## 3 Methodology
### Sort  
SORT [10] iteratively computes the state of the objects being tracked through a KF. The method uses the Hungarian algorithm [34] to accurately associate detected objects (by an object detector) with objects that are being tracked. A detailed overview of the SORT algorithm is represented in Figure 2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Year** & **DL** & **KF** & **Description** \\ \hline \hline \multirow{3}{*}{SORT [10]} & \multirow{3}{*}{2016} & \multirow{3}{*}{\(\times\)} & \multicolumn{3}{c}{Simple and fast KF-based algorithm that} \\  & & & & associates objects based on their bounding box appearance. \\ \hline \multirow{3}{*}{Deep-SORT [11]} & \multirow{3}{*}{2017} & \multirow{3}{*}{\(\times\)} & \multirow{3}{*}{\(\times\)} & KF-based algorithm, associates objects based on their appearance description extracted by a CNN \\  & & & & & re-identification network. \\ \hline \multirow{3}{*}{MOTDT [12]} & \multirow{3}{*}{2018} & \multirow{3}{*}{\(\times\)} & \multirow{3}{*}{\(\times\)} & Deep-SORT related algorithm that uses predicted bounding boxes as candidates for association, in an attempt to solve the occlusion problem. \\ \hline \multirow{3}{*}{GMT-CT [33]} & \multirow{3}{*}{2021} & \multirow{3}{*}{\(\times\)} & \multirow{3}{*}{\(\times\)} & Deep-SORT related algorithm that solves association problems using graph partitioning \\  & & & & & based on appearance features. \\ \hline \multirow{3}{*}{DROP [30]} & \multirow{3}{*}{2020} & \multirow{3}{*}{\(\times\)} & \multirow{3}{*}{\(\times\)} & Associates objects using a confidence-based cost to construct the Hungarian algorithm solver. \\  & & & & & Furthermore, it uses appearance features to determine occlusions in the environment. \\ \hline \multirow{3}{*}{FPSN-MOT [35]} & \multirow{3}{*}{2019} & \multirow{3}{*}{\(\times\)} & \multicolumn{3}{c}{It uses Siamese and Feature Pyramid-based Networks addressing appearance and motion features in the association stage.} \\ \hline \multirow{3}{*}{[PERSON] et al. [37]} & \multirow{3}{*}{2020} & \multirow{3}{*}{\(\times\)} & Deep-SORT related algorithm that uses Siamese network to process association tasks and also introduce optical flow information to the motion model, in order to improve accuracy. \\ \cline{1-1}  & & & & \\ \cline{1-1}  & & & & \\ \end{tabular}
\end{table} 
Table 1: Review of state-of-the-art tracking by detection. (DL = Deep Learning-based; KF = Kalman Filter-based). Figure 2: Overview of the object tracking SORT algorithm. The SORT Data Association module, which is of particular interest in this work, is responsible for matching the KF's predicted bounding boxes with measured bounding boxes on the image, given by the object detector. This module receives, as input, \(N\) detected bounding boxes and \(M\) predicted bounding boxes (acquired from their respective KF). The module formulates a linear assignment problem by computing a cost matrix between each detected bounding box and all predicted bounding boxes (respectively \(D_{i},i\in\{1\dots N\}\) and \(P_{i},i\in\{1\dots M\}\)), with the Intersection over Union (IoU) as metric:  
\[IoU(D,P)= \begin{bmatrix}iou(D_{1},P_{1})&\dots&iou(D_{1},P_{M})\\ iou(D_{2},P_{1})&\dots&iou(D_{2},P_{M})\\ \vdots&\ddots&\vdots\\ iou(D_{N},P_{1})&\dots&iou(D_{N},P_{M})\\ \end{bmatrix}  \tag{1}\]  
where the IoU between a detected bounding box and a predicted bounding box is given by  
\[iou(D_{i},P_{i})=\frac{D_{i}\cap P_{i}}{D_{i}\cup P_{i}}. \tag{2}\]  
After computing the cost matrix, the Hungarian algorithm [34] is used to associate the bounding boxes. The obtained associations are represented in a \(N\times 2\) array, representing \(N\) measurements associated to \(N\) tracks. Associations are also filtered by considering a minimum IoU threshold, discarding associations with IoU lower than the threshold. The KF Estimation module uses a linear constant velocity model to represent each object's motion model. When an object is associated with a tracked object (track), its bounding box is used to update the track state.