I Introduction
Since December 2019, a novel coronavirus (SARSCoV2) has spread from Wuhan to the whole China, and then to many other countries. At the end of January 2020, the World Health Organization (WHO) declared that COVID19 a Public Health Emergency of International Concern [2]. By July 15 2020, more than 12 million confirmed cases, and more than 570,000 deaths cases were reported across the world [1]. While infection rates are decreasing in some countries, numbers of new infections continue quickly growing in many other countries, signaling the continuing and global threat of COVID19 [4, 5, 6].
Up to this point, no effective treatment has yet been proven for COVID19. Therefore for prompt prevention of COVID19 spread, accurate and rapid testing is extremely pivotal. The reverse transcription polymerase chain reaction (RTPCR) has been considered the gold standard in diagnosing COVID19. However, the shortage of available tests and testing equipment in many areas of the world limits rapid and accurate screening of suspected subjects. Even under best circumstances, obtaining RTPCR test results takes more than 6 hours and the routinely achieved sensitivity of RTPCR is insufficient [3]. On the other hand, the radiological imaging techniques like chest Xrays and computed tomography (CT) followed by automated image analysis [26] may successfully complement RTPCR testing. CT screening provides threedimensional view of the lung and is therefore more sensitive (although less widely available) compared to chest Xray radiography.
In a systematic review [9] the authors indicated that CT images are sensitive in detection of COVID19 before observation of some clinical symptoms. Typical signs of COVID19 in CT images consist of unilateral, multifocal and peripherally based ground glass opacities (GGO), interlobular septal thickening, thickening of the adjacent pleura, presence of pulmonary nodules, round cystic changes, bronchiectasis, pleural effusion, and lymphadenopathy [7, 8]
. Accurate and rapid detection and localization of these pathological tissue changes is critical for early diagnosis and reliable severity assessment of COVID19 infection. As the number of affected patients is high in most of the hospitals, manual annotation by welltrained expert radiologists is time consuming and subject to inter and intraobserver variability. Such annotation is tremendous and laborintensive for radiologists and slows down the CT analysis. The urgent need for automatic segmentation of typical COVID19 CT signatures is widely appreciated and deep learning methods can offer a unique solution for identifying COVID19 signes of infection in clinicalquality images frequently suffering from variations in CT acquisition parameters and protocols
[10].In this work, we present a deep learning based framework for automatic segmentation of pathologic COVID19associated tissue areas from clinical CT images available from publicly available COVID19 segmentation datasets. There has been a huge progress in the performance of image segmentation model using various deep learning based frameworks in recent years [11, 12, 13, 14, 15, 16]. Our solution is based on adapting and enhancing a popular deep learning medical image segmentation architecture UNet to for COVID19 segmentation task. As COVID19 tissue regions tend to form connected regions identifiable in individual CT slices, ”connectivity promoting regularization” term was added to the specifically designed training loss function to encourage the model to prefer sufficiently large connected segmentation regions of desirable properties. It is worth to mention that there have been a few works proposed for COVID19 segmentation from CT images very recently. In [17], Fan et al. proposed InfNet, to identify infected regions from chest CT slices. In they proposed model a parallel partial decoder is used to aggregate the highlevel features and generate a global map. Then, the implicit reverse attention and explicit edgeattention are utilized to model the boundaries and enhance the representations. But unfortunately this model used a very small dataset of CT labeled images for segmentation, which consist of a total of 100 CT slices, making it hard to generalize the result, and compare. In terms of Dice score, achieves much higher Dice score, on a larger test set. In [18], Elharrouss et al. proposed an encoderdecoder based model for lung infection segmentation using CTscan images. The proposed model first uses image structure and texture to extract the ROI of infected area, and then uses the ROI along with image structure to predict the infected region. They also train this model on a small dataset of CT images, and achieve reasonable performance. In [19], Ma et al. prepared a new benchmark of 3D CT data with 20 cases that contains 1800+ annotated slices, and provided several pretrained baseline models, that serve as outof thebox 3D segmentation.
The main contributions of our work can be summarized as follows:

Development of an image segmentation framework for detecting pathologic COVID19 regions in pulmonary CT images,

Development of a novel connectivitypromoting regularization loss function,

Quantitative validation showing better performance than some of existing stateoftheart segmentation approaches

Publicly sharing the developed software code facilitating research and medical community use.
Ii The Proposed Framework
Despite a large number of patients suffering from COVID19, despite a growing number of COVID19 volumetric CT scans, the availability of labeled CT images that can be used for training of deep learning methods is still limited. Therefore, our strategy relies heavily on the use of transfer learning, initiating the training from a model previously developed for medical image segmentation (segmentation of neuronal structures in electron microscopic stacks), and adapt it toward this task. To better suit the segmentation task at hand, we employed an architecture similar to the UNet, one of the most successful deep learning medical image segmentation approaches, and modified its loss function to prefer COVID19 specific foreground mask connectivity.
Iia UNet Architecture
UNet is one of the popular segmentation models which is based on encoderdecoder neural architecture and use of skip connections, and was originally proposed by Ronneberger et al. [16]. The network architecture of UNet is illustrated in Fig. 2
. In the encoder part, model gets an image as input and applies multiple layers of convolution, maxpooling and ReLU activation, and compresses the data into a latent space. In the decoder part, the network attempts to decode the information from the latent space using transposed convolution operation (deconvolution) and produce the segmentation mask of the image. The rest of the operations are similar to the aforementioned ones in the encoder part. One difference between UNet and plain encoderdecoder model is the use of skipconnections to send the information from the corresponding highresolution layers of the encoder to the decoder, which can help the network to better capture small details that are present in highresolution. Fig.
2 illustrates the general architecture of a UNet model.Similar to other neural segmentation models, UNet uses the loss function in Eq 1 during training. It is comprised of the weighted cross entropy loss together with the softmax function over the final feature maps.
(1) 
Where : {1, . . . , K} considering that and also K denotes the total number of classes in the dataset. Moreover, the softmax is defined as = where represents the activation in feature channel K. Additionally, : is a weighted map to give some features more importance.
IiB Connectivity Regularization
The segmentation maps usually consist of a number of connected components, and singlepixel regions are rare. To encourage our segmentation model to generate segmentation maps with connected components of desirable sizes, we found that incorporating an explicit regularization term in the training loss function can greatly improve connectivity requirements for the predicted segmentation regions. It is worth noting that conventional UNet can also implicitly learn such behavior from training data to some extent, assuming sufficient data sizes are available, which is not quite the case in our situation. Several strategies were developed and considered to impose desired connectivity requirements within images such as adding groupsparsity or incorporate total variation terms [23, 24, 25]. Based on achieved experience, we decided to use total variation (TV) as its gradient update is computationally attractive during the backward pass stage.
TV penalizes the generated images with large variations among neighboring pixels, leading to more connected and smoother solutions [24]. Total variation of a differentiable function defined on an interval has the following expression if is Riemannintegrable:
(2) 
Total variation of 1D discrete signals () is straightforward, and can be defined as:
(3) 
where is a matrix as below:
For 2D signals (), we can use isotropic or anisotropic versions of 2D total variation [23]. To simplify our optimization problem, we have used the anisotropic version of TV, which is defined as the sum of horizontal and vertical gradients at each pixel:
(4) 
In our case we can add the total variation of the predicted binary mask for COVID19 pixels to the loss function. Adding this 2DTV regularization term to our framework will promote the connectivity of the produced segmentation regions. The new loss function for our model would then be defined as:
(5) 
where is the binary crossentropy loss, which is similar to the sum of crossentropy on all pixels, and defined above.
Iii COVID CT Segmentation Dataset
We have used the COVID19 CT segmentation dataset [28], which contains two versions. The first version of this dataset contains 100 images from 40 patients, which are all labeled as COVID19 class. This dataset has three types of ground truth masks, which are called Ground Glass, Consolidation and Pleural Effusion. The original CT images and all ground truth masks have a size of 512 x 512. The second version of the dataset was expanded to 829 images (from 9 patients) in which 373 of those are labeled as COVID19 and the rest as normal. All ground truth masks as COVID19 have Ground Glass mask but majority of them are missing the latter two. The size of images and masks in the second version of this dataset is 630 x 630. We combined these two versions, which contains a total of 49 people.
Four sample images from this dataset are shown in Figure 3. The images in the first and second rows denote the original images, and their corresponding COVID19 mask, respectively. The images in the first and second columns denote two sample images of normal people, and the images in the third and fourth columns denote two COVID19 images. The white and gray regions in groundtruth masks denote COVID19 regions, while the black pixels denote healthy regions (note that if the mask is entirely black, it means that the given CT image belongs to a healthy person). The red boundary contours are drawn to better show the parts containing COVID19, and are not a part of the original image.
After precise examination of the three types of ground truth masks, and consulting with a boardcertified radiologist, we decided to focus on the Ground Glass mask, and remove the Consolidation and Pleural Effusion masks, as: on one hand very few images have all three types of masks and most of them are missing the latter two, and on the other hand it is verified by our radiologist that the result using only groundglass mask is also acceptable and it can be used to infer the presence of COVID19. Two sample images of COVID19 class with the three types of ground truth masks are shown in Figure 4.
Iiia Training and Test Split
To evaluate the effect of different ground truth masks and the effect of different training/testing set composition, two different splits (of training, validation, and test sets) are selected from this dataset. In split1, we have 729 images (associated with 46 patients) in the train and validation sets, and 200 images (associated with 3 patients) in the test set. In split2, we have 654 images (associated with 35 patients) in the train and validation sets, and 275 images (associated with 14 patients) in the test set. The details of these splits are provided in Table I.
Data  Number of Images in Split1  Number of Images in Split 2 

Training  654  590 
Validation  75  64 
Test  200  275 
Total  929  929 
Additionally, a semisupervised COVID19 segmentation dataset (COVIDSemiSeg) recently reported in [17] and [29] was used to compare our TVUnetapproach with other methods. The COVIDSemiSeg dataset consists of two sets. The first one contains 1600 pseudo labels generated by SemiInfNet model and 50 labels by expert physicians. The second set included 50 multiclass labels. There are 48 images to used for performance assessment in both sets.
Iv Experimental Results
In this section we provide a detailed experimental analysis of the proposed segmentation framework, by presenting both qualitative and quantitative results as well as comparing our results with a baseline approach.
Iva Evaluation Metrics
There are several metrics that are used by the research community to measure the performance of segmentation models, including precision, recall, dice coefficient and mean IoU (mIoU). These metrics are also widely used in medical domain, and are defined as below.
Precision is calculated as the ratio of pixels correctly predicted as COVID divided by total pixels predicted as COVID, and is defined as Eq. 6:
(6) 
where TP refers to the true positive (the number of correctly predicted COVID19 cases) and FP refers to the false positive (the number of wrongly predicted COVID19 cases).
Recall is the ratio of pixels correctly predicted as COVID19 divided by total number of actual COVID19 pixels, and is defined as Eq. 7:
(7) 
where TP is false positiv, and FN refers to the false negative and is the number of pixels mistakenly predicted as nonCOVID.
Precision and Recall are widely used in medical domain, and to get a big picture of model performance usually a paired version of them is used. PrecisionRecall (PR) curve is popular way to look at the model performance holistically, which is a plot of the precision (yaxis) versus the recall (xaxis) rates for different thresholds.
Dice Coefficient (also known as Dice score, or DSC) is another popular metric especially for the multiclass image segmentation. The dice score is defined as Eq. 8:
(8) 
where A and B denote the predicted and groundtruth masks.
Intersection over Union
(also known as Jaccard index) is another popular metric used to evaluate the similarity between ground truth and predicted segmentation masks. It is defined as the size of the intersection divided by the size of the union of the target mask and predicted segmentation map (Eq.
9).(9) 
where A and B are predicted and groundtruth masks. If A and B are both empty, IoU(A,B) is defined as 1. IoU ranges between 0 and 1. MeanIoU is the average IoU values over all classes. It is worth mentioning that Dice coefficient and IoU are positively correlated.
IvB Model Hyperparameters
Hyperparameters are very important, and it is crucial to properly tune their values during the training of machine learning models to achieve good performance, especially in the case of deep neural networks. Hyperparameter tuning can be done in two different ways, automatically and manually. In this work, we manually evaluated few different combinations of hyperparameters and selected the best combination. To simplify the tuning process, we fixed the number of epochs to 100, and the batchsize to 32. We designed and compared different loss functions (such as binary cross entropy (BCE), dice coefficient loss, and BCE plus total variation regularization), different optimizers (such as ADAM, Adagrad, Adadelta and stochastic gradient descent (SGD)), and different learning rates. We used adaptive learning rate scheduling and early stopping criteria as below, which achieved reasonable performance on the validation set:

Learning rate is decayed whenever the validation loss does not improve for 5 continues epochs.

Early stopping is applied whenever the validation loss does not improve for 10 subsequent epochs.
Table II shows the impact of the loss function design on the model performance with binary cross entropy and the proposed connectivity regularized loss function achieving the best performance.
Loss  Optimizer  Learning Rate  mIOU  DSC  Average Precision 

BCE  0.993  0.839  0.92  
BCE+DSC  0.993  0.843  0.91  
BCE+DSC+TV  ADAM  0.001  0.988  0.645  0.91 
BCE+TV  0.995  0.864  0.94 
The impact of the optimizer on the model performance is shown in Table III. As we can see, ADAM achieves the highest performance in terms of all metrics.
Loss  Optimizer  Learning Rate  mIOU  DSC  Average Precision 

ADAM  0.995  0.864  0.94  
SGD  0.985  0.573  0.8  
BCE+TV  Adadelta  0.001  0.991  0.780  0.9 
Adagrad  0.992  0.784  0.9 
Table IV provides the analysis of model performance for two different learning rate values when using (the best performing) ADAM optimization.
Loss  Optimizer  Learning Rate  mIOU  DSC  Average Precision 

0.001  0.995  0.864  0.94  
BCE+TV  ADAM  
0.0001  0.993  0.838  0.92 
Note that the model predicts a probability for each pixel, showing the likelihood of it belonging to the pathologic COVID19 region (zero denotes NonCOVID pixels and one denotes COVID19 pathology). These probabilities are thresholded, different thresholds yield certain sensitivit/specificity rates. Threshold value of 0.3 achieved the best performance on the validation set and was therefore used to report the results of the proposed model. The impact of modifying the threshold values on the model accuracy is given in Section
IVD.IvC Predicted Masks
Qualitative result showing how close our predicted masks are to the groundtruth masks are given in Figure 5 for 5 sample images from the test set. As can be seen when the desired region is very tiny, the conventional UNet model (finetuned on our dataset) cannot distinguish the segmentation region and background very well, while the proposed TVUNet model performs notably better.
IvD Cutoff Threshold Impact on Model Performance
As discussed previously, our model predicts a probability score for each pixel, showing the likelihood of its being in COVID19 pathology region. Different cutoff thresholds can be used on those probabilities to decide COVID19 labeling. By increasing the cutoff threshold, less and less pixels would be labeled as COVID19 pathology. Tables V and VI show the model performance (in terms of precision, recall, and mIoU) for eight different values of cutoff thresholds for Split1 and Split2 datasets. The cutoff threshold of 0.3 results in the highest Dice score, and mIoU metric, and therefore was employed to compare our model with other baseline models.
Threshold  Recall  Precision  mIoU  DSC 

0.1  0.955 0.028  0.736  0.992  0.831 
0.2  0.913 0.039  0. 811  0.994  0.859 
0.3  0.867 0.047  0. 859  0.994  0.863 
0.4  0.813 0.054  0. 900  0.994  0.854 
0.5  0.746 0.060  0. 933  0.993  0.829 
0.6  0.662 0.065  0. 959  0.992  0.783 
0.7  0.547 0.089  0. 978  0.990  0.702 
0.8  0.362 0.066  0. 990  0.986  0.531 
Precision, recall, Dice score, and mIoU rates of TVUnet model for different threshold values for Split 1. Confidence intervals provided for recall metric. Best performance shown in bold font.
Threshold  Recall  Precision  mIoU  DSC 
0.1  0.892  0.626  0.987  0.7363 
0.2  0.833  0.700  0.989  0.7609 
0.3  0.781  0.750  0.990  0.7643 
0.4  0.730  0.789  0.990  0.7582 
0.5  0.674  0.825  0.990  0.7413 
0.6  0.610  0.859  0.990  0.7139 
0.7  0.535  0.890  0.989  0.6692 
0.8  0.422  0.926  0.987  0.5801 
To see the holistic view of the proposed model performance on all possible threshold values, Figures 6 and 7 provide the precisionrecall curves on the test sets in Split 1 and Split 2, respectively. Figure 6 shows average precision of 0.92 for the conventional UNet and 0.94 for our TVUNet for Split 1 dataset (an improvement of around 0.02 in terms of Averageprecision). Figure 7 shows average precision of 0.67 for the conventional UNet and 0.88 for our TVUNet for Split 2, a relative improvement of 31%.
IvE Model Performance Comparison with Finetuned UNet
For a fair comparison between the proposed TVUnet model and the conventional finetuned UNet model, corresponding cutoff thresholds were identified for similar recall rates for each model and compared in terms of other performance metrics. Tables VII and VIII provide the comparison between these two models for four different recall rates. Consistency of our TVUNet model outperforms that of the finetuned UNet model when considering all metrics, showing the added value of the connectivitypromoting regularization. We have an average improvement of around 2% in terms of Dice score in Split 1 and 10.9% in Split 2 studies.
Model  Recall  Precision  mIOU  DSC 

Unet  0.975  0.575  0.985  0.727 
0.945  0.688  0.990  0.798  
0.91  0.765  0.992  0.832  
0.85  0.834  0.993  0.841  
TVUnet  0.975  0.675  0.990  0.798 
0.945  0.760  0.993  0.842  
0.91  0.812  0. 994  0.860  
0.85  0.871  0.995  0.864 
Model  Recall  Precision  mIOU  DSC 

Unet  0.810  0.594  0.983  0.655 
0.643  0.621  0.985  0.633  
0.535  0.655  0.985  0.595  
0.422  0.693  0.984  0.527  
TVUnet  0.810  0.727  0.990  0.764 
0.643  0.842  0.990  0.729  
0.535  0.890  0.989  0.670  
0.422  0.926  0.987  0.580 
IvF Comparison With RecentlyReported COVID19 Segmentation Performance
Quantitative analysis of COVID19 segmentation performance on CT images is beginning to appear in publications of others. One such recent model is InfNet [17], in which reverse attention mechanism is used in an encoderdecoder based model for COVID19 segmentation. This work is trained on COVIDSemiSeg dataset, that was explained in section III, and tested on a subset of the first version of COVIDCTsegmentation dataset. Therefore, for the comparisons in this section our model is trained on COVIDSemiSeg dataset, to have a fair model evaluation setting.
Here we compare the proposed TVUNet model, with the InfNet, and a few promising image segmentation models trained on COVIDSemiSeg dataset, including UNet++ [20], SemiInfNet [17], DeepLabv3 [21], FCN8s [22], and SemiInfNet+FCN8s [17].
Tables IX, X and XI provide the performance comparisons in terms of recall and Dice coefficient, in different settings. As it can be seen from these tables, the proposed TVUNet model achieves very promising results, outperforming other models in two out of three experiments.
Model  Recall  DSC 

UNet++  0.672  0.518 
InfNet  0.692  0.682 
SemiInfNet  0.725  0.739 
TVUNet  0.834  0.800 
Model  Recall  DSC 

DeepLabv3+ (stride=8) 
0.478  0.375 
DeepLabv3+ (stride=16)  0.713  0.433 
FCN8s  0.537  0.471 
SemiInfNet+FCN8s  0.720  0.646 
TVUnet  0.642  0.520 
Model  Recall  DSC 

DeepLabv3+ (stride=8)  0.120  0.117 
DeepLabv3+ (stride=16)  0.245  0.188 
FCN8s  0.212  0.221 
SemiInfNet+FCN8s  0.186  0.238 
TVUNet  0.499  0.465 
IvG Training Convergence Analysis
V Conclusion
A novel deep learning framework for COVID19 segmentation from CT images was reported. We used the popular UNet architecture as the main framework, and improved its performance by an added connectivity promoting regularization term, to encourage the model to generate larger contiguous connected segmentation maps. We showed that the trained model is able to achieve a reasonably high accuracy rate, for detecting of pathologic COVID19 regions. We report the model performance under various hyperparameter settings, which can be helpful for future research by the community to know the impact of different parameters on the final results. We will further extend this work to semisupervised setting, in which a combination of labeled and unlabeled data will be used for training the model. Such an approach will undoubtedly be extremely useful as collecting accurate segmentation labels for COVID19 remains very challenging.
Acknowledgment
The authors would like to thank our radiologist, Doctor Ghazaleh Soufi, for her advice on the important signals in chest CT images for detecting COVID19. We would also like to thank the providers of the publicly available pulmonary CT datasets. M. Sonka’s research effort supported, in part, by NIH grant R01EB004640.
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