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  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>Workshop Agents in Trafic and Transportation, July</journal-title>
      </journal-title-group>
    </journal-meta>
    <article-meta>
      <title-group>
        <article-title>pipeline for extracting decision-support features from trafic scenes</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Vitor A. Fraga</string-name>
          <email>vitor.augusto.fraga@gmail.com</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Lincoln V. Schreiber</string-name>
          <email>lincolnschreiber@gmail.com</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Rafael Kunst</string-name>
          <email>rafaelkunst@unisinos.br</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Jorge Luis V. Barbosa</string-name>
          <email>jbarbosa@unisinos.br</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Gabriel de O. Ramos</string-name>
          <email>gdoramos@unisinos.br</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>1]. Intelligent Transportation</institution>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Graduate Program in Applied Computing, Universidade do Vale do Rio dos Sinos</institution>
          ,
          <addr-line>São Leopoldo</addr-line>
          ,
          <country country="BR">Brazil</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2021</year>
      </pub-date>
      <volume>25</volume>
      <issue>2022</issue>
      <abstract>
        <p>Trafic systems play a key role in modern society. However, these systems are increasingly sufering from problems, such as congestions. A well-known way to eficiently reduce this kind of problem is to perform trafic light control intelligently through reinforcement learning (RL) algorithms. In this context, extracting relevant features from the trafic environment to support decision-making becomes a central concern. Examples of such features include vehicle counting on each queue, identification of vehicles' origins and destinations, among others. Recently, the advent of deep learning has paved to way to eficient methods for extracting some of the aforementioned features. However, the problem of identifying vehicles and their origins and destinations within an intersection has not been fully addressed in the literature, even though such information has shown to play a role in RL-based trafic signal control. Building against this background, in this work we propose a deep learning pipeline for extracting relevant features from intersections based on trafic scenes. Our pipeline comprises three main steps: (i) a YOLO-based object detector fine-tuned using the UAVDT dataset, (ii) a tracking algorithm to keep track of vehicles along their trajectories, and (iii) an origin-destination identification algorithm. Using this pipeline, it is possible to identify vehicles as well as their origins and destinations within a given intersection. In order to assess our pipeline, we evaluated each of its modules separately as well as the pipeline as a whole. The object detector model obtained 98.2% recall and 79.5% accuracy. The tracking algorithm obtained a MOTA of 72.6% and a MOTP of 74.4%. Finally, the complete pipeline obtained an error of 7.53% in terms of origin and destination counts.</p>
      </abstract>
      <kwd-group>
        <kwd>object detection</kwd>
        <kwd>object tracking</kwd>
        <kwd>trafic scenes</kwd>
        <kwd>intersections</kwd>
        <kwd>deep learning</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <sec id="sec-1-1">
        <title>Trafic congestion represents a major challenge in urban areas [</title>
        <p>
          control [
          <xref ref-type="bibr" rid="ref4">4</xref>
          ]. Roughly, considering that trafic light control can be seen as a sequential
decisionmaking problem, RL can be used to learn a behavior able to indicate which action should be
taken for any given trafic condition. In this context, having access to relevant information
describing trafic conditions is essential to enable RL adoption [ 5]. One such information refers
to the origin and destination of each vehicle on the scene, which enables trafic light controllers
to consider the trafic dynamics on the decision-making process.
        </p>
        <p>The extraction of features from trafic scenes can be performed using diferent approaches.
Recurrent approaches include [6]: lane sensors to count vehicles passing through a given location,
connected GPS devices to keep track of vehicles’ routes, laser radars to help reducing collisions,
and so on. However, these approaches typically rely on expensive, intrusive infrastructure.
On the other hand, recent advances in digital image processing leveraged by deep learning
techniques have enabled the adoption of less invasive, more easily deployable approaches. A
particularly interesting direction here refers to the use of intersection cameras coupled with
computer vision techniques to automatically extract relevant trafic information [ 7].</p>
        <p>
          The problem of extracting information from trafic scenes has been increasingly investigated
in the literature [7, 8, 9, 10, 11, 12, 13]. Typically, existing works consider trafic scenes (e.g.,
images, videos) and extract relevant information using classification or object detection models,
such as YOLO [14], SSD [15], CornerNet [16, 17], as well as two-stage approaches like R-CNN [18],
Fast R-CNN [19], and Faster R-CNN [20]. However, these works fail to obtain more complex
trafic information, like the origin and destination of the vehicles, which has shown essential
for trafic light control [
          <xref ref-type="bibr" rid="ref4">4, 5, 21</xref>
          ]. More recently, other works [22, 23] took a step forward by
also proposing tracking methods able to keep track of vehicles’ trajectories along the trafic
scenes. However, to the best of our knowledge, the identification of origins and destinations
has been neglected in the the literature, which has hindered the applicability of RL-based trafic
light control in real world.
        </p>
        <p>Motivated by the need to obtain relevant information for supporting RL-based trafic lights
control, in this work we introduce a complete pipeline for identifying and counting vehicles’
origins and destinations from trafic scenes. Our pipeline includes three main steps. The first
step employs a YOLOv4 network [14] for detecting vehicles in a trafic scene. Our model is
pre-trained on the COCO dataset [24] and then fine-tuned for trafic scenes using aerial images
from intersections, as available in the UAVDT dataset [25]. The second step of our pipeline
consists in a tracking algorithm, which identifies vehicles along frames in order to recognize
their trajectories throughout the intersection. Finally, as the last step, our pipeline identifies the
origin and destination of each vehicle by analyzing the lane from which it has departed and the
lane in which it arrived.</p>
        <p>The proposed pipeline was assessed using previously unseen trafic scenes. The object
detector step obtained a recall of 98.2% and accuracy of 79.5%. The tracking step yielded a
multiple object tracker accuracy (MOTA) of 72.6% and precision (MOTP) of 74.4%. The complete
pipeline obtained an average error as lower as 7.53% in terms of origins and destination counts.
Hence, putting all together, our pipeline has shown to recognize vehicles, their trajectories and
their origin and destinations, thus being able to properly summarize the origin-destination table
for a given trafic intersection.</p>
        <p>The main contributions of this work can be enumerated as follows:
• A customized YOLOv4 neural network [14] fine-tuned with the UAVDT dataset [ 25] for
detecting vehicles at intersections. Our model also features larger input images, with a
shape of 832 × 832.
• A vehicle tracking algorithm to identify the trajectory of a vehicle throughout an
intersection by comparing its position along diferent frames.
• An algorithm for analyzing the vehicles’ trajectories and extracting the number of vehicles
belonging to each origin and destination lanes in the intersection.</p>
        <p>The rest of this paper is organized as follows. Section 2 presents a brief overview of related
work. Section 3 introduces the pipeline presented in this paper. Section 4 presents an empirical
evaluation of our pipeline. Finally, Section 5 brings the concluding remarks.</p>
      </sec>
    </sec>
    <sec id="sec-2">
      <title>2. Related Work</title>
      <p>In this section, we briefly review the literature from two perspectives. As for the first perspective,
we consider approaches related to multi-object tracking, which comprise the first and second
stages of our pipeline. Considering the second perspective, we review works related to trafic
lfow control from video inputs.</p>
      <p>In multi-object detection and object tracking. The detector aims at extracting information
about objects of interest, such as their location in the scene. Currently, most methods that fall
within this category are based on Convolution Neural Networks (CNNs). Roughly, CNN-based
approaches can be divided into one-stage, such as YOLO [14], SSD [15], and CornerNet [16, 17],
and two-stage, such as R-CNN [18], Fast R-CNN [19], and Faster R-CNN [20]. On the other
hand, the tracker aims at identifying the same object throughout diferent scenes. To this end,
the tracker typically relies on detections output by a detector along multiple frames. Object
tracking can then be used for counting unique objects in a video, for example. Some of the
approaches that can be used to perform tracking include IOU Tracker [26], SORT [27], and
DEEP SORT [28].</p>
      <p>When it comes to vehicle counting, however, it is necessary to go beyond. Once vehicles are
detected and tracked throughout a trafic scene, specific methods are necessary to count the
number of vehicles, to estimate the trafic flow, or even to identify the origin and destination of
each vehicle in the scene. For this type of problem, [22] and [29] proposed the use of virtual
lines, which enable trajectories to be associated with given origins and destinations.</p>
      <p>In spite of the promising results achieved in the literature, to the best of our knowledge no
previous work proposed a complete pipeline for extracting and analyzing the origins and
destinations of vehicles within trafic intersections using a combination of deep learning approaches.
In particular, none of them jointly: consider the use of aerial images of intersections,
recognize vehicles, identify their paths, and quantify the number of vehicles for each combination
of origin-destination pairs. The lack of solutions comprising all these aspects motivates the
pipeline we propose in this work.</p>
      <p>1) Object detection phase</p>
      <p>2) Object tracking phase
Frame</p>
      <p>Detects vehicle
objects in frames
For each vehicle detected, a vector is
generated with the following attributes:
(x, y, width, height, confidence)</p>
      <p>Infers if the vehicle
was in the previous
frame</p>
      <p>Was the vehicle in the
previous frame?</p>
      <p>No</p>
      <p>The vehicle is
considered new and
an ID is created for it</p>
      <p>Yes
Groups the current location
of the detected vehicles
with that of the previous</p>
      <p>frame
For each vehicle, a vector containing its ID and all
its previous positions in the scene is returned.</p>
      <p>3) Vehicle entry and exit phase</p>
      <p>Checks if the vehicle
trajectory has touched
the virtual line placed in</p>
      <p>the scene
For each vehicle that touches the virtual
line, the array linked to this line receives
the vehicle ID and increments a counter.</p>
    </sec>
    <sec id="sec-3">
      <title>3. Proposed Pipeline</title>
      <p>This paper introduces a deep learning pipeline for extracting the origin and destination of
vehicles throughout a trafic intersection using aerial images. The underlying idea of our
pipeline is that, by identifying a vehicle and keeping track of its trajectory, it is possible to
identify the lanes through which it has entered and exited the intersection. That information
can then be used to count the number of vehicles on each origin and destination within the
intersection. In order to accomplish that task, our pipeline performs three tasks: (i) vehicle
detection, (ii) vehicle tracking, and (iii) origin-destination identification. The overview of our
pipeline is presented in Fig. 1.</p>
      <p>Roughly speaking, our pipeline starts with a frame being received as input. The first phase is
object detection one (Section 3.2), which detects the vehicles on the frame using a fine-tuned
YOLOv4 network [14]. The network is fine-tuning using the UAVDT dataset, as described in
Section 3.1. Once vehicles are detected, it is time for the object tracking phase (Section 3.3),
where the positions of a vehicle within subsequent frames are used to form its trajectory.
This step is performed using the tracking method proposed in [26]. Finally, the origins and
destinations identification phase (Section 3.3) is responsible for detecting the entrance and
exit points of each trajectory in order to allow summarizing the number of vehicles on each
origin-destination pair within the intersection.</p>
      <sec id="sec-3-1">
        <title>3.1. Dataset</title>
        <p>In order to train and validate our pipeline, we first had to search a dataset featuring trafic footage
with aerial angulation and appropriately annotated vehicles. Meeting these requirements provide
suficient conditions to perform object detection and tracking tasks using CNN architectures.</p>
        <p>We consider the UAVDT dataset [25]. The UAVDT dataset features trafic scenes with diverse
heights (i.e., low, medium, high) and angulations (i.e., front, side, and bird). This dataset includes
50 diferent trafic scenes, totaling over 80,000 frames. However, in order to ensure that the
whole intersection is captured in the scenes, we selected only a subset of scenes that are high
enough to enable all incoming and outcoming lanes to be observed. This includes scenes with
front or side views with at least medium altitude as well as bird view at any altitude. The final
list of scenes is presented in Table 1. These scenes are essential to train the vehicle detector
method, which we describe in detail in the next section.</p>
      </sec>
      <sec id="sec-3-2">
        <title>3.2. Object Detection Phase</title>
        <p>At this stage of the pipeline, the objective is to use the frames provided by the dataset as input to
the detector and thus carry out the identification of vehicles in the scene. During this stage, the
data is provided to the detector for use as input, and the result is the identification of vehicles.</p>
        <p>In order to perform object detection, we employ the YOLOv4 network [14], which can be
considered the state-of-the-art when real-time object detection architecture. The YOLOv4
network is pre-trained with the COCO dataset. However, for the particular case of trafic scenes,
this is not enough to yield satisfactory performance. To this regard, we fine tuned the YOLOv4
network using the UAVDT dataset (described in the previous section) as detailed next.</p>
        <p>We depart from the darknet implementation of YOLOv41 pre-trained on the COCO dataset.
The loaded model had its first 136 layers frozen, while the remaining layers were unfrozen for
training. In this way, we seek to accelerate the learning process while preserving the knowledge
already acquired by the pre-trained model. We further customized the input shape of the
network to 832 × 832 pixels (the original network had an input of 512 × 512 pixels) to improve
the performance of the network on distant scenes. Finally, we set the batch size to 6000 samples
(the original network uses 2000 samples) in order to take into account the RAM limitations of</p>
        <sec id="sec-3-2-1">
          <title>1Available at https://github.com/AlexeyAB/darknet</title>
          <p>our setup. Fig. 2 illustrates the output of this phase.</p>
        </sec>
      </sec>
      <sec id="sec-3-3">
        <title>3.3. Object Tracking Phase</title>
        <p>In the object tracking phase, each vehicle detected in the previous phase is tracked throughout
a sequence of frames in order to enable the identification of its trajectory. This step is essential
to enable the interpretation of the origins of destinations of the vehicles, as performed by the
phase described in the next section.</p>
        <p>We highlight that, although the object detection phase is the one responsible for identifying
the vehicles, it is not able to tell whether an object appearing in subsequent frames represent
the same vehicle. This is precisely the objective of the tracking phase, which needs to compare
the position of vehicles in subsequent frames in order to have a unique correspondence.</p>
        <p>In order to perform this task, we consider the tracker proposed in [26]. This method is based
on the assumption that the detector produces one detection per frame for each vehicle to be
tracked. In other words, for a given vehicle, the distance between its positions in subsequent
frames should be small or should not exist. Furthermore, this method assumes that the bounding
boxes representing the vehicle in two subsequent frames should have a high overlap, as measured
by the Intersect Over Union (IoU) metric.</p>
        <p>Figure 3a illustrates how the tracking technique works. In the figure, two objects are shown
along a sequence of four frames. Each object is delimited by a bounding box and the arrow
denotes its direction. Position are represented as  and  coordinates. As seen, for any object, the
bounding boxes on subsequent frames present a high overlap. Building upon that observation,
the trajectory of an object can be inferred by observing the position of its bounding box along
frames.</p>
        <p>In this sense, after receiving the vehicle detection coordinates, the tracking algorithm starts
its verification to infer whether the vehicle is new on the scene or not. If the vehicle is new,
an ID is assigned to it. Otherwise, the newly perceived coordinates are stored in an array
containing all coordinates previously detected for that particular vehicle. Fig. 3b presents the
result of the tracking method, where an ID is assigned to each vehicle identified in the previous
stage.</p>
      </sec>
      <sec id="sec-3-4">
        <title>3.4. Origin and Destination Identification</title>
        <p>
          At this stage of the pipeline, the objective is to detect the points where a vehicle enters and
exits the intersection. The idea is that, by detecting such points, one can infer the origin and
destination of each vehicle. Recall that, for RL-based trafic light control, this information is of
uttermost importance, as it allows the agent to properly model the flow of vehicles and make
its decisions [
          <xref ref-type="bibr" rid="ref4">4</xref>
          ]. To this end, we define virtual lines in the frames to represent the entrance
and exit points of the intersection, where each virtual line is composed of a pair of  and 
coordinates. The sequence of steps of this phase are depicted in Fig. 4a.
        </p>
        <p>In order to enable the identification of origins and destinations, virtual lines are placed at
the entrances and exits of the intersections. Then, through the data provided by the tracking
phase, it is possible to discover the entire trajectory of the vehicle along the scene based on
the returned array of coordinates. For each coordinate, its center is calculated to generate the
trajectory, as depicted in Fig. 4d. In this way, the trajectory is a set of centroids obtained from
the array of coordinates, as seen in Fig. 4e.</p>
        <p>To be able to know where a vehicle entered and exited the intersection, we calculate the
intersection between the vehicle’s trajectory and the annotated virtual line, as shown in Figs. 4f
and 4g. If the intersection is positive, we store the vehicle ID in an array associated with the
respective straight segment. In addition, we increment a counter that shows how many vehicles
have passed through that line.</p>
        <p>In Fig. 5, we can observe the operation of the pipeline. In the figure, once vehicles and their
trajectories are detected, it is possible to compute through which entrance and exit lines each
vehicle goes through. Such information can then be used to count the number of vehicles on
each origin and destination pair within the given intersection.</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4. Experimental Evaluation</title>
      <p>In this section, we present the experiments performed to assess our pipeline. The main objective
here is to evaluate the performance of each phase of the pipeline, as well as of the complete
pipeline. The evaluation methodology is presented in Section 4.1. Results are then detailed and
discussed in Section 4.2.</p>
      <sec id="sec-4-1">
        <title>4.1. Methodology</title>
        <p>In order to test our pipeline, we selected the scenes M0403 and M0603 from the UAVDT dataset.
For testing each phase of the pipeline, a diferent set of metrics is necessary. For multi-object
tracking tasks, the following metrics can be used [30]:
• IDF1: Global min-cost F1 score.
• IDP: Global min-cost precision.
• IDR: Global min-cost recall.
• Recall: Number of detections over number of objects
• Precision: Number of detected objects over sum of detected and false positives.
• FP: Total number of false positives.
• FN: Total number of misses.</p>
        <p>• IDs: Total number of track switches.</p>
        <p>The primary metrics used to evaluate the vehicle detection method were precision and recall.
In order to evaluate the vehicle tracking method, we employed MOTA and MOTP. The purpose
of adopting these metrics is to highlight the model’s success.</p>
        <p>In order to evaluate the complete pipeline, we need a metric able to compare the number of
vehicles on each origin-destination pair as output by our pipeline in comparison to the ground
truth counting. To this end, we propose a new metric called OD Error, as shown below:
     =
 
∑ |
=0</p>
        <p>−   | ,
 
(1)
where  represents the number of virtual lines in the scene or the number of routes, and
  and   denote the number of vehicles on virtual line  as detected by our pipeline
and represented as ground truth, respectively.</p>
        <p>Our pipeline was trained using Google Colab Pro, featuring a NVIDIA Tesla P100 GPU. The
experiments, in turn, were performed on a standard computer with Intel Core I7 CPU with on
16GB of RAM and a NVIDIA GeForce RTX 2060 GPU.</p>
        <p>In order to better assess the performance of our approach, we adopted [31] as a baseline
method for object detection and tracking, which we consider to be the state of the art in the
context of trafic. As for the origin-destination identification part, we include no comparison
given the lack of works on the topic.</p>
      </sec>
      <sec id="sec-4-2">
        <title>4.2. Results</title>
        <p>We start the results section by analyzing the performance of our pipeline in its first two phases,
the vehicle detector and the vehicle tracker. Table 2 presents the results obtained by our method
and the baseline for the M0603 and M0403 scenes of the UAVDT dataset. As seen, the average</p>
        <p>GT
results obtained by our pipeline outperform the current state-of-the-art approach by a good
margin for most metrics. These results indicate that our pipeline is able to properly detect and
track vehicles. This was made possible because we used a fine-tuned version of the YOLOv4
network, which yielded superior results than those obtained by the siamese network used
in [31]. Moreover, since the our method yields better detections, the tracking phase ends up
outperforming [31] as well.</p>
        <p>The detector achieved an accuracy of 79.5%. This result directly influence the accuracy of the
tracker, which ended up with an MOTP 74.4%. In order to improve the accuracy of the detector,
it is necessary to train the model with more instances of the truck and bus classes, whose
number was not suficient in the UAVDT dataset. Throughout the experiments we observed
that these specific classes end up failing more than cars. In addition, the use bird view images
hinders the identification of smaller objects in the image. To improve this aspect, one could
increase the size of the network at the time of training, which could enhance the accuracy at
the cost of increasing the complexity of the object detection network.</p>
        <p>Table 3 presents the results related to the number of vehicles that passed through each
virtual line drawn in the scenes. Observe that the number of virtual lines is seven and nine
for the M0603 and M0403 scenes, respectively. Results are compared to the annotated ground
truth values. As seen, our method correctly detected all cases in the first scene and mistakenly
detected only 3.38% of the cases in the second scene. We remark that the errors occurred because
the detector failed to identify these vehicles. These errors could be reduced by improving the
accuracy of the detector.</p>
        <p>Table 4 presents the overall results of our pipeline on the M0603 scene by means of the OD
Error metric. Recall that this metric shows for how many vehicles the pipeline failed to identify
their complete trajectories. As seen in the table, our pipeline missed a single vehicle, which
goes from A to F. The error happened because the detector failed to detect that vehicle in a
single frame in the middle of the trajectory. As such, the tracker ended up assigning a diferent
ID to the vehicle once it was detected again on the subsequent frame. From the table, it can also
be observed that our pipeline presented a more substantial error for the E-D pair. In that case,
the error happened because part of the scene is occluded, which prevented the detector from</p>
        <p>GT</p>
        <p>GT
detecting the vehicles on that part of the scene. This situation is illustrated in Fig. 6, where
the vehicle with ID 80 becomes undetectable when passing close to a tree and then becomes
detectable again, thus receiving a new ID.</p>
        <p>Finally, Table 5 presents the overall results of our pipeline on the M0403 scene by means of the
OD Error metric. As seen, only a single vehicle was not properly identified, which represents
a percentage error of 4.35% in the identification of the complete trajectory of the vehicles. In
this scene, no occlusion points exist. However, the error also happened due to a failure in the
detector. After the vehicle started its trajectory entering C, the detector failed, as such the
vehicle ended up receiving a new ID before ending its trajectory.</p>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>5. Conclusion</title>
      <p>
        In this paper, we presented a complete pipeline to extract the origins and destinations of vehicles
from scenes of trafic intersections. This information plays a role on enabling reinforcement
learning agents to control trafic lights [
        <xref ref-type="bibr" rid="ref4">5, 4, 21</xref>
        ] and could also be extended to other trafic
problems.
      </p>
      <p>In general, the pipeline obtained promising results, achieving an average error rate as low
as 7.53% in terms of origins and destinations identification. However, some aspects of the
pipeline presented less impressive results when facing occlusions or even when facing trajectory
interruptions. We achieved an average accuracy of 79.5%, which detracted from the tracker
accuracy, which reached 74.4%.</p>
      <p>As future work, we plan to train the model with a more significant number of instances to
increase its accuracy and thus improve the tracker’s accuracy. Likewise, our model could be
extended to deal with multi-camera settings, which could enable overcome occlusion-related
limitations. Another improvement that we are going to propose is a tracker method capable
of re-identifying the vehicle when it passes through an occlusion point, which could mitigate
discontinuities in the trajectory identification. Together, these changes would pave the way for
a future deployment of our pipeline. Another interesting direction for future work refers to
adopting some of the most recent object detection architectures, such as Vision Transformers [32]
and SWIN Transformers [33], which could improve the vehicles’ detection accuracy.</p>
    </sec>
    <sec id="sec-6">
      <title>Acknowledgments</title>
      <p>We thank the anonymous reviewers for their valuable feedback. This research was partially
supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES)
Finance Code 001, Conselho Nacional de Desenvolvimento Científico e Tecnológico - CNPq
(grants 306395/2017-7 and 314042/2021-0), Fundação de Amparo à Pesquisa do Estado do Rio
Grande do Sul - FAPERGS (grants 17/2551-0001197-0, 19/2551-0001277-2, and
19/2551-00013345), and Fundação de Amparo à Pesquisa do Estado de São Paulo - FAPESP (grant 2020/05165-1).
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