Class Weighted Focal Loss for Improving Class Imbalance in
Semi-supervised Object Detection
Shinichi Hoketsu, Tsubasa Hirakawaa, Takayoshi Yamashitab, and Hironobu FujiyoshicChubu University, 1200 Matsumoto-cho, Kasugai, Aichi, Japan{hoketsu513, hirakawa}@mprg.chubu.ac.jp, {yamashita, fujiyoshi}@isc.chubu.ac.jp

Keywords:

Deep Learning, Object Detection, Semi-supervised Learning, Class Imbalance, In-vehicle Camera Image

Abstract:

Object detection is a task for acquiring environmental information in automated driving. Object detection
is used to detect the position and class of objects in an image. It can be made more accurate by learningwith a large amount of supervised data. However, the high cost of annotating the data makes it difficult tocreate large supervised datasets. Therefore, research using semi-supervised learning for object detection has
been attracting attention. Previous studies on semi-supervised learning in object detection tasks have mainly
conducted evaluation experiments only on large datasets with many classes, such as MS COCO, and PASCAL
VOC. Therefore, the effectiveness of semi-supervised learning for in-vehicle camera data as input has not
yet been demonstrated. We examined the effectiveness of semi-supervised learning in object detection whenin-vehicle camera data are used as input. We also proposed a class weighted focal loss that employs a uniqueweighting method that takes into account the class imbalance problem. Experimental results indicate thatsemi-supervised learning is also effective when vehicle-mounted camera images are used as input. We also
confirmed that the proposed mitigates improves the class imbalance problem and improves accuracy.

1

Introduction

In the field of autonomous driving, it is essential toacquire environmental information such as the positions of surrounding vehicles and pedestrians. Object
detection is used to obtain those information, which
estimates the position and the class of objects existing in an image. Because of the development of deeplearning techniques, various object detection methods have been developed, and the high accuracy havebeen achieved by using a large amount of supervised
data for model training. However, building a largescale supervised dataset requires manual annotations,which is costly due to the high annotation costs.
To achieve higher accuracy while reducing theannotation cost, semi-supervised learning has been
gaining attention in recent years. Although semisupervised learning is widely investigated in generalobject recognition problems, various semi-supervised
object detection methods (Sohn et al., 2020; Xu et al.,2021; Chen et al., 2022; Liu et al., 2021; Liu et al.,2022) has been also proposed. In the previous reabchttps://orcid.org/0000-0003-3851-5221
https://orcid.org/0000-0003-2631-9856
https://orcid.org/0000-0001-7391-4725

search on semi-supervised learning for object detection, evaluation experiments have mainly been conducted using large-scale general object datasets suchas MS COCO (Lin et al., 2015) and PASCAL VOC(Everingham et al., 2010), which contain many object classes. Meanwhile, the effectiveness of semisupervised object detection for in-vehicle camera images has not yet been demonstrated.
In this paper, we aim to verify the effectiveness ofsemi-supervised object detection for in-vehicle camera images. Apart from the large-scale general object datasets, e.g., MS COCO and PASCAL VOC, invehicle camera image dataset has different characteristics. One of the characteristics is class imbalance
problem. In-vehicle camera images are collected only
on the road, which cannot be controlled. Therefore, it
is difficult to adjust the number of collected samples
per each object class, and the in-vehicle camera image
inherently contains the class imbalance problem.
Therefore, we propose to add class weights tothe classification loss in the loss of object detection
model training to address the class imbalance problem, which prevents a decrease in accuracy for classes
that are extremely rare in the dataset. Class weighttaking into account class imbalance sets the classweight on the base in of the total number of objects

in the dataset to optimize the object detection task.
Specifically, a smaller class weight is set for classes
with a large number of samples, while a larger classweight is set for classes with a small number of samples, thereby placing more emphasis on classes with asmall number of samples in the loss calculation. The
implementation of the optimized class weight for theobject-detection task improves the class imbalance
problem.
In our evaluation with BDD100K dataset (Yuet al., 2020), we demonstrate that the semi-supervised
object detection is effective for in-vehicle camera images. Also, we show that our proposed loss function
outperform the conventional supervised and semisupervised approaches.

2

Related Work

Herein, we briefly describe related works on supervised object detection and semi-supervised object detection methods.

2.1

Supervised Object Detection

Supervised object detection methods have been
widely studied in the field of computer vision. Among
various methods have been proposed, the supervised
method can be categorized in to the following two
types: one that uses anchor boxes (Ren et al., 2016;
He et al., 2018; Lin et al., 2018; Tan and Le, 2020)
and the other that is anchor-free (Tian et al., 2019;
Bochkovskiy et al., 2020; Tan et al., 2020; Zhou
et al., 2019). Anchor boxes-based approach are rectangular frames used to indicate regions where objects
may exist. Multiple anchor boxes of different sizes
and aspect ratios can be defined for each anchor on
the feature map. However, the use of anchor boxes
presents several problems, such as the existence ofmultiple hyperparameters including the number of anchor boxes, aspect ratios, and sizes, and the fact thatmost anchor boxes are treated as negative samples,making computation inefficient.
Various anchor-free methods have been proposed
to address the disadvantages of anchor boxes fully
convolutional one-stage object detection (FCOS) uses
a unique index called center-ness instead of anchor
boxes. Center-ness is defined as follows:s∗

centerness =min(l ∗ , r∗ ) min(t ∗ , b∗ )×,max(l ∗ , r∗ ) max(t ∗ , b∗ )(1)where, l ∗ represents the distance from the object
center to the left, r∗ represents the distance to theright, t ∗ represents the distance to the top, and b∗ represents the distance to the bottom. By using centerness, it is possible to prevent the prediction of bounding boxes centered on positions far from the object
center.
In this paper, we use the anchor free approach (i.e.,
FCOS) as an object detector of semi-supervised learning framework.

2.2

Semi-supervised Object Detection

object-detection methods for semi-supervised learning framework have been proposed (Sohn et al., 2020;
Xu et al., 2021; Chen et al., 2022; Liu et al., 2021; Liuet al., 2022). Major approach of semi-supervised object detection is pseudo-labeling.
One of the major pseudo-labeling approach is selftraining and the augmentation driven consistency regularization (STAC) and the variants (Liu et al., 2021;
Liu et al., 2022), which introduce strong augmentation STAC prepares two object-detection models:teacher and student and trains student model by using pseudo-labeling and strong data augmentation.
In this approach, teacher is trained on labeled data
only, while student is trained on both labeled andunlabeled data. The process starts with a burn-in
stage, where teacher is trained. After this stage, theweights of teacher are fixed, and data are input toteacher to make predictions. Non-maximum suppression is executed to remove labels with high uncertainty, and the remaining labels are treated as pseudolabels for student. Strong data augmentation is thenapplied to data similar to those predicted by teacher,and student makes predictions. The loss is calculated by comparing the predictions with the pseudolabels, and Student is trained using this loss. Thismethod can improve accuracy by providing a simple learning method and a large amount of unlabeled
data. However, during Student’s learning stage, theweight of Teacher is fixed, which means that the performance heavily depends on how accurate Teacher
can be trained during the burn-in stage.
The method called Unbiased Teacher (Liu et al.,2021) is used for improving the dependency issue during the burn-in stage. Unbiased Teacher updates theweights of Teacher on the basis of the exponential
moving average using Student’s weights, even after
the burn-in stage, which enables the feedback of Student’s learned knowledge to Teacher. The updating
formula for Teacher’s weights using the exponential
moving average is shown in Equation 2.
θt = αθt + (1 − α)θs

(2)where, θt represents Teacher’s weights, θs repre-

Teacher Refinement
Student Learning

Burn-In Stage

Teacher-Student Mutual Learning Stage
Figure 1: Overview of Unbiased Teacher v2

sents Student’s weights, and α is a hyperparameter.
By gradually bringing Teacher closer to Student using
the exponential moving average, Teacher can obtainStudent’s insights even after the burn-in stage. This
improves the quality of the generated pseudo-labels.

3

MethodOur proposed method adopts Unbiased Teacher v2(Liu et al., 2022) as a semi-supervised object detection framework. Unbiased Teacher v2 (Liu et al.,2022) is an improved version of Unbiased Teacher
that addresses the dependency issue during the burnin stage. Unbiased Teacher v2 is used along with theanchor-free method FCOS, which is not used in traditional semi-supervised learning. Figure 1 shows an
overview of Unbiased Teacher v2. Unbiased Teacher
v2 executes learning in two stages. In the burnin stage the teacher that generates pseudo-labels istrained using only labeled data. After the burn-in
stage, student is trained using the same procedure
as before. However, unlike with STAC, Unbiased
Teacher v2 does not initialize the model with student but uses a replica of teacher as student. Weakdata augmentation is also applied to the data input toteacher, while strong data augmentation is applied tothe data input to student. The loss is then calculated
to obtain the gradient, which is used to update theweights of Student. After updating the weights of student, the weights of teacher are updated using exponential moving average. As data augmentations, weakdata augmentation included horizontal flip, whilestrong data augmentation includes color transformation, grayscale, Gaussian blur, and cutout. The proposed method generates pseudo-labels in anchor-freemethods and improves the learning method for de-tectors using the pseudo-labels. They discuss theissues with the traditional semi-supervised learning
method that uses pseudo-labels and point out the uncertainty of the pseudo-labels predicted by Teacher.
With Unbiased Teacher, the Teacher-predicted results
are thresholded, and predictions exceeding the threshold are always treated as pseudo-labels. However,this method also treats false detections made by the
Teacher as pseudo-labels, which could suppress Student’s learning. To address this issue, they the proposed the Listen 2 Student mechanism. This mechanism does not update the weights if Student’s prediction is correct compared with the Teacher predicted
pseudo-label. This prevents the effect of false detections on Student’s learning. However, it is difficult todetermine whether Teacher’s prediction is correct during Student’s learning phase because the ground truth
is not used. Therefore, the they use negative power
log-likelihood loss (NPLL) (Lee et al., 2022) to evaluate whether Teacher’s prediction is correct. The calculation method for NPLL is shown in Equation 3.

sup
Lreg
=

∑ ηi ∑ids −dg
2δ2s

2

!
!
1
2
+ log δs +2 log 2π2(3)where, δs is the uncertainty of Student’s prediction, dt is Teacher’s regression prediction, ds isStudent’s regression prediction, and ηi is calculated
by computing the mean IoU between the predictedbounding box Bs and pseudo-label Bt . The calculation method for ηi is shown in Equation 4.
ηi =Bs ∩ Bt
Bs ∪ Bt(4)

3.1

Table 1: Number of samples per classes in the train data of
BDD100K dataset

Class Weighted Focal Loss

We propose the introduction of a unique class weight
optimized for the object detection task for the classloss function, focal loss (Lin et al., 2018) as a countermeasure against the class imbalance problem of semisupervised learning in the object-detection task. Focal loss was mitigates the decrease in accuracy due
to the imbalance between foreground and backgroundregions in object detection tasks. However, since it
is focused on foreground and background regions, itcannot be said that it performs a loss calculation thattakes into account the object class. Tuning hyperparameter γ to adjust the magnitude of the loss also requires effort to be made for each dataset. A previous study (Cui et al., 2019) added class weights tofocal loss in the same manner as in this study. However, that study only defined weight-setting methods
for image recognition, and it is difficult to set appropriate weights for object detection.
Therefore, propose a weight setting method specific to the object-detection task to mitigate the classimbalance problem by applying a class weight set foreach class to focal loss. We define the loss function
with class weight added to focal loss as class weighted
focal loss. The formula for calculating class weighted
focal loss is shown in Equation 5.

CW FL (Pt ) = −Wt (1 − pt )γ log (pt )(5)where, Pt represents the class probability, and Wt
is the weight in the object class. The formula for calculating Wt is shown in Equation 6.
Call
)
(6)
Ct
where, Call is the total number of objects in allclasses included in the training data, and Ct is the total
number of predicted objects in the training data for thetarget class. We define the total number of objects as
the total number of boxes in the entire training dataset.
By multiplying Wt with the class loss, we can carryout learning focused on classes with fewer objects.
Wt = log(

4

Experiments

We the effectiveness of the proposed object-detection
method by using in-vehicle camera images. We also
investigated the tendencies when changing γ. Experiments will be evaluated primarily through quantitativeand qualitative evaluations.

4.1

Object class# of samples

Person
Car
Rider
Bus
Truck
Bike
Motor
Traffic light
Traffic sign

104,611815,717
5,166
13,26934,2168,217
3,454
213,002274,594

DatasetThe BDD100K dataset consists of data captured withcar-mounted cameras while driving through cities
such as New York, Boston, Washington DC, and San
Francisco. The images were captured under various environmental conditions including clear skies,
cloudy skies, rain, snow, and various times of day
ranging from early morning to late night, as well as
various traffic conditions ranging from congested toempty roads, resulting in a diverse dataset with manydifferent features. The resolution of the image data
is 1,280 × 740 pixels, and the dataset is comprised of
70,000 training images and 10,000 validation images.
For the object-detection task, nine classes are defined, Person, Car, Rider, Bus, Truck, Bike, Motor,
Traffic light, and Traffic sign. Table 1 shows the number of objects per class in the BDD100K training data.
While the Car class contains many objects, classes
such as Motorcycle, Rider, and Bicycle contain relatively few objects. Additionally, while there are
70,000 training images, some classes, such as Truck
and Bus, have fewer objects than this, indicating that
there are many images in which certain classes are
not present. Therefore, there will be a class imbalance problem, in which the model will tend to overfit
to classes with many samples when trained for object
detection.

4.2

Experimental Settings

We set the experimental conditions on the basisof previous research on object detection in semisupervised learning (Sohn et al., 2020; Xu et al.,2021; Chen et al., 2022; Liu et al., 2021; Liuet al., 2022) and compared out method with semisupervised learning and supervised learning methods.Specifically, we randomly extracted 1, 5, and 10%of the entire dataset as a supervised set and used theremaining data as an unlabeled set. When extracting
supervised sets, we set the 5% set to contain 1% of theTable 2: Comparison of supervised, semi-supervised learning, and proposed method

1%Supervised
Semi-supervised
Proposed

5%

10%

AP

AP50

AP75

AP

AP50

AP75

AP

AP50

AP75

13.37
20.80
19.68

27.19
40.61
37.97

11.22
18.23
17.49

20.93
25.64
26.12

42.35
50.01
50.42

17.99
22.28
23.01

23.33
27.71
28.20

45.80
53.21
53.91

20.59
24.64
25.23

Table 3: Comparison of class accuracy between supervised and semi-supervised learning

Supervised
Semi-supervised
Proposed

Person

Car

Rider

Bus

Truck

Bike

Motor

Traffic light

Traffic sign

22.81
26.95
27.28

40.54
43.29
43.63

13.55
15.59
16.62

34.02
39.48
39.48

31.52
37.94
36.76

14.24
17.58
18.50

12.38
14.56
16.77

14.69
21.34
21.76

26.26
32.70
32.98

data and the 10% set to contain 5% of the data. Thisis because supervised sets can cause large gaps in accuracy in semi-supervised learning experiments. To
account for accuracy deviations, the experiment was
conducted with seed values for each of the five patterns, and comparisons were made on the basis theaverage accuracy.
We used Unbiased Teacher v2 as the semisupervised learning method for object detection. The
backbone was ResNet-50 (He et al., 2015), andthe detector used FCOS. We followed the settings
in a previous study (Liu et al., 2022) for the data
augmentation and hyperparameters used. We also
used a model pre-trained on ImageNet as the pretraining model. The number of training iterations was
180,000, consisting of 30,000 iterations in the burnin stage and 150,000 iterations in the Teacher-Student
Mutual Learning stage. The batch size is set to 16,
with 8 supervised and 8 unsupervised images in eachbatch.
The hyperparameter γ of the proposed method was
set to 1, which achieved the highest accuracy in thisstudy.

4.3

Evaluation Metrics

We used mean average precision (mAP) for evaluation, which is a performance metric that can be calculated by taking the average of precision and recall foreach class. The mAP is defined as follows:∑ APc
mAP = c.
(7)
Nc
Here, Nc is the number of object classes and average
precision (AP) of class c is
Z 1

APc =

p (r) dr.

(8)0where, p denotes precision, r denotes recall, c denotes class, Nc denotes the total number of classes,

and APc denotes the AP for each class.

4.4

Quantitative Results

Table 2 shows the comparison of overall accuracy,
where ”1%”, ”5%”, and ”10%” represent the percentage of labeled data in supervised learning. Notethat unsupervised data are not used with the supervised learning method. The semi-supervised learning
method outperformed the supervised learning method
in overall accuracy, as shown in both Tables 2 and3. This result suggests that semi-supervised learningis effective in datasets consisting only of in-vehicle
camera images. In terms of the difference in AP by
the percentage of labeled data shown in Table 2, thedifference was 7.43 points for 1%, 4.71 points for 5%,
and 4.38 points for 10%. The greater the scarcity oflabeled data, the larger the difference in accuracy between supervised learning and semi-supervised learning. Therefore, semi-supervised learning is superior
in situations where labeled data are scarce. Regarding
the class probabilities in Table 3, it is thought that thedecrease in accuracy due to class imbalance occurs
in semi-supervised learning for classes such as Car,
which have many samples, and classes such as Rider
and Motor, which have few samples, where the difference in accuracy between supervised learning andsemi-supervised learning is small.
Next, we compared a semi-supervised learning
method with our proposed method. Looking at thedifference in AP by the percentage of labeled data
shown in Table 2, the accuracy improved when using
our proposed method with 5% and 10% labeled data.
However, for 1% labeled data, the accuracy of thesemi-supervised method was higher, indicating thatthe accuracy of our proposed method decreases when
the labeled data is scarce. This is because weighting
the data on the basis of randomly sampled 1% causes

Table 4: Accuracy comparison for different γ

1%

5%

10%

γ

AP

AP50

AP75

AP

AP50

AP75

AP

AP50

AP75

0
1
2
3

17.72
19.68
19.44
19.35

33.77
37.97
38.02
37.17

15.90
17.49
17.14
17.19

24.53
26.12
26.04
25.35

47.47
50.42
50.47
49.15

21.86
23.01
22.97
22.24

26.64
28.20
27.93
27.78

50.45
53.91
53.78
52.91

24.20
25.23
24.64
24.89

Table 5: Accuracy comparison by class for different Gammaγ

Person

Car

Rider

Bus

Truck

Bike

Motor

Traffic light

Traffic sign

0
1
2
3

26.68
27.28
27.20
26.91

42.92
43.63
43.27
43.39

15.26
16.62
15.93
15.11

38.07
39.48
40.19
40.73

34.33
36.76
38.16
38.02

18.34
18.50
18.59
17.97

16.12
16.77
16.20
14.62

18.59
21.76
20.90
20.97

29.44
32.98
30.94
32.25

the difference in weights between classes with few
samples and those with many samples to become toolarge. Looking at the differences in accuracy for eachclass shown in Table 3, our proposed method achieves
higher accuracy for all classes except for Truck andBus. The reason the accuracy did not improve forthese classes may be that they share similar featureswith the Car class and weighting alone is not sufficient to distinguish them.

4.5

Effect of γ

We investigated the effects of changing γ with our proposed method. Table 4 shows the comparison of accuracy for different percentages of labeled data, while
Table 5 shows the comparison of class-wise accuracy
when the labeled data were 10%. Based on the resultsin Table 4, except for AP50 when labeled data were5%, the highest accuracy was achieved when γ was set
to 1. Therefore, it can be concluded that setting γ to
1 is appropriate. However, as we can see from Table5, for the Bus, Truck, and Bike classes, the highest
accuracy was achieved when γ was set to 2 or 3. Thisis because as γ increases, the loss for classes that are
similar to the correct class, such as Bus and Truck,is almost ignored even if their confidence scores are
not high. This helps improve the learning of Bus andTruck. Similarly for Bike class, the loss is also almost
ignored when the features are similar to those of theMotor class.

4.6

Qualitative Results

Qualitative evaluation is shown in Figure 2, 3.
With the supervised-learning method (Figure 2b), theTruck on the left side of the image was misclassi-

fied as a Car and a false detection is made around thetire area. With the semi-supervised-learning method(Figure 2c), a Car was not detected in the center
back. However, the proposed method (Figure 2d)
suppressed false detections for the Truck on the left
side of the image and correctly detected the Car
in the center back. When comparing the proposed
method (Figure 2d) with the semi-supervised-learning
method (Figure 2c), the proposed method detected
objects with higher class probabilities than the semisupervised method. However, the proposed method
misclassified the Truck on the left side of the image
as a Car(Figure 2d). Therefore, the proposed method
is not able to acquire features that can distinguish
Trucks similar to Cars through semi-supervised learning.
In a different scenario, as shown in Figure 3, whena rider on a motorcycle is positioned in the center ofthe screen, it becomes evident that only the proposed
method correctly detects them. Furthermore, the proposed method enables the detection of individuals attempting to cross a pedestrian crossing. This demonstrates that using the proposed method allows for the
improved detection rate of minority classes, as evident through qualitative assessment.

5

Conclusion

In this paper, we focus on the semi-supervised object
detection of in-vehicle camera images and we proposed class weighted focal loss. Our method is basedon pseudo-labeling approach (Unbiased Teacher v2)
and we introduce the focal loss weighted by class balances in the training dataset. This enables us to improve detection accuracy on a rare object classes.
In the experiments, we used BDD100K as the(a) Ground truth(b) Supervised-learning method(c) Semi-supervised-learning method(d) Proposed (γ = 1)
Figure 2: Example of Visualization of Object Detection

in-vehicle camera image dataset and evaluated theeffectiveness of the proposed method. The proposed method showed improved accuracy comparedwith conventional supervised- and semi-supervisedlearning object-detection methods except in cases
where the teacher data was 1%. Since the proposed
method calculates weights on the basis the number ofsamples in the dataset, it enables learning that emphasizes classes with fewer samples. However, we foundthat simply adding weights does not sufficiently distinguish between classes with similar characteristics
in some cases, and this does not lead to improved accuracy in certain classes. Future work includes establishing appropriate class-weight settings and a learning method focused on fewer samples.

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