Coronavirus disease 2019 or COVID-19 had become a worldwide pandemic and caused great public health problems [1] [2] [3] . COVID-19 cases can be divided into light, moderate, severe, and extremely severe types from physicians' perspective. Patients of the latter two types exhibited to have a higher intensive care unit (ICU) rates as well as the death rates [4, 5] compared with the other two types. It is therefore essential to identify severe and extremely severe patients as early as possible.
In the Diagnosis and Treatment Protocol for COVID-19 (version 7) [6] released by National Health Commission of China, the clinical characteristics of severe cases include: the decreased lymphocyte count, increased level of inflammatory factors, and rapid development of volume for infected regions on CT images. One patient should be classified and treated as severe case if the volume of infected region would be increased more than 50% within 48 hours. Therefore, continuously monitoring the volume of infected regions may provide valid evidence to predict the prognosis for COVID-19 patients.
However, with infected regions in the lung, the Hounsfiled Unit (HU) value of the lesion regions would be difficult to distinguish with healthy tissues. The infected regions may illustrate as a mist of blur-edged cloud or adhere together with normal tissues on CT images. It would be effort costly for a professional radiologist or physician to separate these lesion regions from healthy lung parenchyma. Furthermore, a set of CT images usually consisted of dozens or hundreds of lung images, which made it almost impossible to analyze the lesion regions quantitatively over the images manually. Therefore, it was urgent to find out an automatic method to estimate the proportion of infected region of lung for COVID-19 from chest CT scans.
To date, several researches had concentrated on the deep learning based models for diagnosing COVID-19. Some studies [7] [8] [9] [10] demonstrated that COVID-19 can be distinguished from other types of pneumonia with good accuracy. Compared with the classifications models, the annotation of CT image samples is highly significant and much more time-consuming in the training of segmentation models for the intact lung as well as infected regions. Shan et al. [11] adopted the human-in-the-loop strategy to iteratively update the annotation of their training samples. Liu et al. [12] synthesized part of their training and test dataset with Generative Adversarial Network (GAN). They achieved 0.706 measured in mean Dice similarity coefficient (m-Dice) for the segmentation of infected regions and 0.961 (Pearson correlation coefficient) for the total percent volume of lung parenchyma that was affected by disease. Ma et al. [13] annotated 20 sets of COVID-19 CT images and utilized previous available lung dataset such as lung cancer to assist the segmentation. Yan et al. [14] also investigated the segmentation of infected regions due to COVID-19. They employed a team of six annotators with deep radiology background and proficient annotating skills to label the areas and boundaries of the intact lung and infection regions due to COVID-19. A feature variation block in the segmentation of infected regions was introduced, which could better differentiate the diseased area from the lung. Furthermore, they used the more effective progressive atrous spatial pyramid pooling in the feature extraction stage as well. The optimum m-Dice achieved in their studies for entire lung and infected regions were 0.987 and 0.726 respectively. These studies suffered from the tremendous effort to label the training samples as well as the relatively low accuracy measured in m-Dice.
In this study, we try to establish a fully automatic deep learning system to estimate the physical proportion of infected region of lung for COVID-19 pneumonia with CT image set. The main contribution of this paper can be summarized as:
First, the HU value of CT images was utilized as threshold to generate the initial "dirty" version of labeled masks for both intact lung and infected regions. These first round labeled samples significantly alleviated the labor expenses of annotation compared with start from scratch.
Then these preliminary samples were revised and improved by two professional radiologists to generate the final training set and test benchmark.
Second, it was observed from our experiment that a certain number of blur-edged healthy structures, which had similar appearance as infected regions, were likely to be identified incorrectly. These kind of healthy tissues included air tube, blood vessel, and blur region of lung at the border etc. Therefore, a deep learning based classifier was employed to further clarify candidate regions that could effectively increase the accuracy of the final segmentation results. In addition, the proposed classifier was much easier to be trained compared with pixel-level segmentation models. Figure 2 showed the whole diagnostic process of COVID-19 report generation in this study.
As the digital gray scale image had the pixel value ranging [0, 255], the raw data of CT were converted from HU to the aforementioned values interval accordingly. The HU data matrix was clipped within [-1200, 600] (any value beyond this was set to -1200 or 600 accordingly) and then linearly normalized to [0, 255] to fit into the digital image format for further processing. Next, the infected regions and the intact lung were segmented separately to achieve corresponding masks.
For the differentiating of infected regions, a deep learning based classifier was utilized to remove unrelated masks that were wrongly distinguished. Finally, the volumes of two parts were calculated according to the masks achieved in above-mentioned steps, and achieve the proportion of infected regions in lung. 
The performance of the proposed method was evaluated using the Dice similarity coefficient (Dice), measuring the similarity between the ground truth and the prediction score maps. It is calculated as follows:
where A is the volume of the segmented lesion region and B denotes the ground truth. The mean Dice (m-Dice) of the whole test benchmark was used to evaluate the final outcomes. Two ground truth masks were used in this study: ground truth for intact lung and ground truth for infected regions. The proportion of infected regions of lung (PoIR) was given by:
Pearson's correlation coefficient was used to evaluate the correlation of two variables:
where N is the total number of observations, xi and yi , i=1, ..., N, are observational variables. We used Pearson's correlation coefficient to calculate the correlation between predicted PoIRs and the corresponding value derived from ground truth. Furthermore, mean absolute percent error (m-APE) , which is a assessing of prediction accuracy of a forecasting method, was herein used to measure the relative errors between the mean predicted PoIRs and the ground truth value on the test benchmark.
The most straightforward way to segment desired lung regions was by aid of the value of HU as the threshold, which reflects the degree of X-ray absorption of different tissues. For instance, the HU value for lung parenchyma usually ranges from -800 to -500 and window of other soft tissue is from +100 to +300. This margin usually is solid enough to separate lung with other tissues. However, when there existed infected regions in lung, the HU value of lung parenchyma could extended to from -750 to 150 (based on our statistics on test benchmark in Fig 3) . Therefore, the segmentation result with the threshold of HU usually is not typically accurate enough for clinical application. Alternatively, these labeled images could be used as the initial annotated samples in our study. 
As mentioned earlier, use of HU threshold cannot properly segmented the intact lung and infected regions. Those infected regions that had a close HU value with other soft tissues cannot be correctly differentiated. Therefore, deep learning techniques were utilized and evaluated in current study.
Training samples with detailed sketch of each infected region and intact lung are highly essential for developing the deep learning models. However, due to ambiguous edge between infected region and normal tissue, it was extremely timing-consuming to annotate thousands of lung CT images. The annotation result achieved by HU threshold was utilized for the preliminary samples. Then, two professional radiologists further manually contoured the intact lung and infected region based on the these "dirty" samples to generate final sample dataset for training and test.
Two deep learning models were utilized: 2D UNet [15] (Fig. 5 ) and 2.5D UNet (Fig. 6) . A two-dimensional (2D) deep learning models can well reflect the intra-slice information. However, they may neglect the inter-slice information and cannot fully leverage the spatial architecture of the three-dimensional (3D) slices of CT scans. On the other hand, 3D models [16, 17] suffer from tremendous increased parameters and the subsequent of hard to converge and overfitting especially for a limited number of training samples. Furthermore, due to the limitation of GPU memory, the original CT images had to be cropped or resized to small-sized cubes as the input for deep learning models. This crop or resize operation would either restrict the maximum inception regions or attenuate the resolution of original CT images. Therefore, a pseudo-3D segmentation or so called 2.5D UNet [18, 19] was used for evaluation purposes, in which the same UNet backbone (with expanded of network parameters) was used. In addition, three neighboring 2D slices were stacked as the inputs during training, so that the 2D network was able to detect a small range of 
It was observed that a certain number of blue-edged healthy structures, which had similar appearance as infected regions, were likely to be identified incorrectly. These kind of healthy tissues included air tube, blood vessel, and blur region of lung at the border etc as shown in Fig 7. (a) Therefore, a ResNet-18 [20] based binary classifier (Fig. 8) , was utilized after the segmentation models to further clarify whether an image patch belonged to infected regions or not.
The masks corresponding to healthy regions were filtered. respectively. The accuracy of m-Dice significantly decreased as many unrelated regions, e.g.
stomach, were wrongly segmented as lung when the threshold of HU was set to below -150. 
UNet and 2.5D UNet were utilized in the present study. For regions with light opacity, the threshold of HU along could achieve satisfactory segmentation results. However, for regions with high opacity, deep learning models could achieve obviously superior results. The m-Dice of UNet and 2.5D UNet of intact lung were 0.972 and 0.967, respectively. There was no significant difference between the two deep learning models. 
The same UNet and 2.5D UNet deep learning models were evaluated. The m-Dice of UNet and 2.5D UNet for infected regions were 0.684 and 0.693, respectively. The latter model further concentrated on the inter-slice characteristics and demonstrated 1.3% improvement on the results.
It was observed that most of the infected regions could be included in the output of the segmented masks. However, many blur-edged normal tissues were wrongly detected as infected regions, including air tube, blood vessel, stomach, and part of the border of lung etc. Therefore, a classifier was followed to further remove those unrelated regions.
The receiver operating characteristic curve (ROC) for the ResNet-18 based classifier was depicted in Figure 11 . Fig. 12 and Table 1 . Table 1 . Summarized m-Dice between predicted masks and the measurement derived from ground truth of our test benchmark.
With the aid of the masks of the intact lung and infected regions, the Pearson's correlation coefficient of the PoIRs could be achieved (0.961), which showed a very strong correlation between the predicted masks and those derived from ground truth. Furthermore, the m-APE of the PoIRs on test benchmark also could be obtained (11.7%), which indicated that the average relative errors between predicted PoIRs and the ground truth value was a lightly more than 10%.
With the rapid development of artificial intelligence technology, experiences of profession radiologists, such as the segmentation of medical images, could be solidified in the deep learning models to accomplish a quantitative analysis report. Several methods were developed to investigate the segmentation of intact lung and infected regions, including the threshold of HU, UNet, and 2.5D UNet. In addition, a fine-tuned classifier was followed to further remove those wrongly segmented healthy regions to improve the accuracy of outputs. We referred to the methodology of the design of nnUNet [21] , which had achieved good results in many different medical segmentation tasks. They suggested that if the objected data is very anisotropic then a 2D
UNet may actually be a better choice. For example, in the segmentation of pancreas, which was a blur-edged objective on the images as well, 2D network actually outperformed 3D counterparts.
As a matter of fact, the most challenge work in the calculation of the proportion of infected regions was the annotation of images, especially for the regions that affected by pneumonia. We utilize the intrinsic HU value of CT images to create the initial version of label images. Even though they were dirty samples, it would be much less effort for professional radiologist to further modify and improve on this first round version. Furthermore, the annotation of samples and the training of a fine-tuned binary classifier were much easier than the pixel-level of segmentation.
Compared with direct result of the state-of-the-art segmentation algorithm, the classifier could improve the m-Dice of infected regions around 9%.
For the calculation of proportion of infected regions, the Pearson's correlation coefficient between predicted and the ground truth showed a strong correlation between them, which would be one of an objective indicator for monitoring the progress of one patient at a fixed interval.
Furthermore, the m-APE showed promising outcomes for the reference for the decision of clinical physicians.
In the future, doctors can carry out quantitative analysis of the severity of COVID-19 patients with this model or combined with other clinical data such as blood oxygenation index. At the same time, they can compare the sequential CT scans of the same case to predict the prognosis and provide reliable basis for treatment.
However, this study had several limitations. In some cases, the segmentation models would possible identify healthy tissues together with valid infected regions and the following classifier could not remove this "valid" infected regions. Therefore, the corresponding mask in such scenario would be larger than the ground truth. Moreover, additional COVID-19 CT cases from different subtypes should be included to promote the accuracy of segmentation and classification.
Some atypical infection signs, such as pleural effusions, cannot be distinguished with this model.