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For multi-target tracking in RGB images, offline approaches have become increasingly popular, due to their superior accuracy. Compared to online (recursive) approaches, offline methods have great advances in that they optimise trajectories over batches of frames. These methods all operate on a set of detections as inpu... |
Despite the large amount of work conducted in this field, big challenges still remain in many applications due to noise and ambiguities. From a likely noisy set of detections, the algorithm must construct an unknown number of trajectories. This task causes ambiguities and thereby errors or inaccuracies. |
Most work mentioned above designs algorithms for general pedestrian tracking. Benchmark datasets within this area often feature a continuous flow of people entering and leaving the scene. The focus of this work is the tracking of players in team sports, which has different properties in people’s behaviour. One of these... |
In this work, we combine the generally well-performing offline tracking strategy with the knowledge of a constant number of players on the field over longer time periods. Specifically, we take advantage of automatic counting, which can help constrain the tracking problem by estimating the number of people present in th... |
3 Overview |
We propose a tracking algorithm for team sports applications that combines an existing counting algorithm and a modified offline tracking algorithm. It runs in two main iterations. The first iteration recognises time periods that can be characterised as stable periods (no people leaving or entering the scene) as well a... |
Fig. 2 |
Fig. 2 |
Illustration of the proposed method. During the first iteration, stable periods of the video sequence are identified and the number of people present is estimated. This is used as an input for the second iteration, in which trajectories are constructed and optimised |
4 Counting people |
In most applications, the recorded scene consists of an area where people move around freely and some possible entrance/exit areas. These entrance/exit areas might be only at the edge of the image or there might be doors in the scene. Assuming that people are not continuously moving in and out of the scene, the number ... |
An estimation of this occupancy pattern can be calculated using the approach presented in [29], which will be described briefly in the remaining part of this section. |
First, we must try to detect all people in each frame. As the cameras are static, background subtraction is applied for segmentations purposes, followed by automatic thresholding. The resulting binary objects are then examined and optionally split vertically or horizontal if they are likely to represent more than one p... |
An uncertainty about whether a true person is detected or not is related to each binary object. The probability of being a true detection is related to the ratio of white pixels within the bounding box and the ratio of white pixels observed on the edge of the bounding box. In experiments, the highest probability of whi... |
$$ w_{p}(i) = \begin{cases} 0, & \text{if}\ r_{p} > 50\%\ \| \ r_{r} < 20\%\\ 0.8, & \text{if}\ r_{r} > 70\% \\ 0.9, & \text{if}\ r_{r} < 30\%\ \| \ r_{r} > 60\% \\ 1, & \text{otherwise} \end{cases} $$ |
The weighting of each detection is combined with a weight describing the uncertainty for each frame, caused by occlusions and clutter. Each frame counting is weighted like this: |
$$ w_{f} = a \cdot \prod\limits_{i=1}^{n} w_{p}(i) + (1-a) \cdot w_{s} $$ |
where n is the number of people, w p (i) is the probability of person i being a true detection (see Eq. 1), and w s is a weight that decreases with the number of splits performed, indicating how cluttered the scene is. a controls the weighting of each part. The observed number in a frame are added to a histogram with t... |
Fig. 3 |
Fig. 3 |
Example of a simple graph. Dark nodes and edges have the highest weight. Edges exist between all nodes in two consecutive periods, but to simplify the illustration, the edges with the lowest weight are not drawn |
In order to split video sequences into stable and unstable periods, we must detect when people are close to the border of the scene and therefore likely to leave or enter the tracking area. The border and tracking areas must be predefined manually for each scene. Periods with people detected within the border area shou... |
Estimating the number of people is done by frame-based detection succeeded by an graph optimisation algorithm, based on Dijkstra’s algorithm [31]. The graph optimisation interprets the stable periods as nodes and transitions (people leaving or entering the scene) as edges. All nodes and edges have a weight factor based... |
Figure 3 illustrates the graph approach. For each stable period, the number of people is represented by circles where a darker colour indicates a higher weight. The lines between two stable periods represent the transitions, also coloured darker for a higher weight. The path through this graph is optimised to the highe... |
For each video sequence, this counting algorithm collects timestamps, numbers and probability weights, which are then transferred to the tracking algorithm. |
5 Tracking by energy minimization |
As a starting point for the offline tracking algorithm, we use the algorithm proposed by Milan et al. [13], which has shown very good results for pedestrian tracking on public datasets. It has publicly available source code1, which we will use for further testing. The aim of this method is to find the optimal solution ... |
$$ \begin{aligned} E(X) =& E_{\text{det}} + \alpha E_{\text{app}} + \beta E_{\text{dyn}} + \gamma E_{\text{exc}} +\\ &\delta E_{\text{per}} + \epsilon E_{\text{reg}} \end{aligned} $$ |
Edet aims to keep the solution close to the detections. Eapp utilises the appearance of different objects to disambiguate data association. Edyn is the dynamic model, using a constant velocity model. Eexc is a mutual exclusion term, introducing the physical constraint that two objects cannot be present in the same spac... |
Ereg is a term that considers the number of targets, and we investigate if the constraint can be integrated in this term. The original Ereg term proposed in [13] is defined as follows: |
$$ E_{\text{reg}}(X)=N+\sum\limits^{N}_{i=1}{\frac{1}{F(i)}} $$ |
where F is the temporal length of trajectory i in frames and N is the total number of trajectories. Thus, the first part of the equation infers that the energy directly increases with the number of trajectories. The second part is the sum of the inverse length of all trajectories; hence, in the minimisation process, it... |
This tracking algorithm takes a detection file as input; thus, it can be applied on both RGB and thermal video, utilising our detection method described in Section 4. |
6 Constraining the tracking algorithm |
We aim to constrain the tracking algorithm to construct approximately n trajectories, where n is the number with the highest probability, estimated by the counting algorithm described in Section 4. Two relevant parameters can intuitively be formulated: the number of targets tracked per frame and the total number of tra... |
In Eqs. 5 and 6, A and B represent similarity measures between the number of targets and the estimated number, per frame and per stable period, respectively: |
$$\begin{array}{*{20}l} A &= \frac{1}{F}\sum\limits^{F}_{i=1}{P(s,n(i))} \end{array} $$ |
$$\begin{array}{*{20}l} B &= \frac{1}{S}\sum\limits^{S}_{s=1}{P(s,N(s))} \end{array} $$ |
where P(s,n) is a discrete probability function constructed from the results of the counting algorithm, which returns the probability of n number of targets in stable period s. The number of targets is given either per frame i in n(i) or per stable period s in N(s). F is the total number of frames, and S is the total n... |
Including the original two terms, we now have four possible terms with the following purposes: |
1. 1. |
Minimise number of targets (orig.) |
2. 2. |
Maximise length of tracks (orig.) |
3. 3. |
Constrain number of targets per frame (A) |
4. 4. |
Constrain number of tracks per stable period (B) |
Since we now know the estimated number of people during each period, the original term 1, which minimises the number of targets, conflicts with the purposes of terms 3 and 4, which add more specific constraints on the number. As a result, we discard term 1 and propose a new Ereg term, including terms 2, 3 and 4: |
$$ {\displaystyle \begin{array}{c}{E}_{\mathrm{reg}}(X)=\sum \limits_{i=1}^N\frac{1}{F(i)}-{w}_1\frac{1}{F}\sum \limits_{i=1}^FP\left(s(i),n(i)\right)\\ {}-{w}_2\frac{1}{S}\sum \limits_{x=1}^SP\left(S(x),N(x)\right)\end{array}} $$ |
A negative sign is applied to the two new terms in order to make the optimal solution a minimum value. A weight (w1, w2) is added to each term, adjusting the influence from each term. These weights will be fitted during an optimisation process, described in Section 7. |
7 Evaluation |
7.1 Datasets |
To prove the robustness of our proposed method, we test on two different sports datasets. One is captured with a thermal camera at an indoor sports arena, while the other is captured with an RGB fisheye camera at an outdoor soccer field. Thermal imaging is used for privacy reasons in the public indoor sports arena. Bot... |
The main dataset we use for both test and training is the thermal data captured in an indoor sports arena. In order to cover the entire field of 20 × 40 m, three images are captured simultaneously and stitched horizontally to a total image size of 1920 × 480 pixels. This dataset is captured during an indoor soccer game... |
Fig. 4 |
Fig. 4 |
A frame from the indoor thermal dataset |
The second dataset is 30 s of video captured at an outdoor soccer field. Twenty-five people are present in most frames, performing different exercises related to soccer. The images are captured with an RGB fisheye camera (Hikvision DS-2CD6362F-I(S)(V)) with a resolution of 2048 × 2048 pixels with 15 fps. The images are... |
In addition, to show the transferability to applications other than sports, we test the tracking algorithm on a 30-s sequence captured in a courtyard environment with a thermal camera of type AXIS Q1922. This is a more general tracking scenario with small groups of pedestrians walking in a scene with few entrance/exit ... |
Fig. 5 |
Fig. 5 |
Frame from the courtyard sequence |
We find that there is a lack of publicly available team sports datasets suitable for multi-target tracking. We will contribute to building a wide purpose dataset by publishing the thermal soccer sequences along with annotations for tracking on our website2. |
7.2 Weight parameters |
The parameters of the original energy function, Eq. 3, are adjusted to the sports scenario, where we discard the appearance term (α) and weigh the dynamic model (β) with 0.5, due to the erratic motion often observed in sports. The remaining terms are weighted equally: α = 0,β = 0.5,γ = 1,δ = 1,ε = 1. |
The weight parameters w1 and w2 introduced in Section 5 are fitted experimentally in order to adjust the influence of each term. We use the 30 s training sequence, described in Section 7.1. Combinations of the following parameter values are tested for w1 and w2: {0, 0.1, 1, 10, 20, 100, 250, 500, 750, 1000}. |
The results seem to be slightly more sensitive to w1, where the accuracy is highest at w1 = 500, while the accuracy varies less than 0.1% with w2 values from 250 to 1000. We fix w2 = 500. The high values are explained by non-normalised terms of the energy function. |
7.3 Counting |
The first iteration consists of the counting algorithm, described in Section 4, which estimates stable and unstable periods as well as the number of people present during stable periods. The counting algorithm is thoroughly evaluated in [29], but we compare here the ground truth number of targets with the estimated num... |
Fig. 6 |
Fig. 6 |
Blue solid lines represent the estimated number of people. The estimated number is only available during frames in stable periods, which are also marked with blue on the x-axis. The red broken line is the ground truth annotated number of targets. a Indoor thermal sequence 1. b Indoor thermal sequence 2. c Indoor therma... |
Figure 6 shows that sports sequences 6ad are dominated especially by stable periods, which is one of the main reasons we propose this method for team sports applications. |
7.4 Comparison |
We compare the results of our method to the original implementation of the tracking algorithm presented in [13]. Furthermore, we compare it to two different tracking algorithms suitable for multi-target tracking with objects of similar appearance. The first is an online tracking algorithm based on the Kalman filter, as... |
7.5 Results |
For evaluating the performance, we use the multiple object tracking accuracy (MOTA) defined in the CLEAR MOT metrics [34]: |
$$ \text{MOTA} = 1- \frac{\sum_{t}{\left(\text{FN}_{t} + \text{FP}_{t} + \text{IDS}_{t} \right)}}{\sum_{t}{g_{t}}} $$ |
where FN t , FP t and IDS t are the number of false negatives, false positives and ID switches, respectively, for time t, while g t is the true number of objects at time t. |
The results are presented in Tables 1, 2, 3, 4, and 5. It is clear for all sequences that compared to the original CEM tracker, the number of true positives increases. For all sports sequences, the number of false positives and false negatives also decreases. The number of ID switches are generally high due to unpredic... |
Fig. 7 |
Fig. 7 |
Frames from thermal sequence 1 (cropped); every third frame is shown. Tracking results from the original CEM tracker are visualised. a Frame 1. b Frame 4. c Frame 7. d Frame 10. e Frame 13. f Frame 16. g Frame 19. h Frame 22. i Frame 25. j Frame 28. k Frame 31. l Frame 34 |
Fig. 8 |
Fig. 8 |
Frames from thermal sequence 1 (cropped); every third frame is shown. Tracking results from our proposed constrained tracker are visualised. a Frame 1. b Frame 4. c Frame 7. d Frame 10. e Frame 13. f Frame 16. g Frame 19. h Frame 22. i Frame 25. j Frame 28. k Frame 31. l Frame 34 |
Table 1 |
Results—indoor thermal sequence 1 |
TP (%) |
FP (%) |
FN (%) |
ID switch |
MOTA (%) |
Original CEM |
Table 2 |
Results—indoor thermal sequence 2 |
TP (%) |
FP (%) |
FN (%) |
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