, ongoing tracks and occluded tracks, this model can operate on those two tracking states in a similar way with some slight changes.  
The function \(SOT_{k}\), as in the state estimation, is the first step to process the incoming frame. An ordinary single object tracker is initialized by the object groundtruth bounding box in the first frame where a certain object existed, and is slowly and constantly updated. However, in MOT, the tracker is initially learned from detections provided by an external detector which contains considerable noise with respect to the location. Moreover, if the object moves closer or away from the viewing point, the scale of the object will also change rapidly. Hence, implementing a single object tracker under a MOT scenario without any supervision will easily lead to identity switches or catastrophic mis-track problems. Benefiting from the tracking-by-detection paradigm, detection can play the role of the supervisor for the tracker. During the state estimation process, we rewrite the function as:  
\[SOT_{k}=\left[SOT_{T}=\left(t,b_{k}^{t-1},d_{j}^{t},\overset{t}{v_{d},k_{j}} \right),SOT_{D}=\left(t,b_{j}^{t},d_{j}^{t},\overset{t}{v_{d},k_{j}}\right) \right]. \tag{3}\]  
For subsequent tracks, \(SOT_{k}\) estimates the score  
the similarity between the detection \(j\) and the object \(k\). The output bounding box can be assigned as follows:  
\[b_{k}=\begin{cases}b_{det}&if\ s_{D_{j}}>s_{T_{k}}\ and\ s_{T_{k}},s_{D_{j}}>s_{ BCVthreshold}\\ b_{tracker}&if\ s_{D_{j}}<s_{T_{k}}\ and\ s_{T_{k}},s_{D_{j}}>s_{BCVthreshold}\\ \prime loss^{\prime}&if\ s_{T_{k}}<s_{BCVthreshold}\\ \prime misaligned^{\prime}&if\ s_{D_{j}}<s_{BCVthreshold} \ and\ s_{T_{k}}>s_{BCVthreshold}\\ \end{cases} \tag{4}\]  
Here, \(s_{BCVthreshold}\) is based on previous tracking information, \(b_{k}^{l-1}\) represents the bounding box of the same object in the previous frame and \(b_{j}^{t}\) for the bounding box of the \(j\)-\(th\) detection in the current frame. Also, results with an untrack mark will be sent to the memory waiting for future re-claim, in order to save computational resources. For occluded tracks, \(b_{k}^{t-1}\), since it did not exist, the estimation of the object should take place at a search area provided by the motion model instead of the previous location, for which we follow the constant velocity assumption (CVA) [21; 22] with a camera motion compensation by calculating the motion information of highly trusted objects' motion trends.  
We take advantage of the idea of the non zero-sum game [27], where scores calculated on the estimation of the tracker and associated detection push each other from frame to frame with the concept that the result can be optimized as long as one of them shows a promising result, in order to better refine the output bounding box and increase the quality of online training samples added to the tracker at each frame. In this way, the single object tracker and the detection can be complementary to each other and improve the performances of each other along the tracking process.