Investigation of the Performance of Different Loss Function Types

Within Deep Neural Anchor-Free Object Detectors

Ala’a Alshubbak

1,2

and Daniel G

orges

Institute of Electromobility, University of Kaiserslautern-Landau, Kaiserslautern, Germany

German Jordanian University, Amman, Jordan

Keywords:

Anchor-Free Object Detection, Deep Learning, ResNet, IOU Losses, Attention Mechanism, Saliency Map.

Abstract:

In this paper, an investigation of different IoU loss functions and a spatial attention mechanism within anchor-

free object detectors is presented. Two anchor-free dense predictor models are studied: FASF and FCOS

models. The models are tested on two different datasets: the benchmark COCO dataset and a small dataset

called OPEDD. The results show that some loss functions and using the attention mechanism outperform their

original counterparts for both the huge multi-class COCO dataset and the small unity-class dataset of OPEDD.

The proposed structure is tested over different backbones: ResNet-50, ResNet-101, and ResNeXt-101. The

accuracy of basic models trained over the coco dataset improves by 1.3% and 1.6% mAP for the FSAF and

FCOS models based on ResNet-50, respectively. On the other hand, it increases by 2.3% and 15.8% for the

same models when trained on the OPEDD dataset. The effect is interpreted using a saliency map.

1 INTRODUCTION

Deep learning is a new machine learning technique

that uses deep neural networks to perform various

tasks e.g in robotics, natural language processing, and

image recognition. In computer vision, these net-

works are trained on large datasets to learn patterns

and features in visual data, enabling them to perform

tasks such as object detection, image classiﬁcation,

and segmentation. By leveraging the representational

power and robustness of deep learning models, com-

puter vision applications can achieve state-of-the-art

performance.

Deep learning-based object detection is divided

into two approaches: anchor-free and anchor-based

detectors (Liu et al., 2020). Anchor-free detectors

are different from anchor-based ones in the technique

used to produce the boundary box of objects. The lat-

ter approach relies on pre-deﬁned anchor boxes, while

the ﬁrst one uses mostly multi-level Feature Pyra-

mid Network (FPN) (Lin et al., 2017a) prediction to

extract the necessary features for each object. The

anchor-based approach is considered the more accu-

rate one, but with some disadvantages. It is more

complex and requires more time in the training phase.

On the other hand, an anchor-free approach is a new

approach that gets rid of some problems present in the

previous approach, such as creating multi-proposed

regions and the imbalance between negative and pos-

itive samples.

Anchor-free detectors are still an emerging area of

research and worth investigating further. Relatively

little effort has been spent so far in improving the

performance of anchor-free detectors and deploying

them in real-time applications. In this work, two of

the anchor-free dense predictors are used, the Feature

Selective Anchor-Free Module (FSAF) (Zhu et al.,

2019a) and the Fully Convolutional One-Stage Ob-

ject Detection (FCOS) (Tian et al., 2019), as those

two models are the most popular dense models that

are based on both FPN and Intersection over Union

(IoU) loss for bounding box regression. In this paper

the effect of using different types of IoU losses within

the anchor-free dense predictors is investigated, with

a focus on applications in rural environments, which

has rarely been discussed before. Figure 1 shows the

general structure of such dense anchor-free models.

In the investigations the spatial attention mechanism

(Zhu et al., 2019b) is included within the backbone of

the models to enhance their performance. It is shown

that by using such technique, anchor-free dense pre-

dictors can be improved depending on to their struc-

ture by 0.8% and 0.4% mAP for FSAF and FCOS

ResNet-50 models, respectively. Moreover this im-

provement does not increase the complexity of the

original deep neural network model.

Alshubbak, A. and Görges, D.

Investigation of the Performance of Different Loss Function Types Within Deep Neural Anchor-Free Object Detectors.

DOI: 10.5220/0012354900003636

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 16th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2024) - Volume 3, pages 401-411

ISBN: 978-989-758-680-4; ISSN: 2184-433X

401

Figure 1: General structure of dense anchor-free model.

The paper is divided into ﬁve sections: the ﬁrst

one introduces previous work while the second one

describes the architecture of the proposed approach.

The third section explains the setup of the environ-

ment, the datasets, and the evaluation criteria. The re-

sults and discussion section provides a detailed expla-

nation of the performance of the proposed approach.

Lastly, future directions are discussed.

2 RELATED WORK

Much previous work has focused on detecting hu-

mans in urban environments using various datasets

such as KITTI (Geiger et al., 2012), Caltech (Doll

et al., 2009) Pedestrian Detection, and Oxford (Mad-

dern et al., 2017). However, the detection of humans

in rural environments remains a challenging task, with

fewer datasets and less effort put into this ﬁeld. The

rural environment is highly unstructured, and its char-

acteristics are different from those of urban envi-

ronments, making it more challenging to detect hu-

mans. Table 1 shows a detailed comparison between

the two environments in terms of detecting humans.

Three approaches are reported in literature to detect

humans in orchards and suburban environments, in-

cluding classical machine learning approaches such

as rigid object detectors and deformable parts models,

as well as deep convolutional neural network mod-

els. Most of the state-of-the-art object detectors based

on deep neural networks have been trained on bench-

mark datasets such as COCO (Lin et al., 2014). Re-

lying on transfer learning between urban and rural

environments leads to low-performance results, and

researchers have had to train new models with new

datasets from the rural domain (Neigel et al., 2020;

Neigel et al., 2021).

The focus of this paper is to investigate models

that are based on a deep learning (DL) approach with

a less complex structure and enhance their perfor-

mance and speed to compete with existing detectors.

Table 1: Difference between urban environment and subur-

ban or rural environment in the detection of humans (Jiang

et al., 2021; Xiang et al., 2020; Kragh et al., 2017).

Items Urban environ-

ment

Suburban environ-

ment

Human

Pose

Limited poses,

such as walking,

standing, and

riding a bike.

More challenging

poses, such as jump-

ing, crouching, lying,

and bending.

HOG

Visual-

ization

Non-uniform,

easy to dis-

cover different

patterns.

Uniform patterns,

have repetitive tex-

ture.

Datasets Rich & multiple

datasets: KITTI,

Caltech-USA,

Oxford dataset .

Fewer datasets, such

as RELLIS-3D (Jiang

et al., 2021), OPEDD

(Neigel et al., 2020),

FieldSAFE (Kragh

et al., 2017), and KIT

MOMA(Xiang et al.,

2020).

Problem Mostly dense ob-

jects

More partially oc-

cluded, dense and

small objects

Back-

ground

Charac-

teristic

Low texture, rep-

resented by hori-

zontal and verti-

cal edges.

More complex texture

distributed over differ-

ent orientations.

Content

Relation

More contextual

information

Less contextual infor-

mation.

Detector

Paradigm

Traditional

methods (SVM,

DPM) and DL

Less work, mostly

DL with sensor fusion

(Jiang et al., 2021)

According to that, only anchor-free detectors are used

and tested with a small, speciﬁc dataset as well as a

benchmark dataset, which will enhance the reliability

of the proposed approach.

3 MODEL ARCHITECTURE

3.1 Model Structure

The architecture of object detectors mainly consists

of three components: the backbone, the neck, and the

head. The ﬁrst two parts are responsible of feature

extraction, while the head part is used for classiﬁca-

tion and regression of an object and its bounding box.

Dense anchor-free detectors share the same structure

using a backbone from the ResNet family (He et al.,

2016; Xie et al., 2017) and a neck using FPN (Lin

et al., 2017a).

The FSAF and FCOS models used in this paper

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402

are different in the way of regression of the bound-

ing boxes of the objects in their head part. The FSAF

model uses the idea of a 4-dimensional vector for re-

gression, while the FCOS model uses a centerness

loss to adjust the bounding box according to the cen-

ter of the object. Both of these models use focal loss

(Lin et al., 2017b) for classiﬁcation.

3.2 Loss Functions

In object detection models, two types of loss func-

tions are used: one for classiﬁcation and another for

regression of bounding boxes. Cross-entropy loss is

mostly used in anchor-based detectors for classiﬁca-

tion, while focal loss is used in anchor-free detectors.

Regression loss is used to optimize the position of the

bounding boxes and smooth L1 loss or cross-entropy

loss is used in anchor-based detectors, while Intersec-

tion over Union (IoU) loss (Yu et al., 2016) is used in

dense predictors. Recently, modiﬁcations have been

proposed for IoU loss to improve its performance, in-

cluding GIoU (Rezatoﬁghi et al., 2019), DIoU, and

CIoU loss (Zheng et al., 2020). The general deﬁni-

tion of the Intersection over Union (IoU) loss is

IoUloss = 1 −

intersection(Bb

Predict

, Bb

Ground

)

union(Bb

Predict

, Bb

Ground

)

(1)

where Bb

Predict

is the bounding box of prediction

while Bb

Ground

is the bounding box of ground truth.

The modiﬁcations of IoU loss for improving its per-

formance are deﬁned by

1. Generalized IoU (GIoU) (Rezatoﬁghi et al., 2019)

IoU

= 1 − IoU +

|c \ union(Bb

Predict

, Bb

Ground

|c|

(2)

where c is the smallest enclosing object covering

both Bb

Predict

and Bb

Ground

2. Distance IoU (DIoU) (Zheng et al., 2020)

IoU

= 1 − IoU + R

DIoU

(3)

where R

DIoU

is a penalty term of the central dis-

tance

DIoU

Predict

, b

Ground

)

(4)

where b

Predict

and b

Ground

are the central points of

Ground

and Bb

Predict

, ρ is the Euclidean distance

between the two center points, and c is the diago-

nal length of the smallest enclosing box covering

the two boxes. Figure 2 shows all parameters that

are used in the adjustment of DIoU loss regres-

sion.

Figure 2: DIoU loss function representation with distance

d between central points of ground truth box (green) and

predicted box (black) and c as diagonal length of the small-

est enclosing box (grey) that covers those two boxes (Zheng

et al., 2020).

3. Complete IoU (CIoU) (Zheng et al., 2020)

IoU

= D

IoU

+ αυ (5)

where α is a trade-off parameter and υ is the as-

pect ratio which are described by

υ =



arctan

− arctan



(6)

α =

(1 − IoU)+ υ

(7)

where w

and h

are the width and height of the

ground truth bounding box and w and h are the

width and height of the predicted bounding box.

The main difference between these losses is the in-

troduction of new terms, such as central point dis-

tance, overlap area, and aspect ratio. Most research

in anchor-based detectors shows that systems using

CIoU loss converge faster and provide more accurate

object localization results. The investigation of dif-

ferent IoU losses within anchor-free detectors has not

been covered yet. It is the topic of this paper.

3.3 Attention Mechanism

The attention mechanism has been inspired by the hu-

man visual system (Guo et al., 2022) with which hu-

mans can understand what is in the scene and where

it is from the initial glance. Essentially, deep neu-

ral network researchers try to further improve the per-

formance of CNNs by adding mechanisms to answer

questions such as what to pay attention to (channel

attention), where to pay attention (spatial attention),

when to pay attention (temporal attention), and which

to pay attention to (branch attention).

In this paper, a spatial attention mechanism (Zhu

et al., 2019b) in a plug-in manner is used instead

of using a combination of channel and spatial ones

Investigation of the Performance of Different Loss Function Types Within Deep Neural Anchor-Free Object Detectors

403

as most researchers mention that a spatial attention

mechanism is suited for dense prediction situations,

while channel attention is rather used for classiﬁca-

tion tasks (Guo et al., 2022).

Figure 3: Plug-in attention block in purple within the resid-

ual block in ResNet (Zhu et al., 2019b).

The spatial attention mechanism in general has

four main factors from which the attention model as-

signs weights to the key with respect to the query (Zhu

et al., 2019b). Those factors are (i) the query and key

content ε1, (ii) the query content and relative position

ε2, (iii) the key content only ε3, and (iv) the relative

position only ε4.

This attention layer has been added into two stages

within the ResNet-50 model: stage 4 (Residual Block

4) and stage 5 (Residual Block 5). Its exact location is

shown in Figure 3, which is between the 3x3 convo-

lutional layer and the 1x1 convolutional layer for all

residual blocks in both stage 4 and stage 5.

Our model uses the factor of key content only (ε3)

which generates higher performance. Figure 4 shows

the modiﬁed structure of the proposed model after

adding the spatial attention block and with the loss

functions.

4 DATASETS AND TRAINING

ENVIRONMENT

4.1 Dataset and Evaluation Criteria

Different datasets have been produced in the ﬁeld of

agriculture as well as suburban and rural settings,

even though those datasets are still fewer than the

ones used to detect and recognize objects in urban set-

tings. In this paper, the dataset OPEDD (Neigel et al.,

Figure 4: Modiﬁed structure of the FSAF model that used

in this work.

2020) is used, which consists of two types of suburban

environments: meadow areas or construction areas. It

consists of 1018 images captured by a stereo camera.

845 images are used for training purposes, 88 images

for testing and 82 images for validation. All samples

contain at least one human as a major category to be

detected.

Three main evaluation parameters are used in this

investigation: the mean average precision (mAP),

the ﬂoating-point operations FLOPs (GFLOPs), and

trained parameters as well as the average iteration

time (seconds per iteration).

The mean average precision is a representation of

the accuracy of the model while the iteration time is

an indication of training speed. On the other hand,

the FLOPs and trained parameters give an initial in-

dication of the complexity of each model. This factor

is not so accurate, as it does not include the attention

mechanism layers. Table 2 shows the FLOPs and the

parameters for different models for comparison. The

bar charts in Figure 5 show the differences in average

iteration time for different anchor-free model struc-

tures for both FSAF and FCOS models.

All methods presented in this paper are tested for

three main sizes of the object (small, medium, and

large) and under different threshold values for Inter-

section over Union (IoU) (50% and 75%). Tables 3,

4, and 5 show the performance of each of the models

used in this paper and the effect of using the spatial

attention mechanism within the structure.

4.2 Training Environment

The experiments are carried out on a machine with

one NVIDIA RTX A6000 GPU using the ResNet

family (He et al., 2016; Xie et al., 2017) for dense

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404

(a) The FSAF model

(b) The FCOS model

Figure 5: Average iteration time for both the FSAF and FCOS models with different structures trained on the COCO bench-

mark dataset.

Table 2: Complexity measurements for both FSAF and

FCOS model with different backbone structures with and

without Spatial Attention Mechanisms.

Model Backbone Structue

Complexity

Flops Param

FSAF

ResNet-50

w/o att 206.28 36.19

w att 207.48 39.74

ResNet-101

w/o att 282.35 55.19

w att 285.8 62.08

ResNeXt-101

w/o att 439.57 93.92

w att 494.49 204.08

FCOS

ResNet-50

w/o att 200.55 32.02

w att 201.75 35.56

ResNet-101

w/o att 276.62 50.96

w att 280.07 57.86

ResNeXt-101

w/o att 438.59 89.79

w att 493.5 199.95

detectors (Kong et al., 2020; Tian et al., 2019; Zhu

et al., 2019a). The original resolution of the input

images is 2208 x 1242, which is changed into differ-

ent sizes, mainly 1333 x 800 for anchor-free dense

predictors. The model is trained over 12 epochs for

the COCO benchmark dataset and over 30 epochs

for the OPEDD dataset. All models are trained on

a batch size of 2 except the FSAF model trained over

the OPEDD dataset where a batch size of 4 is used.

The MMDetection open-source toolbox (Chen et al.,

2019) is partially used to design the modiﬁed model

and plug in the attention mechanism block.

5 RESULTS AND DISCUSSION

5.1 Performance of Models on OPEDD

Dataset

The main result is presented in Table 3. It shows a

comparison in Mean Average Precision (mAP) be-

tween baseline structures of both FSAF and FCOS

dense object detectors and our proposed structures.

It is obviously seen that using the CIoU loss with

the spatial attention mechanism in an anchor-free de-

tector improves the detection accuracy with 2.3 %

mAP compared to the baseline structure of the FSAF

model. Additionally, it shows an increase of 16.1%

mAP compared to the baseline structure of the FCOS

model. Moreover, the result shows that the changes

within the structure and architecture of the FSAF

model enhance the detection of small objects which is

one of the challenging topics in computer vision and

object detection (Tong et al., 2020). The proposed

approach enhances the detection of small, medium,

and large objects by 2.8%, 5.9%, and 1.6% mAP re-

spectively. Corresponding results are obtained for the

FCOS model with a ratio of 2.9%, 11.9%, and 35.6%

mAP, respectively.

Further analysis is mentioned in Table 4. A base-

line structure for both FSAF and FCOS models pre-

trained on a benchmark COCO dataset is used as

a transfer learning stage for training all new pro-

Investigation of the Performance of Different Loss Function Types Within Deep Neural Anchor-Free Object Detectors

405

posed structures on the OPEDD dataset. The results

show that the modiﬁed structure with spatial attention

and GIoU loss outperforms the baseline structure by

0.4% for the FSAF model and by 0.7% for the FCOS

model.

Figure 6 shows exemplary results of detecting hu-

mans using dense predictors. The ﬁgure illustrates

the improvement of the proposed FSAF model with

the new structure over the original structure as well

as over other dense predictor structures such as Fove-

aBox (Kong et al., 2020) and FCOS all of which have

the same backbone of ResNet-50 (He et al., 2016). It

is noticeable that both the FSAF and FCOS models

in their original structure which contains an IOU loss

can not detect humans in occluded situations, while

the proposed modiﬁcation in the FSAF model makes

it more accurate without huge changes in the deep

structure of the neural network.

Figure 6: Results of detecting a human in a dense (oc-

cluded) situation using different dense predictors, a. Fove-

aBox, b. FCOS, c. FSAF with normal IoU loss, and d. new

FSAF structure with an attention mechanism. All models

have the backbone of ResNet-50. .

5.2 Saliency Map for an Explanation of

Deep Neural Network Behavior

A saliency map is a technique used to highlight the

most important features in computer vision that af-

fect the detection process. The D-RISE saliency map

(Petsiuk et al., 2021) is used in this work to give a

clear overview of what is going on behind the models

and their structure. It shows how each model looks

at the features within the images, and how to detect

each category. The D-RISE approach has been cho-

sen over other saliency methods as it has the ability to

explain different types of object detectors, both one-

stage and two-stage detectors. Figure 7 shows the

different saliency maps produced after changing the

FCOS ResNeXt-101 and FSAF ResNet-50 models.

The saliency maps of the ResNeXt backbone model

are darker and more accurate as the model is deeper

with a huge number of layers in its backbone.

5.3 Ablation Study

In order to assess the reliability of the proposed struc-

tures, the proposed modiﬁcations are designed with

both FSAF and FCOS and tested with the huge bench-

mark COCO dataset. The results of two different

backbones are recorded and compared with the origi-

nal structure. Table 5 contains the accuracy of FSAF

and FCOS with a ResNet-50 backbone, respectively.

The results show that both models that have DIoU

and CIoU losses give the most accurate results in

comparison with the theoretical baseline structures,

even when changing the backbone from ResNet-50

to a deeper one such as ResNeXt-101 (see Appendix

A). The modiﬁcation structures show an increasing

of mAP by 1.3% for FSAF model and 1.6% for the

FCOS model. Figure 8 presents some results of the

FCOS model trained on the COCO dataset with dif-

ferent IoU loss functions. It shows that the model with

DIoU detects more objects and enhances the detection

of occluded objects such as humans in the same im-

age. More results of different structures with different

backbones are given in Appendix A.

6 CONCLUSION AND FUTURE

DIRECTIONS

The paper discusses the use of object detection in ru-

ral and suburban areas. It summarizes the existing

efforts to detect objects efﬁciently and describes the

datasets and state-of-the-art anchor-free models used

in this ﬁeld. Furthermore, new anchor-free model

structures are investigated based on different types

of regression losses. Training over the benchmark

COCO dataset with both FSAF and FCOS ResNet-50

models based on CIOU and a spatial attention mech-

anism shows an improvement of the accuracy by 1.3

% and 1.6 % mAP, respectively. The object detection

results with different structures have been interpreted

using a saliency map, which shows the area at which

each model is focused to discover and detect the nec-

essary object. On the other hand, the modiﬁed struc-

tures have been investigated using a speciﬁc dataset

from construction ﬁelds (OPEDD). The results show

that structure based on spatial attention and CIoU loss

for both FSAF and FCOS models increase the accu-

racy by 2.3% and 16.1% mAP respectively.

Moreover, in a comparison between such ap-

proaches and the State-Of-the-Art (SOTA) YOLO

object detection versions, the results show that the

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406

(a) FCOS ResNeXt-101 saliency maps

(b) FSAF ResNet-50 saliency maps

Figure 7: The saliency maps for different models that are tested in this research.

Figure 8: Object detection results for different structures of

FCOS ResNeXt-101 model trained on COCO dataset.

anchor-free models with such a modiﬁcation give

FLOPs values less or slightly higher than YOLO

models. For example, the literature mentions that

the YOLOv5x (Jocher, 2020) has a FLOPs value of

205.7, and the one for YOLOv8x (Hussain, 2023) is

257.8, while the FLOPs for both the FSAF and the

FCOS model based on ResNet-50 mentioned in Table

2 are 207.48 and 201.75; respectively. Even though

those models have inherited an attention mechanism

in their structure. More detailed results for differ-

ent backbone structures in both the FSAF and FCOS

models are mentioned in Appendix A and B. Those

results prove that using either CIoU and DIoU losses

with attention gives more accurate results compared

to the theoretical baseline structure with IoU loss.

For future work, more anchor-free detectors can

be investigated for the different types of loss functions

and different types of attention mechanisms such as

the convolutional block attention module (CBAM)

(Woo et al., 2018) which could enhance their perfor-

mance and accuracy with less change in complexity.

From the authors’ point of view, anchor-free models

are still a springboard for future research. They can

be developed in a semi-supervised approach as well.

Models that contain FPN in their structure are more

compatible with the future direction toward biologi-

cal plausibility (Helmstaedter, 2015).

ACKNOWLEDGEMENTS

This research was supported by German Academic

Exchange Service (DAAD).

Investigation of the Performance of Different Loss Function Types Within Deep Neural Anchor-Free Object Detectors

407

Table 3: Performance of different structures of dense object detectors: FSAF and FCOS models based on ResNet50 backbone

trained directly on the OPEDD dataset. The highest values are mentioned in bold.

Model Backbone Attention Reg loss Bbox-mAP Bbox-mAP-50 Bbox-mAP-75 Bbox-mAP-s Bbox-mAP-m Bbox-mAP-l

Anchor-Free Detectors: Dense Predictors

FSAF ResNet-50

Baseline IoU 22.7 36.1 24.8 5.5 36.5 30.0

ε3(our) IoU 24.8 39.0 26.4 8.0 40.8 31.1

ε3(our) CIoU 25.0 38.4 26.6 8.3 42.4 31.6

ε3(our) DIoU 24.7 38.5 27.5 7.0 41.8 31.2

ε3(our) GIoU 24.4 39.0 26.8 6.3 41.7 31.1

FCOS ResNet-50

Baseline IoU 13.6 28.8 11.2 1.1 12.5 22.6

ε3(our) IoU 24.5 50.1 23.8 1.3 23.9 44.6

ε3(our) CIoU 29.7 54.8 30.7 4.0 24.4 58.2

ε3(our) DIoU 28.9 54.3 29.9 3.8 23.9 56.9

ε3(our) GIoU 27.6 51.2 27.0 1.7 22.8 56.3

Table 4: Performance of different structures of dense object detectors: FSAF and FCOS models based on ResNet50 backbone

pre-trained on COCO dataset, then transfer learning using the OPEDD dataset. The highest values are mentioned in bold.

Model Backbone attention Reg loss Bbox-mAP Bbox-mAP-50 Bbox-mAP-75 Bbox-mAP-s Bbox-mAP-m Bbox-mAP-l

Anchor-Free Detectors: Dense Predictors

FSAF ResNet-50

N IoU 24.1 35.9 26.8 6.7 41.1 31.6

ε3(our) IoU 24.5 38.2 25.5 7.6 39.5 32.0

ε3(our) CIoU 24.1 37.4 26.5 9.2 40.7 30.5

ε3(our) DIoU 23.4 35.7 24.7 6.1 42.0 29.0

ε3(our) GIoU 24.5 37.3 26.8 7.9 38.4 31.8

FCOS ResNet-50

N IoU 24.9 37.0 25.9 3.4 38.2 34.1

ε3(our) IoU 23.7 36.3 25.8 3.1 35.7 32.5

ε3(our) CIoU 24.8 37.8 26.8 3.9 37.3 34.2

ε3(our) DIoU 25.4 39.2 27.1 4.7 38.1 34.9

ε3(our) GIoU 25.6 39.2 26.9 4.7 39.9 34.6

Table 5: Performance of different structures of dense object detectors: FSAF and FCOS models based on ResNet50 backbone

trained on the benchmark COCO dataset. The highest values are mentioned in bold.

Model Backbone Attention Reg loss Bbox-mAP Bbox-mAP-50 Bbox-mAP-75 Bbox-mAP-s Bbox-mAP-m Bbox-mAP-l

Anchor-Free Detectors: Dense Predictors

FSAF ResNet-50

N IoU 36.0 55.5 37.7 19.6 39.6 48.2

ε3(our) IoU 36.3 55.4 38.6 20.1 39.4 47.7

ε3(our) CIoU 37.3 56.8 39.2 21.1 40.0 49.0

ε3(our) DIoU 37.3 56.9 39.2 21.2 40.1 48.6

ε3(our) GIoU 37.2 56.4 39.6 21.0 40.0 49.0

FCOS ResNet-50

N IoU 36.6 56.0 38.8 21.1 40.7 47.1

ε3(our) IoU 37.4 56.3 40.0 21.6 41.1 49.0

ε3(our) CIoU 38.2 57.1 40.6 21.5 42.1 50.0

ε3(our) DIoU 37.8 56.8 40.2 22.0 41.7 49.4

ε3(our) GIoU 38.1 56.9 40.5 22.3 41.9 49.7

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APPENDIX

Further results from training the anchor-free dense

model over the OPEDD dataset and the COCO bench-

mark dataset are presented in this Appendix. These

results show more information about using different

IoU loss functions without the plugin spatial attention

as well as with the integration of such an attention

mechanism.

Appendix A

Results of training different backbones of FSAF and

FCOS models over the COCO dataset are mentioned.

Table 6 shows the results of the training FSAF model

with different IoU loss without an attention mecha-

nism in part (a) as well as with an attention mecha-

nism in part (b). Table 7 shows the same but for the

FCOS model.

Appendix B

FSAF and FCOS models based on different back-

bones are investigated with and without spatial atten-

tion mechanism. Those models are trained over a spe-

ciﬁc OPEDD dataset. Table 8 and Table 9 show de-

tailed results, which express that using another regres-

sion loss rather than IoU improves the accuracy of the

models.

Investigation of the Performance of Different Loss Function Types Within Deep Neural Anchor-Free Object Detectors

409

Table 6: Ablation studies for the FSAF model trained on COCO dataset using different structures of backbones, loss types

and attention.

(a) FSAF model structure with different loss types without using an attention mechanism.

Model Backbone loss

bbox-

mAP

bbox-

mAP-50

bbox-

mAP-75

bbox-

mAP-s

bbox-

mAP-m

bbox-

mAP-l

FSAF ResNet-50

IoU [lit] 36.0 55.5 37.7 19.6 39.6 48.2

CIoU 36.8 55.7 38.9 19.8 39.7 48.0

DIoU 35.3 54.1 37.4 19.2 37.9 46.0

GIoU 35.2 54.0 37.3 18.9 37.8 45.9

FSAF ResNet-101

IoU [lit] 39.3 58.6 42.1 22.1 43.4 51.2

CIoU 38.5 57.7 41.0 20.6 41.7 50.2

DIoU 38.7 57.9 41.0 20.9 42.2 51.2

GIoU 38.6 57.6 41.1 21.6 42.4 50.7

FSAF ResNeXt-101

IoU [lit] 42.4 62.5 45.5 24.6 46.1 55.5

CIoU 41.3 60.9 44.1 23.3 45.0 54.2

DIoU 41.4 61.1 44.6 23.5 45.1 54.7

GIoU 41.2 60.8 44.2 23.0 45.1 53.6

(b) FSAF model structure with different loss types and using an attention mechanism.

Model Backbone att Loss

bbox-

mAP

bbox-

mAP-50

bbox-

mAP-75

bbox-

mAP-s

bbox-

mAP-m

bbox-

mAP-l

FSAF ResNet-50 ε3

IoU 36.3 55.4 38.6 20.1 39.4 47.7

CIoU 37.3 56.8 39.2 21.1 40.0 49.0

DIoU 37.3 56.9 39.2 21.2 40.1 48.6

GIoU 37.2 56.4 39.6 21.0 40.0 49.0

FSAF ResNet-101 ε3

IoU 37.8 57.0 40.2 21.3 41.5 49.3

CIoU 40.0 59.9 42.7 22.4 43.8 52.0

DIoU 40.1 59.7 42.7 22.5 44.0 52.3

GIoU 39.8 59.3 42.3 22.5 43.3 52.4

FSAF ResNeXt-101 ε3

IoU 42.4 62.8 45.3 24.5 46.4 55.5

CIoU 40.2 59.9 42.8 22.9 43.7 52.3

DIoU 43.0 63.5 46.1 25.5 46.9 56.6

GIoU 42.5 62.7 45.6 24.5 46.3 56.1

Table 7: Ablation studies on FCOS model trained on COCO dataset using different structures of backbones, loss types and

attention.

(a) FCOS model structure with different loss types without using an attention mechanism.

Model Backbone loss

bbox-

mAP

bbox-

mAP-50

bbox-

mAP-75

bbox-

mAP-s

bbox-

mAP-m

bbox-

mAP-l

FCOS ResNet-50

IoU [lit] 36.6 56.0 38.8 21.1 40.7 47.1

CIoU 36.7 55.3 39.0 20.0 40.7 47.3

DIoU 37.0 55.6 39.5 21.0 40.6 47.9

GIoU 37.0 55.5 39.4 21.1 40.9 47.5

FCOS ResNet-101

IoU [lit] 39.1 58.3 42.1 22.7 43.3 50.3

CIoU 38.8 57.53 41.3 22.42 42.86 50.23

DIoU 39.08 58.04 41.77 22.31 43.07 50.46

GIoU 39.22 58.16 42.02 22.79 43.47 50.06

FCOS ResNeXt-101

IoU [lit] 42.6 62.3 45.6 25.7 46.3 54.6

CIoU 42.87 62.35 46.16 26.89 46.70 54.66

DIoU 43.04 62.28 46.22 26.85 46.59 55.02

GIoU 42.85 62.19 46.48 26.94 46.60 53.94

(b) FCOS model structure with different loss types and using an attention mechanism.

Model Backbone att Loss

bbox-

mAP

bbox-

mAP-50

bbox-

mAP-75

bbox-

mAP-s

bbox-

mAP-m

bbox-

mAP-l

FCOS ResNet-50 ε3

IoU 37.4 56.3 40.0 21.6 41.1 49.0

CIoU 38.2 57.1 40.6 21.5 42.1 50.0

DIoU 37.8 56.8 40.2 22.0 41.7 49.4

GIoU 38.1 56.9 40.5 22.3 41.9 49.7

FCOS ResNet-101 ε3

IoU 39.50 58.30 42.46 22.58 43.40 51.90

CIoU 39.87 58.97 42.57 23.23 43.99 51.84

DIoU 40.07 59.14 43.12 23.18 43.89 51.77

GIoU 39.91 59.03 42.50 23.13 43.89 51.95

FCOS ResNeXt-101 ε3

IoU 43.4 63.2 46.6 26.8 47.4 55.2

CIoU 43.8 63.3 47.2 27.5 47.8 56.0

DIoU 43.3 62.8 46.6 26.9 47.0 55.1

GIoU 43.7 63.0 47.0 26.6 47.7 56.5

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410

Table 8: The results of training the FSAF model on the OPEDD dataset, pretrained on the COCO dataset with different

structures of backbones, loss types and attention.

(a) FSAF model structure with different loss types without using an attention mechanism.

Model Backbone loss

bbox-

mAP

bbox-

mAP-50

bbox-

mAP-75

bbox-

mAP-s

bbox-

mAP-m

bbox-

mAP-l

FSAF ResNet-50

IoU [lit] 24.1 35.9 26.8 6.7 41.1 31.6

CIoU 24.6 38.0 26.7 8.4 43.7 30.1

DIoU 24.7 40.1 26.5 6.0 38.5 31.8

GIoU 25.1 39.2 28.0 7.5 41.1 31.9

FSAF ResNet-101

IoU [lit] 24.6 37.3 28.0 6.8 38.2 32.2

CIoU 25.4 37.6 28.0 5.7 41.6 33.7

DIoU 25.3 38.0 28.7 5.2 40.6 33.2

GIoU 25.1 37.2 27.4 5.3 40.4 33.5

FSAF ResNeXt-101

IoU [lit] 26.3 40.1 28.9 8.0 41.1 34.4

CIoU 27.5 40.1 30.0 9.6 41.8 36.0

DIoU 26.9 39.5 30.0 6.9 43.4 34.3

GIoU 26.6 39.4 29.7 6.4 45.9 33.9

(b) FSAF model structure with different loss types and using an attention mechanism.

Model Backbone att Loss

bbox-

mAP

bbox-

mAP-50

bbox-

mAP-75

bbox-

mAP-s

bbox-

mAP-m

bbox-

mAP-l

FSAF ResNet-50 ε3

IoU 24.5 38.2 25.5 7.6 39.5 32.0

CIoU 24.1 37.4 26.5 9.2 40.7 30.5

DIoU 23.4 35.7 24.7 6.1 42.0 29.0

GIoU 24.5 37.3 26.8 7.9 38.4 31.8

FSAF ResNet-101 ε3

IoU 24.6 38.7 25.8 5.1 40.1 32.8

CIoU 24.0 36.7 25.3 5.6 39.8 31.8

DIoU 24.8 36.9 26.8 4.7 37.4 33.4

GIoU 24.5 38.5 25.7 7.5 39.6 31.8

FSAF ResNeXt-101 ε3

IoU 26.7 41.0 29.2 8.1 41.6 34.3

CIoU 26.8 41.4 29.4 7.1 41.4 34.4

DIoU 26.3 40.0 30.2 8.2 44.7 33.6

GIoU 26.9 40.2 30.3 8.4 41.4 34.9

Table 9: The results of training the FCOS model on the OPEDD dataset, pre-trained on coco dataset with different structures

of backbones, loss types and attention.

(a) FCOS model structure with different loss types without using an attention mechanism.

Model Backbone loss

bbox-

mAP

bbox-

mAP-50

bbox-

mAP-75

bbox-

mAP-s

bbox-

mAP-m

bbox-

mAP-l

FCOS ResNet-50

IoU [lit] 24.9 37.0 25.9 3.4 38.2 34.1

CIoU 25.4 39.6 25.8 4.8 37.7 33.9

DIoU 25.4 37.9 28.1 4.1 39.3 35.1

GIoU 25.8 38.3 26.9 4.3 39.7 35.5

FCOS ResNet-101

IoU [lit] 23.0 36.5 24.9 5.1 36.7 30.7

CIoU 23.6 37.2 25.0 5.2 37.8 32.0

DIoU 23.9 38.3 23.6 3.4 36.4 32.1

GIoU 25.1 37.1 27.2 3.2 40.8 33.6

FCOS ResNeXt-101

IoU [lit] 24.0 37.1 25.2 6.4 37.8 31.3

CIoU 25.1 37.1 28.1 6.0 40.1 32.7

DIoU 26.5 38.7 28.4 5.4 39.6 35.1

GIoU 25.1 38.1 26.2 6.4 38.9 32.1

(b) FCOS model structure with different loss types and using an attention mechanism.

Model Backbone att Loss

bbox-

mAP

bbox-

mAP-50

bbox-

mAP-75

bbox-

mAP-s

bbox-

mAP-m

bbox-

mAP-l

FCOS ResNet-50 ε3

IoU 23.7 36.3 25.8 3.1 35.7 32.5

CIoU 24.8 37.8 26.8 3.9 37.3 34.2

DIoU 25.4 39.2 27.1 4.7 38.1 34.9

GIoU 25.6 39.2 26.9 4.7 39.9 34.6

FCOS ResNet-101 ε3

IoU 23.4 35.6 25.2 4.9 37.3 31.5

CIoU 24.4 38.7 24.8 3.9 36.8 33.6

DIoU 23.8 37.9 24.2 4.5 37.6 31.9

GIoU 23.5 36.1 25.8 4.5 37.1 32.6

FCOS ResNeXt-101 ε3

IoU 26.1 38.7 28.5 4.2 42.3 34.3

CIoU 25.0 37.8 26.1 6.0 38.2 33.1

DIoU 25.5 37.5 26.5 4.1 38.6 34.4

GIoU 26.0 37.5 27.3 5.3 42.9 33.8

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411