# Robust Segmentation of Optic Disc and Cup from Fundus Images Using Deep
Neural Networks

Aniketh Manjunath, Subramanya Jois, and Chandra Sekhar Seelamantula, Senior
Member, IEEE
Manuscript submitted to IEEE Transactions on Image Prcessing on September 29,
2019. Paper ID: TIP-21464-2019.R1. This work was supported by the Ministry of
Human Resource Development and Indian Council for Medical Research under the
IMPRINT India Initiative (Domain: Healthcare; Project No.: 6013).
Aniketh Manjunath was with the Department of Electrical Engineering, Indian
Institute of Science, Bangalore 560012, India. He is presently with University
of Southern California, Los Angeles, CA 90007, USA (email<EMAIL_ADDRESS>
Subramanya Jois was with the Department of Electrical Engineering, Indian
Institute of Science, Bangalore 560012, India. He is presently with Concordia
and McGill Universities (CREATE Innovation program), Montréal, Quebec, Canada
(email<EMAIL_ADDRESS>
Chandra Sekhar Seelamantula is with the Department of Electrical Engineering,
Indian Institute of Science, Bangalore 560012, India. (Email: css@iisc.ac.in).

###### Abstract

Optic disc (OD) and optic cup (OC) are regions of prominent clinical interest
in a retinal fundus image. They are the primary indicators of a glaucomatous
condition. With the advent and success of deep learning for healthcare
research, several approaches have been proposed for the segmentation of
important features in retinal fundus images. We propose a novel approach for
the simultaneous segmentation of the OD and OC using a residual encoder-
decoder network (REDNet) based regional convolutional neural network (RCNN).
The RED-RCNN is motivated by the Mask RCNN (MRCNN). Performance comparisons
with the state-of-the-art techniques and extensive validations on standard
publicly available fundus image datasets show that RED-RCNN has superior
performance compared with MRCNN. RED-RCNN results in Sensitivity, Specificity,
Accuracy, Precision, Dice and Jaccard indices of 95.64%, 99.9%, 99.82%,
95.68%, 95.64%, 91.65%, respectively, for OD segmentation, and 91.44%, 99.87%,
99.83%, 85.67%, 87.48%, 78.09%, respectively, for OC segmentation. Further, we
perform two-stage glaucoma severity grading using the cup-to-disc ratio (CDR)
computed based on the obtained OD/OC segmentation. The superior segmentation
performance of RED-RCNN over MRCNN translates to higher accuracy in glaucoma
severity grading.

###### Index Terms:

Optic Disc, Optic Cup, Retinal fundus, Segmentation, CDR, MRCNN, RED-RCNN.

##  I Introduction

Glaucoma is a leading cause of blindness caused by an irreparable and
irreversible damage to the optic nerve head (ONH) due to increased intraocular
pressure [1]. Millions of neuronal cells of the visual network converge at the
ONH and transmit the visual information from the photoreceptors to the higher
levels of processing in the brain. The optic disc (OD) is a two-dimensional
representation of the ONH in a retinal fundus image. In the case of glaucoma,
the neuroretinal rim tissue gets progressively damaged, which is characterized
by cupping or a depression on the OD. The depressed region — termed as the
optic cup (OC) — appears as a bright region originating from the ONH. Accurate
segmentation of OD and OC is crucial for the assessment of glaucoma severity.
A fast, automated, and accurate segmentation of the OD and OC would enable
medical experts to provide reliable diagnosis. Typically, severity assessment
of glaucoma is carried out based on the calculation of the cup-to-disc ratio
(CDR) or Inferior/Superior/Nasal/Temporal (ISNT) ratio compared against the
disc-damage-likelihood scale (DDLS) [2].

Figure 1:  Simultaneous OD & OC segmentation using the proposed RED-RCNN.

This paper: We employ a deep learning approach for fast, simultaneous, and
accurate segmentation of OD and OC without imposing shape constraints. Neural
networks employed for segmentation typically require a ground-truth for
training, which is often provided by an expert. In cases where multiple expert
outlines are available, we need a method for combining them into a single
robust outline by taking into account inter-expert variability. We develop a
median-based approach for fusing multiple expert annotations into a single
one, in order to train the segmentation networks. The starting point for our
network architecture is the mask region convolutional neural network (MRCNN),
which has proven to be successful for the task of image segmentation on
standard datasets [3]. We show that the MRCNN could be improved by
incorporating a residual encoder-decoder network (REDNet) in the mask branch
instead of a fully convolutional network (FCN) [4]. The new architecture,
referred to as RED-RCNN, gives significantly superior results. The details are
deferred until Sec. IV, but an illustration that gives a flavor of the
accuracy of segmentation obtained using RED-RCNN is shown in Fig. 1. The
validations are reported on several standard publicly available datasets and
comparisons are provided with state-of-the-art algorithms. The RED-RCNN
consistently outperforms the state-of-the-art on almost all the datasets. A
two-stage glaucoma analysis on the REFUGE dataset using the CDR parameter
shows that RED-RCNN has a superior classification accuracy than MRCNN.

##  II Related Literature

While some works in the literature have focused exclusively on the
segmentation of the OD or OC, the recent ones have focused on the simultaneous
segmentation of OD and OC. Hence, we classify the related literature under
these headings.

###  II-A Optic Disc Segmentation

Lowell et al. [5] employed an active contour model to detect the OD based on
local image gradients. Abramoff et al. used a pixel feature classification
technique to segment the OD into cup, rim, and background from colour stereo
photographs [6]. Aquino et al. employed a template-based approach using
feature extraction followed by the circular Hough transform to extract the
disc boundary [7]. Shijian designed a transform that estimates the OD center
and its boundary based on image variations [8], while Dey et al. used a
normalized cross-correlation with a template for disc localization followed by
affine snakes in a gradient vector field for OD segmentation [9]. Cardoso et
al. presented a model using a combination of the circular Hough transform and
multiscale energy filter for localization and 3-D roughness index value and
morphology in conjunction with a fuzzy set representation [10]. The advent of
deep learning led to a shift from the use of image processing techniques to
learning-based models with a significant improvement in the segmentation
performance. Maninis et al. designed a CNN that uses a base-shared network and
a specialized layer to segment the OD and demonstrated that the results
obtained surpassed human performance [11].  Mohan et al. presented a Fine-Net
CNN model that produces semantic OD boundaries [12] and augmented the results
by cascading the Fine-Net CNN with a prior-CNN reported in [13]. Recently,
Wang et al. reported improved segmentation performance by augmenting the
vanilla U-Net with a fully convolutional network (FCN) [14].

###  II-B Optic Cup Segmentation

Segmenting the OC is a more challenging task due to the low-contrast boundary.
Xu et al. proposed a learning framework operating on a sliding window approach
to localize the optic cup [15]. The sliding windows generate candidate samples
that are ranked using a support vector regression model employing a radial-
basis kernel. The final detection is performed using nonmaximal suppression.
Recently, Yang et al. proposed a technique to minimize the influence of blood
vessels on the segmentation by using an inpainting model for filling the blood
vessels within the OD region [16]. In another attempt, Xu et al. employed an
unsupervised approach for the classification of OC superpixels within a low-
rank representation framework [17].

###  II-C Optic Disc and Optic Cup Segmentation

In general, the features that lead to a reliable OD segmentation are different
from those that give an accurate OC segmentation. Hence, several works have
used differential features for each segmentation task. Joshi et al. used a
multidimensional image representation obtained from the colour and texture
features to provide a robust outline of the OD [18]. Subsequently, the OC is
segmented based on vessel bends and pallor information. Cheng et al. proposed
a superpixel classification approach for OD and OC segmentation that accounted
for the quality of segmentation through a self-assessment reliability score
[19]. Zheng et al. integrated OD and OC segmentation within a graph-cut
framework that incorporates priors on the location, shape, and size of OD and
OC boundaries for training a Gaussian mixture model, which is then used to
estimate the posterior probabilities [20]. Sevastopolsky introduced a modified
U-Net to sequentially segment the OD and OC regions [21]. Zilly et al.
proposed an ensemble learning method to extract OC and OD using CNNs, where an
entropy-sampling technique was used to select informative points, and a graph-
cut algorithm was employed to obtain the final segmentation result [22]. Singh
et al. used the U-Net followed by a multi-scale matching network for
segmenting the OD and OC regions [23]. Ghassabi et al. considered colour,
intensity, and orientation contrast computed using Gabor filters as the input
to a Winner-take-all neural network for OD segmentation, and the colour
features were provided as input to a self-organizing map neural network for OC
segmentation [24]. Recently, Edupuganti et al. demonstrated that an FCN based
OD-OC segmentation is competitive with the state of the art [25]. Agrawal et
al. employed an ensemble of CNNs where, in addition to the visual features,
spatial coordinates are fed to the network to improve the segmentation
performance [26]. Fu et al. proposed a U-Net backbone with multi-level inputs
and polar transformation to improve the segmentation performance [27]. Al-
Bander et al. proposed FC-DenseNet and extensively validated their OD and OC
segmentation methodology [28] on multiple datsets. Along similar lines as in
[27], Liu et al. proposed a cartesian-polar network with parallel branches of
feature encoders that learn translation-equivariant representations on a
cartesian grid and rotation-equivariant representations on a polar grid [29].
Jiang et al. proposed a two-level strategy using a deep network: a coarse
segmentation that fits bounding boxes to the OD and OC, followed by a fine
segmentation within the bounding box achieved using a disc-attention module
[30]. Yu et al. combined a pretrained ResNet and a U-Net to solve the
segmentation problem [31]. The use of a pretrained network accelerates
learning and achieves high performance. Yin et al. proposed the PM-Net for
optic nerve-head localization and used the Pyramid RoIAlign together with a
multi-label head strategy for incorporating priors for improving the OD and OC
segmentation performance [32]. Kumar et al. used active discs for segmenting
the OD and OC by maximizing the local contrast function [33].

Figure 2:  (a1) & (a2) show the multiple expert annotations for OD and OC,
respectively, on a sample image taken from the Drishti-GS dataset [34]; (b1) &
(b2) show the $x$ and $y$ coordinate functions, respectively, vs. the polar
angle $\theta$ (cf. (a1)); (c1) & (c2) show the median contour (green) for the
OD and OC, respectively. Figure 3:  The (a) $x$ and (b) $y$ coordinate
functions vs. the polar angle $\theta$ obtained from six expert outlines of
the OC on a sample image taken from RIGA dataset [34]. The median results in a
more robust fusion than the mean.

##  III Robust Fusion of Multiple Expert Annotations

Training a neural network to perform OD and OC segmentation typically requires
ground-truth annotations from expert ophthalmologists and in many cases, more
than one such annotation may be available. Of the publicly available datasets,
Drishti-GS [35], RIGA [34], and REFUGE [36] contain both disc and cup
outlines, out of which Drishti-GS and RIGA contain annotations from multiple
clinical experts. Neural networks typically require a single ground-truth for
training, which calls for a robust way of fusing the multiple annotations into
a single one. Taking the intersection of the multiple annotations may be
conservative, whereas taking the union would bias the ground-truth toward
annotations covering a larger area, which is not preferred either. We develop
a method for fusing annotations in a way that is robust to inter-expert
variability.
Figs. 2(a1) & (a2) show multiple expert outlines of the optic disc and cup,
respectively. Figs. 2(b1) & (b2) show plots of the $x$ and $y$ coordinates of
the disc outlines as a function of the polar angle $\theta$ (Fig. 2(a1)). A
similar plot for the cup outlines is shown in Figs. 3(a) & (b). We observe
that the median is more robust to inter-expert variability and is a better
candidate than the mean for fusing multiple annotations. Figs. 2(c1) & (c2)
show the median ground-truth outlines of the OD and OC, respectively.

##  IV The Proposed Approach

The proposed residual encoder-decoder region CNN (RED-RCNN) approach is based
on the mask region convolutional neural network (MRCNN) and the residual
encoder-decoder network (REDNet) [4], neither of which were used for OD/OC
segmentation. We highlight the features of the MRCNN and REDNet and then
proceed with the proposed approach.

###  IV-A Mask Region Convolutional Neural Network (MRCNN)

Figure 4:  Workflow in an MRCNN detailing the simultaneous OD and OC
segmentation.

$\begin{array}[]{cc}\hskip
2.84526pt\includegraphics[width=195.12767pt]{bibtex/images/M2.png}&\hskip
2.84526pt\includegraphics[width=195.12767pt]{bibtex/images/M1.png}\\\
\mbox{(a)}&\mbox{(b)}\\\ \end{array}$

Figure 5:  The Fine Segmentation Network of (a) the MRCNN, and (b) the
proposed RED-RCNN, with Type-1 (T1), Type-2 (T2), Type-3 (T3) being different
types of skip connections.

Mask R-CNN (MRCNN) [3] is a deep neural network used for instance segmentation
of objects, i.e., it can differentiate objects in an image through detection
and delineation of the regions of interest. MRCNN is an extension of the
Faster R-CNN (FRCNN) [37]. A block diagram of MRCNN is shown in Fig. 4. It has
a multistage architecture comprised of three main blocks: a backbone network
in tandem with a feature pyramid network (FPN) that together perform
multiscale feature extraction on a colour fundus image; a region proposal
network (RPN) that performs coarse segmentation on the multiscale feature
maps; and a fine segmentation network that refines the segmentation map
obtained from the preceding two blocks.
The backbone consists of top-down, bottom-up and lateral connections. The top-
down connection generates feature maps. The bottom-up connection is usually a
CNN that extracts features from the input image. Lateral connections allow for
additions and convolutions between the top-down and bottom-up pathways. The
RPN scans the feature maps and determines the regions that have a high
probability of containing an object. It outputs a region of interest (RoI)
containing a bounding box and a coarse segmentation map. The RoI is aligned
with the multiscale feature maps and fed to a fine segmentation network (FSN),
which in turn outputs the class labels, a refined bounding box, and a fine
segmentation mask.

###  IV-B Residual Encoder-Decoder Network (REDNet)

The accuracy of segmentation can be improved if the context of the pixel with
its neighbors is also taken into account. There are several segmentation
approaches that are based on fully convolutional networks (FCNs) that
downsample the feature maps using a max-pool layer after each convolution.
Badrinarayanan et al. [38] pointed out that max-pooling results in the loss of
location information, which is crucial for segmentation and instead suggested
using pooling-indices to keep track of the locations of the max-values at the
expense of more memory for storing the locations. As an alternative to storing
the indices, Noh et al. [39] used a deconvolution layer that learns to
optimally upsample the input. Mao et al. [4] designed a residual encoder-
decoder network by eliminating the max-pool layer and used deconvolutions
along with residual skip connections to get more accurate segmentation maps.

###  IV-C Residual Encoder-Decoder Region CNN (RED-RCNN)

Although MRCNN has been used for several object segmentation tasks, it has
never been applied to fundus images. We begin with employing the MRCNN for
simultaneous OD and OC segmentation, the results of which will be reported in
the subsequent section. The results show that MRCNN by itself is quite
competitive with the state-of-the-art approaches. Further, we leverage the
superior segmentation performance of the REDNet and employ it in the mask
branch of the fine segmentation network. Also, the standard MRCNN uses a
single deconvolutional layer in the final stage of segmentation, essentially
for upsampling the segmentation map to match the size of the input image. On
the other hand, REDNet has a deconvolutional layer in the decoder for every
convolutional layer in the encoder, thus giving rise to a learnt stage-wise
upsampling mechanism. Drozdzal et al. [40] highlighted the importance of skip
connections in deep networks, showing better gradient flow, resulting in
faster convergence and superior performance. We experimented with three types
of skip connections:  Type-1 (T1): between two consecutive convolutional
layers; Type-2 (T2): between every pair of convolutional and deconvolutional
layers; and Type-3 (T3): between a convolutional block and a deconvolutional
block (each block comprising two layers). We found that T3 (cf. Fig. 5(b))
gave the best performance, which is further explained in Sec. V-D. Therefore,
we used REDNet with Type-3 skip connections in the mask branch of the MRCNN.
Henceforth, we shall refer to MRCNN with REDNet as RED-RCNN. Effectively, the
RED-RCNN comprises the MRCNN in Fig. 4 but with the fine segmentation network
as given in Fig. 5(b). A comprehensive evaluation and comparison of the
segmentation performance of MRCNN and RED-RCNN vis-à-vis the state of the art
will be reported in Sec. V.

TABLE I: An overview of the datasets used for validation.

Dataset | # Images | Resolution | OD | OC | # Experts
---|---|---|---|---|---
| used |  | ground-truth | ground-truth |
Drishti-GS [35] | 101 | 2896 $\times$ 1944 |  |  | 4
REFUGE [36] | 800 | 2124 $\times$ 2056 |  |  | 1
|  | 1634 $\times$ 1634 |  |  |
RIGA [34] | 750 | varying |  |  | 6
IDRiD [41] | 81 | 4288 $\times$ 2848 |  | $\times$ | 1
DRIONS-DB [42] | 50 | 600 $\times$ 400 |  | $\times$ | 1
MESSIDOR [43] | 1200 | 2240 $\times$ 1488 |  | $\times$ | 1

###  IV-D Loss Function for the Mask Branch

The original proponents of MRCNN used binary cross-entropy ($BCE$) as the loss
function for the mask branch. Since the segmentation performance is typically
quantified using the intersection over union ($IoU$), we prefer to augment the
$BCE$ loss with the $IoU$ for training the network as it is likely to improve
the segmentation performance. However, since $IoU$ is not differentiable, we
employ a differentiable approximation to the $IoU$ proposed by Rahman and Wang
[44], given by

${\widehat{IoU}}=\frac{\sum_{ij}X_{ij}Y_{ij}}{\sum_{ij}X_{ij}+Y_{ij}-X_{ij}Y_{ij}},$
(1)

where $ij$ denotes the pixel index, $X_{ij}$ is the prediction, and $Y_{ij}$
is the ground-truth. We consider a convex combination of $BCE$ and
${\widehat{IoU}}$:

$\mathcal{L}_{mask}=\alpha\,BCE+(1-\alpha)\,{\widehat{IoU}},\alpha\in[0,1],$
(2)

for training the mask branch in both MRCNN and RED-RCNN. The choice of
$\alpha$ will be explained in the next section. The loss functions for
obtaining the class labels (sparse softmax cross-entropy) and the bounding box
(smooth L1 loss) are retained as proposed in the original MRCNN paper.

$\begin{array}[]{cccccc}\includegraphics[width=64.61028pt]{bibtex/images/1.png}&\includegraphics[width=64.61028pt]{bibtex/images/2.png}&\includegraphics[width=64.61028pt]{bibtex/images/3.png}&\includegraphics[width=64.61028pt]{bibtex/images/4.png}&\includegraphics[width=64.61028pt]{bibtex/images/5.png}&\includegraphics[width=64.61028pt]{bibtex/images/6.png}\\\
\mbox{(a1) $BCE$}&\mbox{(a2) ${\widehat{IoU}}$}&\mbox{(a3) Aug.
Loss}&\mbox{(b1)}&\mbox{(b2)}&\mbox{(b3)}\\\ \end{array}$

$\begin{array}[]{ccc}\includegraphics[width=146.99913pt]{bibtex/images/Log_Loss_BCE.pdf}&\includegraphics[width=146.99913pt]{bibtex/images/Log_Loss_IOU.pdf}&\includegraphics[width=146.99913pt]{bibtex/images/Log_Loss_BCE_IOU.pdf}\\\
\mbox{(d)}&\mbox{(e)}&\mbox{(f)}\\\ \end{array}$

Figure 6:  To illustrate the advantage of the augmented loss function: (a1),
(a2), and (a3) show the OC predictions obtained using BCE, $\widehat{IoU}$,
and the augmented loss, respectively; (b1), (b2), and (b3) characterize the
accuracy of the predictions shown in (a1), (a2), and (a3), respectively, in
comparison with the ground-truth. The color coding is as follows: yellow: true
positive; red: false negative; green: false positive. (b3) shows the highest
true positives and the lowest false positives and false negatives. The
subplots (d), (e), and (f) show the histograms (y-axis on log-scale) of pixel
intensities in the predictions shown in (a1), (a2), and (a3), respectively;
$0$ and $255$ correspond to the background and foreground, respectively.

##  V Experimental Validation

###  V-A Datasets

We carried out extensive validation on publicly available datasets: Drishti-
GS[35], REFUGE [36], RIGA [34], IDRiD [41], DRIONS-DB [42], and MESSIDOR [43].
A summary of the number of images used, image resolution, availability of the
OD and OC ground-truth, and the number of expert annotations, for each of the
datasets is shown in Table I.

###  V-B Network Training

The implementation and hyper-parameter tuning of RED-RCNN is based on that of
MRCNN [45]. As in the case of MRCNN, an RoI is considered positive only if its
IoU is greater than 0.5. We use ResNet101-FPN [46] as the backbone network.
All the images are resized such that the maximum row/column dimensions do not
exceed 1024 while maintaining the image aspect-ratio by zero-padding
appropriately. For the purpose of initialization, we use MRCNN pretrained on
the COCO dataset, which is also available at [45]. The training is performed
on two Nvidia RTX 2080Ti GPUs using ADAM optimizer [47] with a learning rate
of 0.01, momentum of 0.9, and a weight decay of 0.0001, for 450 iterations.
A fundus image has only one instance of the OD and OC. Hence, the maximum
number of ground-truth instances in the MRCNN is set to 1 and the number of
proposals generated by RPN is reduced to 32. While testing, we set 0.9 as the
detection threshold in the fine segmentation network.
We used Drishti-GS, REFUGE, and RIGA datasets for training as they contain
both OD and OC outlines. During the training phase, we choose a random
$70\%-20\%$ split of the data, where the $70\%$ part is used for training and
the $20\%$ part is used for cross-validation. The remaining $10\%$ is not seen
during training. Each iteration is composed of 100 passes of random image
batches of size eight from the training set. After every iteration, the model
is cross-validated on the $20\%$ data and the model performance (the loss
function values) and the corresponding weights are recorded. Both MRCNN and
RED-RCNN models are trained for 450 iterations. Once the training phase is
complete, we selected the weights that gave the best performance on the cross-
validation set and then validated the corresponding model on the $10\%$ unseen
data.

###  V-C Choice of $\alpha$ and the Significance of the Augmented Loss

Setting $\alpha$ to either 0 or 1 reduces the loss in Eq. (2) to the standard
$\widehat{IoU}$ or BCE loss functions, respectively. For most neural networks
that perform segmentation, accurate classification of the OC boundary within
the OD still remains a challenge. In the final stages of training a network,
we observed that the predictions along the boundaries of the RoI have varying
probabilities, whereas those within the RoI have more homogeneous
probabilities. Using the BCE loss alone results in negligible gradients for
learning in the final stages, which is because large portions of the image
except at the boundaries have nearly homogeneous predictions. On the other
hand, using $\widehat{IoU}$ loss would be beneficial but it requires a large
number of iterations to achieve convergence. Hence, we considered a convex
combination of the two losses. To begin with, the parameter $\alpha$ was
initialised at a high value and then decreased progressively. Consequently,
the weight $(1-\alpha)$ assigned to $\widehat{IoU}$ went up in the later
stages, which helped in generating sufficient gradients to facilitate learning
and to classify the boundary pixels with a higher accuracy. In our
implementation, the parameter $\alpha$ was initialized to 0.7, and decremented
by 0.01 once in every ten iterations. The initial value $\alpha=0.7$ was fixed
experimentally.
Using the augmented loss also serves an important purpose. The network outputs
after scaling have pixel intensities distributed between 0 and 255.
Segmentation of the RoI is performed by setting a single threshold on the
predicted outputs, for classifying the pixels as foreground or background. A
single threshold was found to be suboptimal due to the misclassification of
the boundary pixels along the RoI. Augmenting the BCE loss with
$\widehat{IoU}$ reduced the rate of misclassificaton of the boundary pixels.
Figure 6 shows the OC predictions and the true positives, false positives, and
false negatives in comparison with the ground-truth. The best results are
obtained in the case of the augmented loss function. Figs. 6(d)-(f) show that
the augmentation results in a more decisive action — the histograms are edge-
peaked and fewer pixels have intermediate intensities, thereby reducing the
sensitivity to the choice of the single threshold value of $127$.

###  V-D Skip Connection

As mentioned in Sec. IV-C, we consider three types of skip connections in the
Residual Encoder-Decoder network. Figure 7(a) and (b) show the loss values as
a function of the iterations on the train and test data, respectively, for the
three types of skip connections considered. The figure shows that Type-3 skip
connection, which links a convolutional block and the deconvolutional block,
gives the best results. Therefore, for all further evaluations of the RED-
RCNN, we consider the mask branch with Type-3 skip connection only.

$\begin{array}[]{cc}\includegraphics[width=208.13574pt]{bibtex/images/LOSS_GG.png}&\includegraphics[width=208.13574pt]{bibtex/images/VAL_LOSS_GG.png}\\\
\mbox{(a)}&\mbox{(b)}\\\ \end{array}$

Figure 7:  A comparison of the augmented loss on (a) the training data, and (b) the test data, for various types of skip connections. Although all three types result in comparable training losses upon convergence, the testing loss is the least in the case of Type-3 skip connection. TABLE II: Training and test data performance of MRCNN and RED-RCNN for OD segmentation. The average values are highlighted on grey background. +Train dataset (1460 images): 91 (Drishti) + 719 (REFUGE) + 650 (RIGA); ∗Test dataset (190 images): 10 (Drishti) + 81 (REFUGE) + 99 (RIGA). Network | Datasets | Sensitivity | Specificity | Accuracy | Precision | Dice | Jaccard
---|---|---|---|---|---|---|---
| (Total no. of images) |  |  |  |  |  |
|  ($+$) Drishti-GS | 0.9471 | 0.9995 | 0.9979 | 0.9845 | 0.9654 | 0.9331
MRCNN |  ($+$) RIGA | 0.9431 | 0.9998 | 0.999 | 0.9865 | 0.9643 | 0.9310
|  ($+$) REFUGE | 0.9118 | 0.9998 | 0.9983 | 0.9845 | 0.9468 | 0.8989
| (1460) | 0.934 | 0.9997 | 0.9984 | 0.9851 | 0.9588 | 0.921
|  ($+$) Drishti-GS | 0.9852 | 0.9982 | 0.9978 | 0.9462 | 0.9653 | 0.9329
RED-RCNN |  ($+$) RIGA | 0.9623 | 0.9994 | 0.9989 | 0.9615 | 0.9619 | 0.9266
|  ($+$) REFUGE | 0.9594 | 0.9996 | 0.999 | 0.9779 | 0.9686 | 0.9392
| (1460) | 0.9689 | 0.999 | 0.9985 | 0.9618 | 0.9652 | 0.9329
|  ($*$) Drishti-GS | 0.8362 | 0.9997 | 0.9949 | 0.99 | 0.9066 | 0.8292
MRCNN |  ($*$) RIGA | 0.9390 | 0.9997 | 0.9988 | 0.9755 | 0.9569 | 0.9174
|  ($*$) REFUGE | 0.9192 | 0.9998 | 0.9985 | 0.989 | 0.9528 | 0.9099
| (190) | 0.8981 | 0.9997 | 0.9974 | 0.9848 | 0.9387 | 0.8855
RED-RCNN |  ($*$) Drishti-GS | 0.9839 | 0.9975 | 0.9971 | 0.9216 | 0.9517 | 0.9078
$+$: Train dataset |  ($*$) RIGA | 0.9623 | 0.9994 | 0.9989 | 0.9615 | 0.9619 | 0.9266
$*$: Test dataset |  ($*$) REFUGE | 0.9572 | 0.9996 | 0.9989 | 0.9743 | 0.9657 | 0.9336
Average | (190) | 0.9678 | 0.9988 | 0.9983 | 0.9524 | 0.9597 | 0.9226
TABLE III: Training and test data performance of MRCNN and RED-RCNN for OC segmentation. The average performance indices are also provided. +Train dataset (1460 images): 91 (Drishti) + 719 (REFUGE) + 650 (RIGA); ∗Test dataset (190 images): 10 (Drishti) + 81 (REFUGE) + 99 (RIGA). Network | Datasets | Sensitivity | Specificity | Accuracy | Precision | Dice | Jaccard
---|---|---|---|---|---|---|---
| (Total no. of images) |  |  |  |  |  |
|  ($+$) Drishti-GS | 0.6111 | 0.9999 | 0.9934 | 0.995 | 0.7572 | 0.6092
MRCNN |  ($+$) RIGA | 0.8788 | 0.9998 | 0.9994 | 0.949 | 0.9125 | 0.8391
|  ($+$) REFUGE | 0.8472 | 0.9997 | 0.999 | 0.9162 | 0.8804 | 0.7863
| (1460) | 0.7790 | 0.9998 | 0.9972 | 0.9534 | 0.8500 | 0.7448
|  ($+$) Drishti-GS | 0.8253 | 0.9995 | 0.9966 | 0.9691 | 0.8915 | 0.8042
RED-RCNN |  ($+$) RIGA | 0.9138 | 0.9997 | 0.9994 | 0.9268 | 0.9203 | 0.8523
|  ($+$) REFUGE | 0.8785 | 0.9998 | 0.9993 | 0.9614 | 0.9181 | 0.8486
| (1460) | 0.8725 | 0.9996 | 0.9984 | 0.9524 | 0.9099 | 0.8350
|  ($*$) Drishti-GS | 0.8698 | 0.9988 | 0.9978 | 0.8443 | 0.8569 | 0.7496
MRCNN |  ($*$) RIGA | 0.8641 | 0.9998 | 0.9993 | 0.9414 | 0.9011 | 0.82
|  ($*$) REFUGE | 0.825 | 0.9997 | 0.9989 | 0.922 | 0.8708 | 0.7712
| (190) | 0.8529 | 0.9994 | 0.9986 | 0.9025 | 0.8762 | 0.7802
RED-RCNN |  ($*$) Drishti-GS | 0.9855 | 0.9965 | 0.9964 | 0.6794 | 0.8043 | 0.6727
$+$: Train dataset |  ($*$) RIGA | 0.914 | 0.9997 | 0.9994 | 0.925 | 0.9194 | 0.8509
$*$: Test dataset |  ($*$) REFUGE | 0.8438 | 0.9999 | 0.9992 | 0.9656 | 0.9006 | 0.8192
Average | (190) | 0.9144 | 0.9987 | 0.9983 | 0.8567 | 0.8748 | 0.7809
TABLE IV: Performance comparison of MRCNN and RED-RCNN for OD segmentation on unseen data. The average performance indices are also provided. The unseen dataset has 1331 images comprised as follows: 50 (Drions-DB) + 81 (IDRiD) + 1200 (MESSIDOR). Network | Datasets | Sensitivity | Specificity | Accuracy | Precision | Dice | Jaccard
---|---|---|---|---|---|---|---
| (Total no. of images) |  |  |  |  |  |
| IDRiD | 0.9285 | 0.9995 | 0.9982 | 0.9713 | 0.9495 | 0.9038
MRCNN | Drions-DB | 0.875 | 0.9993 | 0.9954 | 0.9745 | 0.9221 | 0.8554
| MESSIDOR | 0.9329 | 0.9997 | 0.9991 | 0.9735 | 0.9528 | 0.9098
| (1331) | 0.9121 | 0.9995 | 0.9975 | 0.9731 | 0.9414 | 0.8896
| IDRiD | 0.9241 | 0.9992 | 0.9979 | 0.9562 | 0.9399 | 0.8866
RED-RCNN | Drions-DB | 0.9547 | 0.9986 | 0.9973 | 0.9572 | 0.956 | 0.9156
| MESSIDOR | 0.9563 | 0.9997 | 0.9993 | 0.9699 | 0.9631 | 0.9288
Average | (1331) | 0.945 | 0.9991 | 0.9981 | 0.9611 | 0.953 | 0.9103
TABLE V: Performance comparison (on test dataset) of RED-RCNN (the proposed method) for optic disc segmentation with the state-of-the-art techniques. The symbol $-$ indicates that the corresponding value has not been reported by the authors. The unseen dataset used for evaluating RED-RCNN has 1521 images and is comprised as follows: 50 (Drions-DB) + 81 (IDRiD) + 1200 (MESSIDOR) + 10 (Drishti) + 81 (REFUGE) + 99 (RIGA). Algorithm | Datasets | Sensitivity | Specificity | Accuracy | Precision | Dice | Jaccard
---|---|---|---|---|---|---|---
| (Total no. of images) |  |  |  |  |  |
Dey et al. [9] | IDRiD | 0.923 | 0.999 | – | – | 0.943 | 0.896
| Dristhi-GS | 0.932 | 0.999 | – | – | 0.958 | 0.921
| RIM-ONE | 0.953 | 0.961 | – | – | 0.933 | 0.88
| MESSIDOR | 0.924 | 0.976 | – | – | 0.912 | 0.857
| Drions-DB | 0.919 | 0.997 | – | – | 0.913 | 0.85
| (1583) | 0.9302 | 0.9864 |  |  | 0.931 | 0.88
Maninis et al. [11] | Drions-DB | – | – | – | – | 0.971 | 0.944
| RIM-ONE | – | – | – | – | 0.959 | 0.921
| (269) |  |  |  |  | 0.965 | 0.933
Mohan et al. [12] | MESSIDOR | – | – | – | – | 0.957 | 0.92
| Drishti-GS | – | – | – | – | 0.964 | 0.931
| Drions-DB | – | – | – | – | 0.955 | 0.914
| (1411) |  |  |  |  | 0.959 | 0.922
Mohan et al. [13] | MESSIDOR | – | – | – | – | 0.968 | 0.939
| Drishti-GS | – | – | – | – | 0.9713 | 0.947
| Drions-DB | – | – | – | – | 0.966 | 0.935
| (1411) |  |  |  |  | 0.968 | 0.94
Aretm et al. [21] | Drions-DB | – | – | – | – | 0.94 | 0.89
| RIM-ONE | – | – | – | – | 0.95 | 0.89
| (269) |  |  |  |  | 0.945 | 0.89
Zilly et al. [22] | Drishti-GS | – | – | – | – | 0.973 | 0.947
| RIM-ONE | – | – | – | – | 0.942 | 0.89
| MESSIDOR | – | – | – | – | 0.90 | 0.818
| (1409) |  |  |  |  | 0.938 | 0.885
Singh et al. [23] | REFUGE | – | – | 0.934 | – | – | –
| (400) |  |  |  |  |  |
Edupuganti et al. [25] | Drishti-GS | – | – | – | – | 0.967 | 0.936
| (51) |  |  |  |  |  |
Agrawal et al. [26] | REFUGE | – | – | – | – | 0.88 | 0.786
| (400) |  |  |  |  |  |
Fu et al. [27] | ORIGA | – | – | – | – | 0.963 | 0.926
| (325) |  |  |  |  |  |
Al-Bander et al. [28] | ORIGA | 0.961 | 0.999 | 0.999 | – | 0.9653 | 0.9334
| Drions-DB | 0.9232 | 0.999 | 0.997 | – | 0.9415 | 0.8912
| ONHSD | 0.9376 | 0.999 | 0.999 | – | 0.9556 | 0.9155
| Drishti-GS | 0.9268 | 0.999 | 0.997 | – | 0.949 | 0.9042
| RIM-ONE | 0.8737 | 0.998 | 0.992 | – | 0.9036 | 0.8289
| (664) | 0.924 | 0.999 | 0.997 |  | 0.943 | 0.895
Liu et al. [29] | ORIGA | – | – | – | – | 0.972 | 0.946
| (325) |  |  |  |  |  |
Jiang et al. [30] | ORIGA | – | – | – | – | 0.967 | 0.937
| (325) |  |  |  |  |  |
Yu et al. [31] | RIGA (Magrabia) | – | – | – | – | 0.969 | 0.942
| Drishti-GS | – | – | – | – | 0.964 | 0.932
| RIM-ONE | – | – | – | – | 0.949 | 0.907
| (324) |  |  |  |  | 0.96 | 0.927
Yin et al. [32] | ORIGA | – | – | – | – | 0.966 | 0.934
| REFUGE | – | – | – | – | 0.954 | 0.912
| (725) |  |  |  |  | 0.96 | 0.923
Kumar et al. [33] | Drishti-GS | 0.9962 | 0.9698 | 0.9732 | – | 0.9282 | 0.8707
| Drions-DB | 0.8410 | 0.996 | 0.985 | – | 0.9062 | 0.8341
| MESSIDOR | 0.8840 | 0.9894 | 0.9882 | – | 0.8760 | 0.7858
| Forus | 0.9457 | 0.9957 | 0.9911 | – | 0.9642 | 0.9319
| Bosch | 0.9649 | 0.9998 | 0.9968 | – | 0.9531 | 0.9109
| (1597) | 0.9263 | 0.9901 | 0.9868 |  | 0.9255 | 0.8666
Kim et al. [48] | MESSIDOR | 0.98 | 0.99 | 0.99 | – | 0.969 | 0.940
| (1200) |  |  |  |  |  |
Proposed method | Drishti-GS | 0.9839 | 0.9975 | 0.9971 | 0.9216 | 0.9517 | 0.9078
| RIGA | 0.9623 | 0.9994 | 0.9989 | 0.9615 | 0.9619 | 0.9266
| REFUGE | 0.9572 | 0.9996 | 0.9989 | 0.9743 | 0.9657 | 0.9336
RED-RCNN | IDRiD | 0.9241 | 0.9992 | 0.9979 | 0.9562 | 0.9399 | 0.8866
| Drions-DB | 0.9547 | 0.9986 | 0.9973 | 0.9572 | 0.956 | 0.9156
| MESSIDOR | 0.9563 | 0.9997 | 0.9993 | 0.9699 | 0.9631 | 0.9288
Average | (1521) | 0.9564 | 0.999 | 0.9982 | 0.9568 | 0.9564 | 0.9165
TABLE VI: Performance comparison (on test dataset) of RED-RCNN for optic cup segmentation with the state-of-the-art techniques. A $-$ indicates that the corresponding value has not been reported by the authors. The unseen dataset used for evaluating RED-RCNN has 190 images and is comprised as follows: 10 (Drishti) + 81 (REFUGE) + 99 (RIGA). Algorithm | Datasets | Sensitivity | Specificity | Accuracy | Precision | Dice | Jaccard
---|---|---|---|---|---|---|---
| (Total no. of images used) |  |  |  |  |  |
Yang et al. [16] | RIM-ONE | – | – | – | – | 0.813 | 0.685
| (94) |  |  |  |  |  |
Aretm et al. [21] | Drions-DB | – | – | – | – | 0.85 | 0.75
| RIM-ONE | – | – | – | – | 0.82 | 0.69
| (269) |  |  |  |  | 0.835 | 0.72
Zilly et al. [22] | Drishti-GS | – | – | – | – | 0.871 | 0.771
| RIM-ONE | – | – | – | – | 0.824 | 0.701
| (209) |  |  |  |  | 0.847 | 0.736
Singh et al. [23] | REFUGE | – | – | 0.8341 | – | – | –
| (400) |  |  |  |  |  |
Edupuganti et al. [25] | Drishti-GS | – | – | – | – | 0.897 | 0.813
| (51) |  |  |  |  |  |
Agrawal et al. [26] | REFUGE | – | – | – | – | 0.64 | 0.471
| (400) |  |  |  |  |  |
Fu et al. [27] | ORIGA | – | – | – | – | 0.87 | 0.77
| (325) |  |  |  |  |  |
Al-Bander et al. [28] | ORIGA | 0.9195 | 0.999 | 0.998 | – | 0.8659 | 0.7688
| Drishti-GS | 0.7413 | 0.999 | 0.995 | – | 0.8282 | 0.7113
| RIM-ONE | 0.9052 | 0.994 | 0.993 | – | 0.6903 | 0.5567
| (455) | 0.855 | 0.997 | 0.995 |  | 0.795 | 0.679
Liu et al. [29] | ORIGA | – | – | – | – | 0.886 | 0.796
| (325) |  |  |  |  |  |
Jiang et al. [30] | ORIGA | – | – | – | – | 0.883 | 0.791
| (325) |  |  |  |  |  |
Yu et al. [31] | RIGA (Magrabia) | – | – | – | – | 0.891 | 0.812
| Drishti-GS | – | – | – | – | 0.874 | 0.781
| RIM-ONE | – | – | – | – | 0.793 | 0.683
| (324) |  |  |  |  | 0.852 | 0.758
Yin et al. [32] | ORIGA | – | – | – | – | 0.884 | 0.792
| REFUGE | – | – | – | – | 0.875 | 0.777
| (725) |  |  |  |  | 0.88 | 0.785
Kumar et al. [33] | Drishti-GS | 0.8589 | 0.9698 | 0.9690 | – | 0.7532 | 0.6143
| Drions-DB | 0.6175 | 0.9979 | 0.9884 | – | 0.73 | 0.5898
| MESSIDOR | 0.8357 | 0.9883 | 0.9823 | – | 0.7303 | 0.5911
| Forus | 0.7466 | 0.9952 | 0.9867 | – | 0.8027 | 0.6801
| Bosch | 0.7584 | 0.9959 | 0.9917 | – | 0.7213 | 0.5804
| (436) | 0.7634 | 0.9894 | 0.9836 |  | 0.742 | 0.611
Proposed method | Drishti-GS | 0.9855 | 0.9965 | 0.9964 | 0.6794 | 0.8043 | 0.6727
RED-RCNN | RIGA | 0.914 | 0.9997 | 0.9994 | 0.925 | 0.9194 | 0.8509
| REFUGE | 0.8438 | 0.9999 | 0.9992 | 0.9656 | 0.9006 | 0.8192
Average | (190) | 0.9144 | 0.9987 | 0.9983 | 0.8567 | 0.8748 | 0.7809

###  V-E Performance Measures

The standard performance measures used for OD and OC segmentation are
Sensitivity, Specificity, Accuracy, Precision, Dice index, and Jaccard index
[49, 50]. Sensitivity measures the magnitude of positives that are correctly
identified as positives, whereas Specificity measures the magnitude of
negatives that are correctly identified as negatives. Precision expresses the
proportion of all predictions that are actually relevant or present in the
ground-truth. Accuracy is the ratio between the correct predictions and the
total number of predictions.
The Dice and Jaccard indices using network predictions (A) and the ground
truth (B) are: $\text{Jaccard}=\frac{|A\;\cap\;B|}{|A\;\cup\;B|},\text{and
}\text{Dice}=\frac{2\,|A\;\cap\;B|}{|A|\;+\;|B|}.$ We compute the Pearson
correlation coefficient (PCC) between the CDRs obtained from the ground truth
and the prediction.

$\begin{array}[]{ccccc}\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/image15prime.png}&\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/image33prime.png}&\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/image43prime.png}&\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/image97prime.png}&\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/image111prime.png}\\\
\mbox{(a1)}&\mbox{(a2)}&\mbox{(a3)}&\mbox{(a4)}&\mbox{(a5)}\\\
\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/image15_cd.png}&\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/image33_cd.png}&\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/image43_cd.png}&\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/image97_cd.png}&\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/image111_cd.png}\\\
\mbox{(b1)}&\mbox{(b2)}&\mbox{(b3)}&\mbox{(b4)}&\mbox{(b5)}\\\
\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/image15_od.png}&\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/image33_od.png}&\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/image43_od.png}&\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/image97_od.png}&\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/image111_od.png}\\\
\mbox{(c1)}&\mbox{(c2)}&\mbox{(c3)}&\mbox{(c4)}&\mbox{(c5)}\\\
\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/imagve15_oc.png}&\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/image33_oc.png}&\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/image43_oc.png}&\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/image97_oc.png}&\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/image111_oc.png}\\\
\mbox{(d1)}&\mbox{(d2)}&\mbox{(d3)}&\mbox{(d4)}&\mbox{(d5)}\\\ \end{array}$

Figure 8:  Segmentation of optic disc and optic cup using RED-RCNN. (a1)$-$(a5) are fundus images; (b1)$-$(b5) show the OD outline (green) & OC outline (blue), respectively ; (c1)$-$(c5) show the OD segmentation performance; and (d1)$-$(d5) show the OC segmentation performance; yellow: true positive; red: false negative; green: false positive. TABLE VII: Database-specific comparison of simultaneous OD and OC segmentation techniques. Dataset | Algorithm | OD | OC
---|---|---|---
Dice | Jaccard | Dice | Jaccard
|  Zilly et al. [22] | 0.942 | 0.89 | 0.842 | 0.701
RIM-ONE |  Al-Bander et al. [28] | 0.903 | 0.828 | 0.69 | 0.556
|  Yu et al. [31] | 0.949 | 0.907 | 0.793 | 0.683
|  Fu et al. [27] | 0.963 | 0.926 | 0.87 | 0.77
|  Al-Bander et al. [28] | 0.965 | 0.933 | 0.865 | 0.768
ORIGA |  Liu et al. [29] | 0.972 | 0.946 | 0.886 | 0.796
|  Jiang et al. [30] | 0.967 | 0.937 | 0.883 | 0.791
|  Yin et al. [32] | 0.966 | 0.934 | 0.884 | 0.792
|  Zilly et al. [22] | 0.973 | 0.947 | 0.871 | 0.771
|  Edupuganti et al. [25] | 0.967 | 0.936 | 0.897 | 0.813
Drishti-GS |  Al-Bander et al. [28] | 0.949 | 0.904 | 0.828 | 0.711
|  Yu et al. [31] | 0.964 | 0.932 | 0.874 | 0.781
|  Kumar et al. [33] | 0.928 | 0.87 | 0.75 | 0.61
| Proposed method | 0.951 | 0.907 | 0.804 | 0.672
RIGA |  Yu et al. [31] | 0.969 | 0.942 | 0.891 | 0.812
| Proposed method | 0.961 | 0.926 | 0.914 | 0.851
REFUGE |  Agrawal et al. [26] | 0.88 | 0.786 | 0.64 | 0.471
|  Yin et al. [32] | 0.954 | 0.912 | 0.875 | 0.777
| Proposed method | 0.965 | 0.933 | 0.90 | 0.819

###  V-F Results

MRCNN versus RED-RCNN: The first set of comparisons pertains to the OD
segmentation performance. The results of both training and test data
performance are presented in Table II. The training data performance
corresponds to the scenario where the entire dataset was used for training and
the validation was also carried out on the entire dataset. The test data
performance corresponds to the scenario where 90% of the dataset (with a
70%$-$20% split as explained in Sec. V-B) was used for training, and the
results have been reported on the unseen 10%. We observe that the training
data performance of both the models is comparable for most performance
measures with RED-RCNN being marginally better than MRCNN in terms of
Sensitivity and Dice and Jaccard indices. On the other hand, the test data
performance of RED-RCNN is clearly superior to that of MRCNN. A similar set of
results for OC segmentation is provided in Table III. Overall, we observe that
RED-RCNN is superior to MRCNN on both training and test datasets. Proceeding
further, we validated the performance of MRCNN and RED-RCNN on completely new
datasets (IDRiD, Drions-DB, MESSIDOR), i.e., datasets not used even partially
for training. The OD segmentation results are shown in Table IV. A similar
table could not be generated for OC segmentation since these datasets do not
have ground-truth OC annotations (cf. Table I). The results show that RED-RCNN
is superior to MRCNN and is better at generalizing to unseen data. Hence, for
the subsequent comparisons with respect to the state-of-the-art techniques, we
use RED-RCNN and show its OD and OC segmentation performance in Fig. 8.

$\begin{array}[]{ccc}\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/u1.png}&\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/u11.png}&\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/u21.png}\\\
\mbox{(a1)}&\mbox{(b1)}&\mbox{(c1)}\\\
\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/u2.png}&\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/u12.png}&\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/u22.png}\\\
\mbox{(a2)}&\mbox{(b2)}&\mbox{(c2)}\\\
\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/u3.png}&\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/u13.png}&\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/u23.png}\\\
\mbox{(a3)}&\mbox{(b3)}&\mbox{(c3)}\\\
\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/u4.png}&\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/u14.png}&\includegraphics[width=68.28644pt,height=51.21504pt]{bibtex/images/u24.png}\\\
\mbox{(a4)}&\mbox{(b4)}&\mbox{(c4)}\\\ \end{array}$

Figure 9:  Segmentation performance on unseen data (green: OD outline; blue:
OC outline). The images (a1)$-$(a4) are taken from Drions-DB [42]; (b1)$-$(b4)
from IDRiD [41]; and (c1)$-$(c4) from MESSIDOR [43].

RED-RCNN versus the state-of-the-art techniques: We compare the test data
performance of the proposed method against the state-of-the-art techniques for
OD (Table V) and OC (Table VI) segmentation. The results indicate that the
overall performance of the proposed model is significantly better than most
state-of-the-art approaches. The database-specific comparison of simultaneous
OD and OC segmentation techniques is shown in Table VII. We observe a small
decrease in the segmentation performance on the Drishti-GS [35] dataset. The
images in the Drishti-GS dataset have poor contrast in comparison with those
in the RIGA and REFUGE datasets used for training. Drishti-GS has 101 images,
whereas RIGA and REFUGE have 750 and 800 images, respectively. The mismatch in
contrast accompanied by the differences in the dataset sizes could have been
the reason for poor performance on this specific dataset. Examples
illustrating segmentation performance of the proposed method on unseen data
taken from [41, 42, 43] are shown in Fig. 9. The Pearson correlation
coefficient computed between the CDR predictions and the CDR ground-truth is
higher for RED-RCNN than for MRCNN as shown in Fig. 10.
Two-stage classification of Glaucoma severity: Based on the OD and OC
boundaries generated by MRCNN and RED-RCNN, we compute the vertical CDR from
the vertical OD and OC diameters and perform a two-stage classification of
glaucoma severity. The threshold on the vertical CDR for two-stage
classification is set to 0.5, in accordance with the International Council of
Ophthalmology (ICO) guidelines [51]. The validations are carried out on the
REFUGE dataset because, unlike the other datasets, it not only has OD and OC
outlines, but also the ground-truth for two-stage glaucoma severity grading,
which is necessary to compute the Sensitivity, Specificity, and Overall
Classification Accuracy (OCA). The results are shown in Table VIII. While the
Sensitivity of MRCNN is higher than that of RED-RCNN, the Specificity and OCA
of RED-RCNN are significantly better than that of MRCNN. The superior
segmentation accuracy of RED-RCNN translates to a superior accuracy in
glaucoma severity grading.

$\begin{array}[]{cc}\includegraphics[width=108.405pt]{bibtex/images/RES3_new1.png}&\includegraphics[width=108.405pt]{bibtex/images/RES3_new2.png}\\\
\mbox{(a)}&\mbox{(b)}\\\ \end{array}$

Figure 10: Pearson’s correlation coefficient (PCC) between the vertical CDRs
computed from the ground-truth and the prediction obtained using (a) MRCNN,
and (b) RED-RCNN for both training and validation data. The PCC values are
higher for RED-RCNN than MRCNN.

##  VI Conclusions

We addressed the problem of optic disc and cup segmentation in retinal fundus
images using a deep neural network operating within the framework of instance
segmentation. Considering that DNNs meant for segmentation tasks ideally
require a single ground-truth for training, we developed a robust approach to
fuse multiple expert annotations into a single one. We then deployed the
standard MRCNN for performing simultaneous optic disc and cup detection, which
was hitherto not explored. We further improved upon by the segmentation
capability of the MRCNN by incorporating a residual encoder-decoder network in
the mask branch. The resulting RED-RCNN architecture is more accurate than
MRCNN and also more robust to variability as evidenced by the performance on a
large variety of fundus image databases. The superior quality of segmentation
comes from the encoder-decoder structure that is a part of the REDNet, which
gives rise to a learnt, hence optimal, successive oversampling capability. The
easy flow of gradients by means of skip connections is another attractive
feature of the REDNet. The high performance of RED-RCNN on unseen data also
emphasizes its superior generalization capability. Comparisons with state-of-
the-art techniques on several publicly available databases showed that RED-
RCNN is superior to several state-of-the-art methods, considering standard
performance assessment measures. We also found that the superior segmentation
capability of RED-RCNN translated to superior performance in two-stage
glaucoma classification as well.

TABLE VIII: CDR-based two-stage Glaucoma classification performance on the REFUGE dataset [36]. Se: Sensitivity; Sp: Specificity; OCA: Overall Classification Accuracy. Technique | Se | Sp | OCA
---|---|---|---
Expert outline | 0.849 | 0.771 | 0.779
MRCNN | 0.918 | 0.769 | 0.784
RED-RCNN | 0.836 | 0.926 | 0.917

##  VII Acknowledgments

We would like to thank the providers of the publicly available fundus image
datasets, which facilitated the experimental validation. We would also like to
thank the Spectrum Lab Healthcare Team for insightful technical discussions.

## References

  * [1] D. Garway-Heath and R. Hitchings, “Quantitative evaluation of the optic nerve head in early glaucoma,” _British Journal of Ophthalmology_ , vol. 82, no. 4, pp. 352–361, 1998.
  * [2] J. Henderer, “Disc-damage likelihood scale (DDLS),” _The British Journal of Ophthalmology_ , vol. 90, no. 4, p. 395, 2006.
  * [3] K. He, G. Gkioxari, P. Dollár, and R. Girshick, “Mask R-CNN,” _Proc. IEEE Intl. Conf. on Computer Vision_ , pp. 2961–2969, 2017\.
  * [4] X.-J. Mao, C. Shen, and Y.-B. Yang, “Image restoration using convolutional auto-encoders with symmetric skip connections,” _arXiv preprint arXiv:1606.08921_ , 2016.
  * [5] J. Lowell, A. Hunter, D. Steel, A. Basu, R. Ryder, E. Fletcher _et al._ , “Optic nerve head segmentation,” _IEEE Trans. Med. Imag._ , vol. 23, no. 2, pp. 256–264, 2004.
  * [6] M. D. Abramoff, W. L. Alward, E. C. Greenlee, L. Shuba, C. Y. Kim, J. H. Fingert, and Y. H. Kwon, “Automated segmentation of the optic disc from stereo color photographs using physiologically plausible features,” _Invest. Ophth. & Vis. Sci._, vol. 48, no. 4, pp. 1665–1673, 2007\.
  * [7] A. Aquino, M. E. Gegúndez-Arias, and D. Marín, “Detecting the optic disc boundary in digital fundus images using morphological, edge detection, and feature extraction techniques,” _IEEE Trans. Med. Imag._ , vol. 29, no. 11, pp. 1860–1869, 2010.
  * [8] S. Lu, “Accurate and efficient optic disc detection and segmentation by a circular transformation,” _IEEE Trans. Med.Imag._ , vol. 30, no. 12, pp. 2126–2133, 2011.
  * [9] S. Dey, K. Tahiliani, J. H. Kumar, A. Pediredla, and C. S. Seelamantula, “Automatic segmentation of optic disc using affine snakes in gradient vector field,” in _Proc. IEEE Intl. Conf. on Acoustics, Speech and Signal Processing (ICASSP)_ , 2019, pp. 1204–1208.
  * [10] C. d. F. dos Santos Cardoso, G. A. Carrijo, J. C. Ferreira, and J. C. M. dos Santos, “Automatic optic disc segmentation using a 3D morphologic fuzzy Histon roughness index,” _Res. on Biomed. Eng._ , pp. 1–14, 2019.
  * [11] K.-K. Maninis, J. Pont-Tuset, P. Arbeláez, and L. van Gool, “Deep retinal image understanding,” in _Proc. Intl. Conf. on Med. Imag. Comp. and Comp.-Assist. Interv., Springer_ , 2016, pp. 140–148 .
  * [12] D. Mohan, J. H. Kumar, and C. S. Seelamantula, “High-performance optic disc segmentation using convolutional neural networks,” in _Proc. IEEE Intl. Conf. on Imag. Proc. (ICIP)_ , 2018, pp. 4038–4042.
  * [13] ——, “Optic disc segmentation using cascaded multiresolution convolutional neural networks,” in _Proc. IEEE Intl. Conf. on Imag. Proc. (ICIP)_ , 2019, pp. 834–838 .
  * [14] L. Bi, Y. Guo, Q. Wang, D. Feng, M. Fulham, and J. Kim, “Automated segmentation of the optic disk and cup using dual-stage fully convolutional networks,” _arXiv preprint arXiv:1902.04713_ , 2019.
  * [15] Y. Xu, D. Xu, S. Lin, J. Liu, J. Cheng, C. Y. Cheung _et al._ , “Sliding window and regression based cup detection in digital fundus images for glaucoma diagnosis,” in _Proc. Intl. Conf. on Med. Image Comp. and Comp.-Assist. Interv., Springer_ , 2011, pp. 1–8.
  * [16] C. Yang, M. Lu, Y. Duan, and B. Liu, “An efficient optic cup segmentation method decreasing the influences of blood vessels,” _Biomed. Eng. Online_ , vol. 17, no. 1, p. 130, 2018.
  * [17] Z. U. Rehman, S. S. Naqvi, T. M. Khan, M. Arsalan, M. A. Khan, and M. Khalil, “Multi-parametric optic disc segmentation using superpixel based feature classification,” _Expert Systems with Applications_ , vol. 120, pp. 461–473, 2019.
  * [18] G. D. Joshi, J. Sivaswamy, and S. R. Krishnadas, “Optic disk and cup segmentation from monocular color retinal images for glaucoma assessment,” _IEEE Trans. Med. Imag._ , vol. 30, no. 6, pp. 1192–1205, 2011.
  * [19] J. Cheng, J. Liu, Y. Xu, F. Yin, D. W. K. Wong, N.-M. Tan _et al._ , “Superpixel classification based optic disc and optic cup segmentation for glaucoma screening,” _IEEE Trans. Med. Imag._ , vol. 32, no. 6, pp. 1019–1032, 2013.
  * [20] Y. Zheng, D. Stambolian, J. O’Brien, and J. C. Gee, “Optic disc and cup segmentation from color fundus photograph using graph-cut with priors,” in _Proc. Intl. Conf. on Med. Image Comp. and Comp.-Assist. Interv., Springer_ , 2013, pp. 75–82.
  * [21] A. Sevastopolsky, “Optic disc and cup segmentation methods for glaucoma detection with modification of U-Net convolutional neural network,” _Patt. Recog. Imag. Anal., Springer_ , vol. 27, no. 3, pp. 618–624, 2017\.
  * [22] J. Zilly, J. M. Buhmann, and D. Mahapatra, “Glaucoma detection using entropy sampling and ensemble learning for automatic optic cup and disc segmentation,” _Comp. Med. Imag. and Graphics_ , vol. 55, pp. 28–41, 2017\.
  * [23] V. K. Singh, H. A. Rashwan, A. Saleh, F. Akram, M. M. K. Sarker, N. Pandey _et al._ , “REFUGE challenge 2018-Task 2: Deep optic disc and cup segmentation in fundus images using U-Net and multi-scale feature matching networks,” _arXiv preprint arXiv:1807.11433_ , 2018.
  * [24] Z. Ghassabi, J. Shanbehzadeh, and K. Nouri-Mahdavi, “A unified optic nerve head and optic cup segmentation using unsupervised neural networks for glaucoma screening,” in _Proc. 40th Ann. Intl. Conf. IEEE Eng. in Med. and Bio. Soc. (EMBC)_ , 2018, pp. 5942–5945.
  * [25] V. G. Edupuganti, A. Chawla, and A. Kale, “Automatic optic disk and cup segmentation of fundus images using deep learning,” in _Proc. 25th IEEE Int. Conf.on Image Process. (ICIP)_ , 2018, pp. 2227–2231.
  * [26] V. Agrawal, A. Kori, V. Alex, and G. Krishnamurthi, “Enhanced optic disk and cup segmentation with glaucoma screening from fundus images using position encoded CNNs,” _arXiv preprint arXiv:1809.05216_ , 2018.
  * [27] H. Fu, J. Cheng, Y. Xu, D. W. K. Wong, J. Liu, and X. Cao, “Joint optic disc and cup segmentation based on multi-label deep network and polar transformation,” _IEEE Trans. Med. Imag._ , vol. 37, no. 7, pp. 1597–1605, 2018 .
  * [28] B. Al-Bander, B. M. Williams, W. Al-Nuaimy, M. A. Al-Taee _et al._ , “Dense fully convolutional segmentation of the optic disc and cup in colour fundus for glaucoma diagnosis,” _Symmetry_ , vol. 10, no. 4, p. 87, 2018 .
  * [29] Q. Liu, X. Hong, W. Ke, Z. Chen, and B. Zou, “DDNet: Cartesian-polar dual-domain network for the joint optic disc and cup segmentation,” _arXiv preprint arXiv:1904.08773_ , 2019.
  * [30] Y. Jiang, L. Duan, J. Cheng, Z. Gu, H. Xia, H. Fu _et al._ , “JointRCNN: A region-based convolutional neural network for optic disc and cup segmentation,” _IEEE Trans. Biomed. Eng._ , pp. 1–10, 2019\.
  * [31] S. Yu, D. Xiao, S. Frost, and Y. Kanagasingam, “Robust optic disc and cup segmentation with deep learning for glaucoma detection,” _Comp. Med. Imag.and Graphics_ , vol. 74, pp. 61–71, 2019 .
  * [32] P. Yin, Q. Wu, Y. Xu, H. Min, M. Yang, Y. Zhang, and M. Tan, “Pm-net: Pyramid multi-label network for joint optic disc and cup segmentation,” in _in Proc. Intl. Conf. on Medical Image Comp. and Comp.-Assist. Interv._ Springer, 2019, pp. 129–137 .
  * [33] J. R. H. Kumar, C. S. Seelamantula, Y. H. Kamath, and R. Jampala, “Rim-to-disc ratio outperforms cup-to-disc ratio for glaucoma prescreening,” _Scientific Reports_ , vol. 9:7099, 2019.
  * [34] A. Almazroa, S. Alodhayb, E. Osman, E. Ramadan, M. Hummadi, M. Dlaim _et al._ , “Retinal fundus images for glaucoma analysis: the RIGA dataset,” in _Medical Imaging: Imaging Info. for Healthcare Res. and Appl._ , vol. 10579. Intl. Soc. for Opt. and Photonics, 2018, p. 105790B.
  * [35] J. Sivaswamy, S. Krishnadas, A. Chakravarty, G. Joshi, and A. S. Tabish, “A comprehensive retinal image dataset for the assessment of glaucoma from the optic nerve head analysis,” _JSM Biomed. Imag. Data Papers_ , vol. 2, no. 1, p. 1004, 2015.
  * [36] “REFUGE Retinal Image Grand Challenge,” https://refuge.grand-challenge.org/home/, accessed: 2019-03-30.
  * [37] S. Ren, K. He, R. Girshick, and J. Sun, “Faster R-CNN: Towards real-time object detection with region proposal networks,” _Adv. in Neural Inf. Process. Sys._ , pp. 91–99, 2015.
  * [38] V. Badrinarayanan, A. Kendall, and R. Cipolla, “SegNet: A deep convolutional encoder-decoder architecture for image segmentation,” _IEEE Trans. Pattern Analysis and Machine Intelligence_ , vol. 39, no. 12, pp. 2481–2495, 2017.
  * [39] H. Noh, S. Hong, and B. Han, “Learning deconvolution network for semantic segmentation,” in _Proc. IEEE Intl. Conf. on Comp.Vision_ , 2015, pp. 1520–1528.
  * [40] M. Drozdzal, E. Vorontsov, G. Chartrand, S. Kadoury, and C. Pal, “The importance of skip connections in biomedical image segmentation,” in _Deep Learning and Data Labeling for Medical Applications_. Springer, 2016, pp. 179–187.
  * [41] P. Porwal, S. Pachade, R. Kamble, M. Kokare, G. Deshmukh, V. Sahasrabuddhe _et al._ , “Indian diabetic retinopathy image dataset (IDRiD): A database for diabetic retinopathy screening research,” _Data_ , vol. 3, no. 3, p. 25, 2018.
  * [42] E. J. Carmona, M. Rincón, J. García-Feijoó, and J. M. Martínez-de-la Casa, “Identification of the optic nerve head with genetic algorithms,” _Artificial Intelligence in Medicine_ , vol. 43, no. 3, pp. 243–259, 2008.
  * [43] E. Decencière, X. Zhang, G. Cazuguel, B. Lay, B. Cochener, C. Trone _et al._ , “Feedback on a publicly distributed database: the MESSIDOR database,” _Image Analysis & Stereology_, vol. 33, no. 3, pp. 231–234, 2014.
  * [44] M. A. Rahman and Y. Wang, “Optimizing intersection-over-union in deep neural networks for image segmentation,” in _Proc. Int.Symp. on Visual Computing, Springer_ , 2016, pp. 234–244.
  * [45] W. Abdulla, “Mask R-CNN for object detection and instance segmentation on Keras and TensorFlow,” https://github.com/matterport/Mask_RCNN, 2017\.
  * [46] K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in _Proc. IEEE Conf. on Comp. Vision and Pattern Recognition_ , 2016, pp. 770–778.
  * [47] D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” _arXiv preprint arXiv:1412.6980_ , 2014.
  * [48] J. Kim, L. Tran, E. Y. Chew, S. Antani, and G. R. Thoma, “Optic disc segmentation in fundus images using deep learning,” in _Med.Imaging: Imag. Informatics for Healthcare, Res., and Appl._ , vol. 10954. International Society for Optics and Photonics, 2019, pp. 109 540H:1–6.
  * [49] W. R. Crum, O. Camara, and D. L. Hill, “Generalized overlap measures for evaluation and validation in medical image analysis,” _IEEE Trans. Med. Imag._ , vol. 25, no. 11, pp. 1451–1461, 2006.
  * [50] H.-H. Chang, A. H. Zhuang, D. J. Valentino, and W.-C. Chu, “Performance measure characterization for evaluating neuroimage segmentation algorithms,” _Neuroimage_ , vol. 47, no. 1, pp. 122–135, 2009.
  * [51] “ICO Glaucoma Guidelines - 2015,” http://www.icoph.org/enhancing_eyecare/glaucoma.html, 2015.


# Congestion Control in the Cellular-V2X Sidelink

Brian McCarthy  School of Computer Science and Information Technology,
University College Cork, Cork, Ireland
{b.mccarthy<EMAIL_ADDRESS>Aisling O’Driscoll  School of Computer
Science and Information Technology, University College Cork, Cork, Ireland
{b.mccarthy<EMAIL_ADDRESS>
###### Abstract

This paper presents a detailed quantitative evaluation of standardised
Decentralised Congestion Control (DCC) and packet dropping mechanisms for
Cellular V2X (C-V2X). Based on the identified shortcomings, an Access layer
DCC scheme, RRI adaptive, is then proposed. RRI adaptive accommodates the
sidelink scheduling mechanism Sensing Based Semi-Persistent Scheduling (SB-
SPS), eliminating incompatibilities between current standards and the
scheduling mechanism, to avoid unnecessary and reoccurring collisions. Two
variants are proposed; one is an evolution of the ETSI Reactive DCC mechanism
and the other aligns with the 3GPP approach based on channel occupancy ratio
(CR). Both approaches are compared with current ETSI and 3GPP standards and
exhibit improved performance. An evaluation of existing DCC standards and RRI
Adaptive to meet the Quality of Service (QoS) requirements of vehicular
cooperative awareness applications is also conducted.

###### Index Terms:

Cellular V2X, LTE-V, sidelink, congestion control, Mode 4, Mode 2, packet
dropping, SB-SPS.

##  I Introduction

Cooperative awareness between vehicles or between vehicles and infrastructure
forms the basis for future envisaged vehicular communication services. There
are currently two communication technologies i.e. the well studied and mature
IEEE 802.11p (ITS-G5 in Europe) or the emerging cellular equivalent known as
C-V2X. C-V2X defines two modes as part of the 3GPP (3rd Generation Partnership
Project) Release 14 LTE-V standard [1] and forming the basis for new radio
(NR-V2X) in 3GPP Release 16 [2]. In Mode 3 (scheduled), the cellular base
station allocates and manages the resources necessary for V2V PC5
communications. In Mode 4 (autonomous) each vehicle (VUE) selects its radio
resources for V2V communications using the distributed scheduling algorithm
SB-SPS. Mode 4 represents the baseline performance for C-V2X.

Irrespective of whether wireless or cellular V2X technology is employed, both
may be faced with handling a congested radio environment due to limited
spectrum, widespread vehicular deployment and frequent packet exchange. As
such, congestion control techniques are hugely important to manage channel
load and radio interference. DCC mechanisms as defined by ETSI (European
Telecommunications Standards Institute) have been well studied over the past
decade for ITS-G5 [3, 4, 5] but have not been adequately investigated for
C-V2X. The operation of the C-V2X MAC differs significantly from that of
ITS-G5, particularly with respect to MAC layer scheduling. SB-SPS assumes
packets arrive periodically and bases its resource reservation algorithm on
this assumption. However, if packets arrive aperiodically in accordance with
the ETSI CAM (Cooperative Awareness Message) generation rules or due some
congestion control mechanism based on transmission rate control (TRC), this
can lead to prohibitively high packet collisions. Furthermore, as SB-SPS
maintains resources for a defined period known as a grant, these collisions
may reoccur over the duration of the grant. Some initial studies [6, 7] have
investigated the application of packet dropping for SB-SPS but no study
considers all ETSI and 3GPP DCC and packet dropping standards as in this
paper.

To address the identified shortcomings, this paper proposes Access layer DCC
mechanisms that are compliant with the SB-SPS algorithm yet address the
problem of excessive collisions due to the perception of unused yet reserved
resources. This is achieved by adapting the resource reservation interval
(RRI) within the SB-SPS grant in line with measured CBR (Channel Busy Ratio)
as per the ETSI DCC mechanism or channel occupancy as per 3GPP. This simple
approach drastically reduces the collisions by ensuring that resource usage is
more predictable and does not result in reoccurring collisions within an SB-
SPS grant.

It is also important to recognise that while Access layer congestion control
may improve radio conditions and in turn the measured packet delivery rates,
it may not improve the performance achieved at the application layer. If a
high number of application layer or cooperative awareness packets are delayed
or dropped this may render the service unsafe or unusable. As such, it is of
the utmost importance to consider the impact of Access layer DCC on the upper
layer applications. To the author’s knowledge, this paper is the first to do
so for C-V2X and to investigate the impact of all DCC standards on these QoS
requirements.

The rest of this paper is organised as follows: Section II gives an overview
of standardised ETSI and 3GPP DCC approaches as well as state of the art DCC
research. Our proposed C-V2X DCC Access mechanisms that account for the C-V2X
MAC layer are presented in Section III and evaluated in Section IV. Section V
provides concluding remarks.

††This work has been submitted to the IEEE for possible publication. Copyright
may be transferred without notice, after which this version may no longer be
accessible.

##  II Congestion Control for Vehicular Communications

###  II-A ETSI Decentralised Congestion Control (DCC)

ETSI defines a number of DCC mechanisms in [8], originally developed for
ITS-G5. The de-facto mechanism is transmission rate control which works by
increasing the delay between packet transmissions based on the CBR. The means
by which this delay is determined is how ETSI distinguishes between it’s TRC
mechanisms, namely DCC Reactive and DCC Adaptive.

DCC Reactive is the original approach specified by ETSI based on a state
machine, where the state is associated with a particular CBR range. Depending
on the CBR, a delay is introduced between consecutive packets to control the
transmission rate. This is shown in Table I. The maximum allowed transmission
rate for a CBR range is enforced using Toff, the time period before a new
consecutive packet can be transmitted. DCC Adaptive, is a rate control
mechanism based on the LIMERIC algorithm [3]. It uses an algorithmic approach
to calculating the delay rather than a predefined lookup table. It is designed
to adjust packet rate transmission to converge on a target CBR, with a default
of 68%. DCC Adaptive better considers factors such as stability and fairness
to ensure no node is starved. Amador et. al. provide a detailed analysis of
ETSI DCC Adaptive in [9].

TABLE I: ETSI Access Reactive DCC as specified in [8]. CBR | State | Packet Rate | Toff
---|---|---|---
CBR $<$ 0.3 | Relaxed | 10Hz | 100ms
0.3 $\leq$ CBR $\leq$ 0.40 | Active 1 | 5Hz | 200ms
0.40 $\leq$ CBR $\leq$ 0.50 | Active 2 | 2.5Hz | 400ms
0.50 $\leq$ CBR $\leq$ 0.60 | Active 3 | 2Hz | 500ms
CBR $>$ 0.60 | Restrictive | 1Hz | 1000ms

###  II-B ETSI C-V2X Congestion Control

In recent years, ETSI have set out some details relating to congestion control
for C-V2X [10]. Specifically, they describe how CBR and CR are to be measured.
CBR provides an estimation of the overall channel congestion by measuring the
ratio of subchannels over the last 100 subframes where the sidelink RSSI
(S-RSSI) exceeds a predefined threshold. The CR measures the number of
subchannels used by each vehicle over a historical time period as well as the
number that will be used based on the current configured grant. In Table II
ETSI specifies the maximum CR limit for each vehicle based on the measured
CBR. If the measured CR exceeds the limit for the current CBR range, the
vehicle must reduce it’s CR using a particular congestion control mechanism.
ETSI highlights that this can include packet dropping, MCS adaptation and
power control but do not specify precise implementations.

TABLE II: ETSI C-V2X Congestion Control - Maximum CR limit per CBR range and packet priority [10]. CBR | Priority 1-2 | Priority 3-5 | Priority 6-8
---|---|---|---
0 $\leq$ CBR $\leq$ 0.3 | no limit | no limit | no limit
0.3 $<$ CBR $\leq$ 0.65 | no limit | 0.03 | 0.02
0.65 $<$ CBR $\leq$ 0.8 | 0.02 | 0.006 | 0.004
0.8 $<$ CBR $\leq$ 1 | 0.002 | 0.003 | 0.002

###  II-C 3GPP C-V2X Congestion Control

The 3GPP C-V2X standard also does not provide a specific congestion control
mechanisms but, similarly to ETSI, defines the CBR and CR measurements under
which it should be invoked. It also specifies a table shown in Table III, as
part of a 3GPP working group, which is less reactive than the ETSI equivalent
at lower CBR levels.For the remainder of this paper we assume packet dropping
is the congestion control mechanism invoked by this table.

TABLE III: 3GPP C-V2X Congestion Control - Maximum CR limit per CBR range and packet priority [11]. CBR | CR limit
---|---
CBR $\leq$ 0.65 | no limit
0.65 $<$ CBR $\leq$ 0.675 | 1.6e-3
0.675 $<$ CBR $\leq$ 0.7 | 1.5e-3
0.7 $<$ CBR $\leq$ 0.725 | 1.4e-3
0.725 $<$ CBR $\leq$ 0.75 | 1.3e-3
0.75 $<$ CBR $\leq$ 0.775 | 1.2e-3
0.8 $<$ CBR $\leq$ 0.825 | 1.1e-3
0.825 $<$ CBR $\leq$ 0.85 | 1.1e-3
0.85 $<$ CBR $\leq$ 0.875 | 1.0e-3
0.875 $<$ CBR | 0.8e-3

###  II-D Literature Review

One of the initial works to evaluate the impact of packet dropping for C-V2X
is by Mansouri et. al [12]. It evaluates the performance of packet dropping
based on the 3GPP C-V2X CR limits as per Table III. This paper highlights some
of the issues that we discuss in Section IV-C where VUEs mistakenly choose the
same channel resources. The most similar work to the approach proposed in this
paper is a reservation splitting technique by Wendland et. al [7]. The authors
split a single SB-SPS grant into multiple sub-grants of lower frequency (e.g.
10Hz $\rightarrow$ 2 x 5Hz) and when the network is congested, individual sub-
grants can be disabled without interrupting the SB-SPS grant mechanism. This
approach is analogous to the proposed RRI Adaptive mechanism in that turning
off a grant is similar to changing the RRI i.e. a single 5hz grant is the same
as a grant with an increased RRI of 200ms. They compare their scheme against
ETSI C-V2X DCC as per Table II. While the reservation splitting approach
reduces recurring collisions within a single grant, it does not support
dynamically re-enabling grants as congestion changes. In contrast the proposed
RRI Adaptive approaches allow this to occur and work within the existing SB-
SPS mechanism without requiring any changes. Sepulcre et. al. [13] recently
investigated the efficacy of packet dropping to meet application QoS
requirements as a congestion control mechanism for ITS-G5. The authors show
that application PDR is impacted by packet dropping and performs worse than if
no congestion control was applied despite improvements in radio performance.
However, it is our premise that packet dropping can form part of a congestion
control solution for C-V2X as seen in Fig 7(b) and Table VI where we observe
similar IPG and increased neighbour awareness. This also highlights a need for
further investigation into whether the transmission frequency of CAMs and
other cooperative awareness services can be increased such that they are only
transmitted when meaningful and without impacting the awareness of vehicles. A
similar premise was recently discussed by Bazzi et. al [14].

Other approaches look at combining mechanisms such as rate control, power
control and MCS adaptation. The most prevalent of these is the SAE DCC
mechanism [15] that uses power and rate control. The rate control algorithm is
derived from the Limeric algorithm [3] and power control is based on The
Stateful Utilization- based Power Adaptation (SUPRA) which is designed to
control communication range [16]. Research in [17, 18, 19, 20] investigate the
performance of the SAE standard for congestion control. Generally, these
authors have shown performance increases over standard rate control while
showing minor improvements from power control, with the need for further study
before determining their effectiveness for C-V2X.

Notably, all the mechanisms described thus far are Access layer approaches.
Such mechanisms have limitations when simultaneously considering multiple
application layer services with different QoS requirements. As such, ETSI has
begun defining the Facilities layer DCC which coordinates between Access layer
congestion control mechanisms and higher layer services. It can also operate
as a standalone mechanism without lower layers. The goal is to ensure that
nodes can predict available resources and more intelligently distribute
channel resources across the services that they are tasked with fulfilling.
ETSI has not yet standardised Facilities layer DCC but some works [21, 22, 23,
9] have investigated possible implications and implementations.

##  III Proposed Adaptive RRI Approaches

In Section IV it is shown that traditional TRC mechanisms like DCC or packet
dropping are incompatible with the SB-SPS mechanism when a scheduled
transmission is missed, leading to unnecessary collisions. To overcome this,
two adaptive RRI mechanisms are proposed. These mechanisms adjust the time
between transmissions based on the current CBR measurement, while considering
the RRI of the SB-SPS grant. Two variants are proposed;

  * •

RRIlookup: This is based on a TRC mechanism similar to DCC Reactive, which
uses a lookup table to determine the packet delay i.e. Toff, based on the
measured CBR. However in this case the delay offset is linked to a multiple of
the default RRI and an SCI is broadcast indicating the new RRI. This controls
the rate of packet transmission without missing a scheduled resource
reservation slot.

  * •

RRICR_limit: This approach is based on packet dropping to reduce an individual
VUE’s CR-limit. This is similar to the ETSI and 3GPP C-V2X approaches in that
it is also based on a CBR CR limit table. Given a particular CBR, representing
the overall measured congestion of the channel, if it is determined that the
VUE’s CR exceeds the CR limit for that CBR, the RRI will be increased such
that the CR is brought below the limit. An SCI is then broadcast indicating
the new RRI. When the CBR returns to a lower range and CR can be increased, a
new RRI will is chosen that maintains the new limit.

As both of these approaches operate at the MAC layer, they represents Access
layer congestion control mechanisms. We also employ the DCC averaging
mechanism where RRI transitions only occur after 1 second of CBR exceeding a
threshold and RRIs are decreased after 5 seconds of lower measured CBR. This
results in a more stable level of CBR for all nodes. Fig. 1 illustrates the
concept underpinning both adaptive RRI approaches (shown as per timeline B)
with the default SB-SPS operation shown as per timeline A. In A, after
transmission T1, congestion occurs. This results in a delay by a TRC
congestion control mechanism or a packet drop. The consequence is that a
packet is not transmitted in the next scheduled resource reservation slot i.e.
a missed transmission (MT). As a result, an SCI is not transmitted so
neighbouring VUEs believe the resource(s) to be free. However as the SB-SPS
grant is maintained, and may be utilised in the future e.g. transmission T3, a
collision on that resource can occur. In contrast, the proposed adaptive RRI
mechanisms shown in B, explicitly considers the RRI in the grant when adding a
delay in the case of RRIlookup or packet dropping in the case of CR limit.
When transmission T1 occurs it is determined the new RRI and an SCI is
broadcast with the new RRI to all neighbouring VUEs. This ensures that
neighbouring VUEs are informed of when the vehicle next intends to transmit
and can utilise the free resources in the interim.

Figure 1: RRI Adaptive approaches versus previous approaches.

##  IV Results

The road environment, vehicular density and other key simulation parameters
used in this evaluation are summarised in Table IV. This is designed to allow
for comparison with a previous study [6]. Application packets are generated
periodically (100ms) but only the most recent packet is transmitted i.e. older
intermediate packets are dropped if a newer packet is generated.

TABLE IV: Simulation Parameters. Parameter | Value
---|---
Vehicular scenario
Vehicular density | 0.46 veh/m
Road length | 600 m
Number of lanes | 3 in each direction (6 in total)
Vehicle Speed | 50km/h
SUMO step-length | 1ms
Channel settings
Carrier frequency | 5.9 GHz
Channel bandwidth, No. subchannels | 10 MHz, 3
Subchannel size | 16 Resource Blocks
Application layer
Packet size | 190 Bytes
Transmission frequency ($F_{Tx}$) | 10 Hz
MAC & PHY layer
Resource keep probability | 0
RSRP threshold | -126 dBm
RSSI threshold | -90 dB
Propagation model | Winner+ B1
MCS | 6 (QPSK 0.5)
Transmission power ($P_{Tx}$) | 23 dBm
Noise figure | 9 dB
Shadowing variance LOS | 3 dB

###  IV-A ETSI Access layer Congestion Control

We investigate the efficacy of the standardised ETSI DCC mechanism, designed
for ITS-G5, to the 3GPP C-V2X standard, and compare to it’s performance
without congestion control (labelled C-V2X-No DCC). Fig. 2 shows the PDR,
considering two C-V2X SB-SPS configurations. The first assumes the default
configuration where grant breaking is enabled (labelled DCC Reactive (GB)) and
with the sl-reselectAfter parameter set to 1. This means that the grant is
broken if a single reserved resource is not used i.e. other vehicles will
perceive future grant resources to be free. The second configuration assumes
grant breaking is disabled (labelled DCC Reactive (no GB)).

We can observe that DCC has a large detrimental impact on the PDR performance
of C-V2X when grant breaking is enabled. This is for the same reasons that
cause the sharp decline of SB-SPS when scheduling aperiodic application
traffic, as discussed in detail in [24]. As described in Section II-A, DCC
introduces a delay in the packet inter-arrival time (mean of 300ms). If the
packet inter-arrival time increases beyond a maximum of 198ms, assuming a
resource reservation interval (RRI) of 100ms (2n-2 where n=RRI)[24], this
breaks the grant. Grant breaking leads to a rise in collisions due to VUEs
contending for an increasingly small CSR pool. This is compounded by constant
rescheduling, increasing the risk of VUEs selecting the same resource, thereby
decreasing the overall PDR. To alleviate this, grant breaking can be disabled
which improves performance due to reduced resource rescheduling, as shown in
Fig. 2. However DCC Reactive (No GB) also incurs a degradation in PDR when
compared with C-V2X-No DCC. This is because disabling grant breaking
introduces an additional source of error, as discussed by Harri et al [6]. If
reserved resources go unused but the grant is maintained, an SCI is not sent.
Thus, neighbouring VUEs may mistakenly believe the resources to be free,
leading to unnecessary collisions. For the remainder of the paper we will
consider DCC Reactive (No GB) as a baseline, herein referred to as DCC
Reactive.

Figure 2: ETSI Access layer DCC (Reactive).

We next compare DCC Reactive against the other defined approach in the ETSI
standard, namely DCC Adaptive. We consider default DCC Adaptive behaviour
where the CBR converges to a target of 68%. We also evaluate with a CBR target
of 20%, comparable to the mean CBR that was measured for DCC Reactive, to
allow for direct comparison.

The impact on PDR is shown in Fig. 3(a). Notably DCC Adaptive (68%) incurs
similar performance to no congestion control due to comparable CBR, as shown
in Fig. 3(b). Of greater interest, is the comparison between DCC Adaptive and
DCC Reactive for a comparable CBR of 20%. DCC reactive performs poorly for the
reasons already discussed and due to drawbacks associated with stability [4].
It is notable that when CBR is reduced to a target of 20%, the performance of
DCC Adaptive greatly improves PDR by up to 21%. Thus the performance of DCC
Adaptive is further explored in comparison with alternative mechanisms in
Section IV-C.

(a) ETSI DCC PDR.

(b) ETSI DCC CBR.

Figure 3: Impact of DCC variants on PDR & CBR (No grant breaking).

###  IV-B ETSI & 3GPP Packet Dropping

The limitations of the ETSI DCC mechanisms when applied to C-V2X have been
shown, caused by incompatibility with the default SB-SPS algorithm. ETSI and
3GPP congestion control recommendations are next evaluated with an emphasis on
packet dropping. As described in II-B and II-C, this method of congestion
control simply drops packets before transmission to maintain a specific CR
limit according to a lookup table. Three CR limit lookup tables are
considered:

  * •

The recently defined ETSI CR limit table as shown in Table II. A traffic
priority of 6-8 is assumed as other priorities had negligible impact. This is
labelled Packet Dropping (ETSI).

  * •

As part of a 3GPP working group, Qualcomm have also proposed a CR limit table
[11]. This is labelled Packet Dropping (3GPP).

  * •

An adapted 3GPP CR limit table, with lower CBR thresholds i.e. designed to
more aggressively manage congestion and to produce a mean CBR closer to 20% in
line with the DCC Reactive scheme. This is labelled Packet Dropping
(Aggressive).

The PDR performance can be seen in Fig. 4(a). Packet Dropping (ETSI) performs
identically to no congestion control both in terms of PDR and CBR. Packet
Dropping (3GPP) performs marginally better due to a reduced CBR of approx.
10%, as shown in Fig. 4(b), although this only translates into a PDR
improvement of 3% at distances exceeding 150m as seen in Fig. 4(a). Adopting a
more aggressive approach to reducing CBR in the case of Packet Dropping
(Aggressive), improves PDR by up to 17% at distances beyond 100m. However, the
improvement in PDR does not correlate with the significantly lower CBR.

(a) Packet Dropping PDR.

(b) Packet Dropping CBR.

Figure 4: ETSI & 3GPP Packet Dropping.

###  IV-C Adaptive RRI - Access layer Performance

Based on the drawbacks of existing standardised approaches, we next evaluate
the performance of the proposed adaptive RRI congestion control schemes as
described in Section III. These are compared against C-V2X-No DCC, DCC
Reactive, DCC Adaptive (CBR target of 20%) and Packet Dropping (Aggressive).
In all cases we consider grant breaking to be disabled.

TABLE V: Absolute number of colliding grants. CBR | Congestion Control Mechanism | Mean Colliding Grants ($\gamma$) |  $\gamma$MT (%) |  $\gamma$NF (%) |  $\gamma$TSim (%)
---|---|---|---|---|---
20% | C-V2X-No DCC | 5076 | - | 3645 | 1431
DCC Adaptive | 2286 | 678 | 0 | 1608
DCC Reactive | 4885 | 338 | 399 | 4148
Packet Dropping (Aggressive) | 1565 | 889 | 0 | 676
RRILookup | 427 | - | 258 | 169
RRICRlimit | 62 | - | 0 | 62
60% | DCC Adaptive | 4954 | 842 | 2626 | 1486
RRICRlimit | 768 | - | 558 | 210

Fig. 5(a) shows the PDR performance of RRIlookup outperforms DCC Adaptive by
up to 5% PDR but Fig. 5(b) demonstrates less stability with respect to CBR.
This is because it inherits the instability of a table lookup mechanism such
as DCC Reactive. It exhibits considerably less mean colliding grants when
compared to standardised DCC approaches as shown in Table V. More notably,
RRICR_limit shows significantly improved PDR over all schemes (a mean of 11%
when compared to DCC Adaptive) even those with comparable CBR. It also
exhibits the lowest number of mean colliding grants.

(a) Packet Delivery Rate.

(b) Channel Busy Ratio.

Figure 5: Comparative congestion control at 20% CBR.

The mean colliding grants is a significant metric as it represents the
resources utilised by 2 or more VUEs simultaneously, due to poor CSR selection
in SB-SPS. Colliding grants can occur for three reasons:

  1. 1.

A missed transmission causing a VUE to not send an SCI. Neighbouring VUEs will
mistakenly believe a resource to be free in future reserved slots, when they
may be utilised. This is denoted as $\gamma$MT in Table V.

  2. 2.

In congested radio conditions, when no resources are determined to be free,
VUEs will select resources with low RSRP and RSSI measurements. This is
denoted as $\gamma$NF in Table V.

  3. 3.

When neighbouring VUEs reserve the same resources within a single RRI as a
result of highly similar selection windows. As neighbouring VUEs may have
similar historical RSRP/RSSI measurements they are likely to have similar CSRs
which can result in selecting the same resource(s). This is denoted as
$\gamma$TSim in Table V.

DCC and packet dropping mechanisms are very susceptible to colliding grants
due to $\gamma$MT, because of the incompatibility of their schemes with the
SB-SPS RRI mechanism. This is evident in Table. V. Also, as the reserved
resources are maintained for 5-15 sub-frames, as determined by the Resource
Reselection Counter (RRC), recurring colliding grants represent multiple
avoidable half duplex errors in the channel as well as increasing
interference. In contrast, the RRI Adaptive approaches account for this and
hence incur significantly less colliding grants by eliminating $\gamma$MT and
reducing $\gamma$NF and $\gamma$TSim. The RRIlookup CBR variance results in a
higher number of colliding grants than the more stable RRICR_limit.

While RRICR_limit demonstrates significantly higher PDR (Fig. 5(a)), it incurs
comparable application performance to DCC Adaptive, discussed further in
Section IV-D. This is attributable to aggressive congestion control with CBR
of approx. 20% (for comparison with schemes such as DCC Reactive). Given that
this can result in under utilisation of the channel, a CBR of approximately
60% is considered in Fig. 6. This aligns with previous ITS-G5 studies that
have investigated maximum throughput at 60% [5]. RRICR_limit is compared
against C-V2X-No DCC and DCC Adaptive, which is the closest in performance.
RRICR_limit exhibits a significant PDR improvement of up to 18% and 14%
respectively.

(a) Packet Delivery Rate.

(b) Channel Busy Ratio.

Figure 6: Comparative congestion control at 60% CBR.

###  IV-D Adaptive RRI - Application Layer Performance

It is important to consider the performance of the proposed congestion control
mechanisms for the applications that they service, particularly as vehicular
communications often has geotemporal relevance. Specifically, we consider the
impact on the Inter-Packet Gap (IPG), which represents the average elapsed
time between receptions from neighbouring VUEs. We also consider mean
awareness which is the percentage of vehicles a VUE is aware of in a given
communication range. The maximum lifetime of a CAM before it is discarded by a
VUE is 1 second.

In Fig. 7(a), RRIlookup demonstrates the lowest IPG while exhibiting better
PDR (Fig. 5(a)), except for RRICR_limit. It demonstrates higher mean neighbour
awareness than current standardised approaches as shown in Table VI, but lower
than DCC Adaptive and RRICR_limit. The IPG demonstrated by RRICR_limit is
similar to that of DCC Adaptive but exhibits much higher PDR. As shown in
Table VI, it also demonstrates high neighbour awareness. Application layer
performance for a CBR of 60% is also considered. In Table VI, RRICR_limit with
aggressive does little to impact neighbour awareness when compared to 60%. It
does however impact the IPG. RRICR_limit incurs higher IPG at 20% CBR as the
level of congestion control is very aggressive. Fig. 7(b) shows the IPG for
60% CBR, with a mean of 165ms for C-V2X-No DCC, 180ms for RRICR_limit and
190ms for DCC Adaptive respectively.

(a) IPG at 20% CBR.

(b) IPG at 60% CBR.

Figure 7: Inter-Packet Gap (IPG) performance of congestion control mechanisms.
TABLE VI: Neighbour VUE Awareness (200m-300m)

CBR | Congestion Control Mechanism | Awareness % | Std. Dev. %
---|---|---|---
20% | C-V2X-No DCC | 92.22 | 4.43
DCC Adaptive | 94.85 | 3.46
DCC Reactive | 74.55 | 9.76
Packet Dropping (Aggressive) | 80.41 | 5.58
RRILookup | 90.91 | 4.38
RRICR_limit | 97.94 | 2.13
60% | DCC Adaptive | 97.80 | 2.72
RRICR_limit | 97.75 | 2.24

##  V Conclusion

In this paper a new DCC approach, RRI adaptive, is proposed which is fully
compatible with the SB-SPS mechanism. We have shown that RRI adaptive enables
much higher performance in terms of PDR while maintaining lower IPG and higher
mean neighbour awareness than existing standardised approaches. Future work
will seek to modify RRI adaptive to avoid a table based approach which is
prone to CBR instability. Open research questions also exist relating to
Facilities layer congestion control that considers multiple simultaneous V2X
services with diverse QoS requirements.

## Acknowledgements

This publication has emanated from research conducted with the financial
support of Science Foundation Ireland (SFI) under Grant No: 17/RC-PhD/3479.

## References

  * [1] _Study on LTE-based V2X services (v14.0.0, Release 14)_ , 3GPP, July 2016, 3GPP TR 36.885.
  * [2] _Release 16 Description; Summary of Rel-16 Work Items (V1.0.0 , Release 16))_ , 3GPP, Dec 2020, 3GPP TR 21.916.
  * [3] G. Bansal, J. B. Kenney, and C. E. Rohrs, “Limeric: A linear adaptive message rate algorithm for dsrc congestion control,” _IEEE Transactions on Vehicular Technology_ , vol. 62, no. 9, pp. 4182–4197, 2013.
  * [4] A. Rostami, S. Member, B. Cheng, S. Member, G. Bansal, K. Sjoberg, M. Gruteser, and J. B. Kenney, “Channel Congestion Control Approaches,” vol. 17, no. 10, pp. 1–14, 2016.
  * [5] J. B. Kenney and G. Bansal, “Controlling Congestion in Safety-Message Transmissions,” no. December, pp. 1–8, 2013.
  * [6] A. Mansouri, V. Martinez, and J. Härri, “A first investigation of congestion control for lte-v2x mode 4,” in _2019 15th Annual Conference on Wireless On-demand Network Systems and Services (WONS)_ , 2019, pp. 56–63.
  * [7] P. Wendland, G. Schaefer, and R. S. Thoma, “LTE-V2X Mode 4: Increasing robustness and DCC compatibility with reservation splitting,” _2019 8th IEEE International Conference on Connected Vehicles and Expo, ICCVE 2019 \- Proceedings_ , pp. 0–5, 2019.
  * [8] ETSI, “ETSI TS 102 687 - V1.2.1 - Intelligent Transport Systems ( ITS ); Decentralized Congestion Control Mechanisms for Intelligent Transport Systems operating in the 5 GHz range ;,” _ETSI standard_ , vol. 2, pp. 1–14, 2018\.
  * [9] O. Amador, I. Soto, M. Uruena, and M. Calderon, “GoT: Decreasing DCC queuing for CAM messages,” _IEEE Communications Letters_ , vol. 24, no. 12, pp. 2974–2978, 2020.
  * [10] ETSI TS 103 574 V0.3.1, “Intelligent Transport Systems (ITS); Access layer part; Congestion Control for the Cellular: V2X PC5 interface,” vol. 1, pp. 1–12, 2018.
  * [11] Qualcomm, “R1-1611594 Congestion control for V2V,” Tech. Rep., 2016, 3GPP TSG-RAN WG1 No.87.
  * [12] A. Mansouri, V. Martinez, and J. Harri, “A First Investigation of Congestion Control for LTE-V2X Mode 4,” _2019 15th Annual Conference on Wireless On-demand Network Systems and Services, WONS 2019 - Proceedings_ , pp. 56–63, 2019\.
  * [13] M. Sepulcre, J. Mira, G. Thandavarayan, and J. Gozalvez, “Is Packet Dropping a Suitable Congestion Control Mechanism for Vehicular Networks?” in _IEEE Vehicular Technology Conference_ , vol. 2020-May. Institute of Electrical and Electronics Engineers Inc., may 2020.
  * [14] A. Bazzi, G. Cecchini, B. M. Masini, and A. Zanella, “Should i Really Care of That CAM?” _IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC_ , vol. 2018-Septe, 2018.
  * [15] S. o. A. E. SAE International, “On-board system requirements for v2v safety communications. Standard Doc J2945/1,” 03 2016.
  * [16] Y. P. Fallah, N. Nasiriani, and H. Krishnan, “Stable and fair power control in vehicle safety networks,” _IEEE Transactions on Vehicular Technology_ , vol. 65, no. 3, pp. 1662–1675, 2016.
  * [17] B. Toghi, M. Saifuddin, Y. P. Fallah, and M. O. Mughal, “Analysis of distributed congestion control in cellular vehicle-To-everything networks,” _arXiv_ , 2019.
  * [18] B. Toghi, M. Saifuddin, M. O. Mughal, and Y. P. Fallah, “Spatio-temporal dynamics of cellular V2X communication in dense vehicular networks,” _arXiv_ , 2019.
  * [19] Y. Yoon and H. Kim, “Balancing Power and Rate Control for Improved Congestion Control in Cellular V2X Communication Environments,” _IEEE Access_ , vol. 8, pp. 105 071–105 081, 2020.
  * [20] J. Choi and H. Kim, “A QoS-Aware Congestion Control Scheme for C-V2X Safety Communications,” _IEEE Vehicular Networking Conference, VNC_ , vol. 2020-Decem, pp. 23–26, 2020.
  * [21] I. Khan and J. Härri, “Integration Challenges of Facilities-Layer DCC for Heterogeneous V2X Services,” _IEEE Intelligent Vehicles Symposium, Proceedings_ , vol. 2018-June, no. Iv, pp. 1131–1136, 2018.
  * [22] M. I. Khan, M. Sepulcre, and J. Harri, “Cooperative Wireless Congestion Control for Multi-Service V2X Communication,” _IEEE Intelligent Vehicles Symposium, Proceedings_ , no. Iv, pp. 1357–1363, 2020.
  * [23] Q. Delooz, R. Riebl, A. Festag, and A. Vinel, “Design and Performance of Congestion-Aware Collective Perception,” _IEEE Vehicular Networking Conference, VNC_ , vol. 2020-Decem, 2020.
  * [24] B. McCarthy, A. Burbano-Abril, V. R. Licea, and A. O’Driscoll, “Opencv2x: Modelling of the v2x cellular sidelink and performance evaluation for aperiodic traffic,” _arXiv_ , 2021.