Multi-class semantic segmentation of breast tissues from MRI images using U-Net based on Haar wavelet pooling

Multi-class semantic segmentation of breast tissues from MRI images using U-Net based on Haar wavelet pooling | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Multi-class semantic segmentation of breast tissues from MRI images using U-Net based on Haar wavelet pooling Kwang Bin Yang, Jinwon Lee, Jeongsam Yang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2465906/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 20 Jul, 2023 Read the published version in Scientific Reports → Version 1 posted 11 You are reading this latest preprint version Abstract MRI images for breast cancer diagnosis are inappropriate for reconstructing the natural breast shape in a standing position because they are taken in a lying position. Some studies have proposed methods to present the breast shape in a standing position using ordinary differential equation of the finite element method. However, it is difficult to obtain meaningful results because breast tissues have different elastic moduli. This study proposed a multi-class semantic segmentation method for breast tissues to reconstruct breast shape using U-Net based on Haar wavelet pooling. First, a dataset was constructed by labeling the skin, fat, and fibro-glandular tissues and the background from MRI images taken in a lying position. Next, multi-class semantic segmentation was performed using U-Net based on Haar wavelet pooling to improve the segmentation accuracy for breast tissues. The U-Net based on Haar wavelet pooling effectively extracted breast tissue features while reducing information loss of the image in a subsampling stage using multiple sub-bands. In addition, the proposed network is robust to overfitting. The proposed network showed an mIOU of 87.48 for segmenting breast tissues. The proposed networks showed high-accuracy segmentation for breast tissue with different elastic moduli to reconstruct the natural breast shape. Biological sciences/Cancer/Breast cancer Biological sciences/Cancer/Cancer imaging Physical sciences/Engineering/Electrical and electronic engineering Breast shape reconstruction Multi-class semantic segmentation Discrete wavelet transform U-Net semantic segmentation Wavelet U-Net Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 1. Introduction The International Agency for Research on Cancer has reported that breast cancer is one of the most prevalent cancers worldwide, accounting for 11.7% of all cancer cases 1 . Due to increasing incidence of breast cancer, the demand for breast reconstruction surgery is also continuously increasing owing to breast removal. In the preparation stage for breast reconstruction surgery, a natural breast shape in a standing position is necessary before mastectomy. However, plastic surgeons can access only magnetic resonance imaging (MRI) or computed tomography (CT) images taken with patient lying in a prone position during the examination process. Consequently, they are limited in producing a natural-shaped breast implant in the standing position solely from images in a prone position. To overcome this limitation, studies have been conducted on reconstructing breast shapes in the standing position from prone-position MRI images by obtaining an approximate solution through ordinary differential equation of the finite element method for deformations caused by the center of gravity acting on the breast 2,3 . However, it is difficult to obtain meaningful results from these studies for the natural breast shape in a standing position because elastic moduli of breast tissues such as skin, fat, and fibroglandular tissue affected by gravity are different from every other. To address this issue, this study proposed a deep learning network using U-Net based on Haar wavelet pooling to segment breast tissues for reconstructing the breast shape in the standing. To train the deep learning network, we constructed a dataset consisting of background, skin, fat, and fibroglandular tissues from MRI breast images. For labeling of the dataset, the median filter, Otsu’s threshold algorithm, and a template-based segmentation method were utilized. In the subsampling stage of the conventional U-Net, the max pooling is sensitive to overfitting. It may cause a significant error during data segmentation because weak information about the breast tissue is lost. To improve the segmentation accuracy of breast tissues, we utilized the Haar wavelet pooling instead of the max pooling to robust for overfitting. The U-Net based on Haar wavelet pooling simultaneously uses a low-low (LL) sub-band that holds approximate values of the input image and three distinct frequency sub-bands (low-high (LH), high-low (HL), and high-high (HH)) with detailed edge feature information. Therefore, it can effectively extract features of breast tissues by reducing the loss of image information in the subsampling stage. It also implements a deep learning network that is robust to overfitting. To compare performances of the proposed network and other networks described in previous studies for segmenting breast tissues, various experiments with max pooling and average pooling were conducted. The proposed U-Net based on Haar wavelet pooling achieved a mean intersection over union (mIoU) of 87.48, which was higher than those of other methods. 2. Literature Review 2.1. Deep learning-based breast tissue segmentation method Previous studies on breast image analysis have used binary segmentation methods to diagnose breast diseases such as breast cancer and breast tumors 4–6 . However, such methods were time-consuming and labor-intensive because the region of interest (ROI) for the breast tissue was manually set. Moreover, these methods had a disadvantage in that the quality of segmented tissues varied depending on the skill level of the worker and the algorithm used. Recently, various deep learning-based algorithms have been introduced for medical image processing to overcome such disadvantages. Table 1. Comparison of deep learning-based segmentation methods for breast tissues in existing studies. Related study Backbone model Input images # of segment classes including background Segmented tissue Soulami et al. (2021) End-to-End U-Net Mammogram 2 Breast cancer Negi et al. (2020) RDA-U-Net Ultrasound 2 Breast tumor Ilesanmi et al. (2021) VEU-Net 2 Breast tumor Zhang et al. (2019) U-Net MRI 3 Fat, Fibroglandular tissue Zhang et al. (2021) U-Net (Transfer learning) 3 Fat, Fibroglandular tissue Huo et al. (2021) nnU-Net 3 Fat, Fibroglandular tissue Ours Haar wavelet pooling U-Net MRI 4 Skin, Fat, Fibroglandular tissue Table 1 summarizes segmentation methods for breast tissues based on deep learning with MRI breast images used in previous studies. Most deep learning-based networks that segment breast tissues modified the U-Net 7 to perform segmentation for a single class, such as breast cancer, breast tumor, and breast density. To detect breast cancer in digital mammography, Soulami et al. have improved the segmentation performance by proposing a deep learning network based on the end-to-end U-Net method 8 . Further, to segment tumors in breast ultrasound images, Negi et al. have used a deep learning network called RDA-U-Net and the Wasserstein GAN algorithm and reported remarkable performance 9 . Ilesanmi et al. have proposed a variant-enhanced block that combines max pooling and average pooling to segment tumors in breast ultrasound images, consequently improving the accuracy of semantic segmentation for tumors by using the VEU-Net network 10 . Many studies have been conducted to segment fibroglandular tissues known to account for a large proportion of breast tissues using deep learning. Zhang et al. have segmented fat and fibroglandular tissues from MRI breast images using a U-Net 11 . Subsequently, Zhang et al. have improved the segmentation accuracy by performing transfer learning for fat and fibroglandular tissues in a deep learning model that segments breast density of MRI breast images 12 . Huo et al. have improved the segmentation accuracy of fibroglandular tissues by adopting nnU-Net to segment the entire breast and fibroglandular tissues in DCE-MRI breast images 13 . In contrast to most previous studies that used binary segmentation methods, our study performed multi-class semantic segmentation through U-Net based on Haar wavelet pooling to segment various types of breast tissues for breast shape reconstruction. 2.2. Deep learning method based on wavelet pooling for images The wavelet pooling used in the sampling operation of deep learning algorithms has an advantage of decreasing the effect of noise on segmentation by filtering the input image before sampling. Previous studies have conducted various image segmentation tasks by combining wavelet pooling and deep learning 14,15 . Table 2 summarizes improved performances of image classification, segmentation, recognition, and restoration using wavelet pooling-based deep learning in previous studies. Table 2. Comparison of deep learning methods based on wavelet pooling for images. Related study Deep learning purpose Wavelet transform Deep learning type Image dataset 16 Image fusion Discrete wavelet transform CNN COCO 17 Image restoration Multi-level wavelet transform Multi-level wavelet CNN Berkeley segmentation dataset, DIV2K, Waterloo exploration database 18 Image classification Discrete wavelet transform CNN MNIST, CIFAR-10, SHVN, KDEF 19 Super resolution Stationary wavelet transform VDR-Net Brain MRI (IXI-MR dataset) 20 Semantic segmentation Discrete wavelet transform U-Net Brain MRI (MICCAI dataset) 21 Semantic segmentation Multi-scale wavelet transform WU-Net Pediatric echocardiographic (CAMUS dataset) Ours Semantic segmentation Discrete wavelet transform Haar wavelet pooling U-Net Breast MRI (TCIA breast-diagnosis) Previous studies have proposed an unsupervised image fusion algorithm for image restoration and classification that combines a deep learning network with a multi-scale discrete wavelet transform 16–18 . Suryanarayana et al. have converted low-resolution MRI images into high-resolution MRI images by combining VDR-Net with wavelet pooling that uses both low and high frequencies 19 . Alijamaat et al. have combined U-Net with wavelet pooling of low-frequency component (LL band) characterized by high image pixel concentration while maintaining the overall trend of images to improve the segmentation performance for multiple sclerosis of the brain 20 . Zhao et al. have improved the performance of congenital heart disease diagnosis in pediatric echocardiography images by combining low-frequency information of multi-scale wavelet with WU-Net 21 . Existing studies cited above have demonstrated that the combination of wavelet pooling and deep learning algorithms can improve image performance in various applications such as classification, segmentation, recognition, and restoration. This study improve the semantic segmentation performance for breast tissues by combining Haar wavelet pooling with U-Net. In particular, the image output through the high-frequency filter of wavelet pooling can effectively express locations of breast tissues and expression of micro-soft tissues by emphasizing edge features for vertical, horizontal, and diagonal components. Furthermore, characteristics of fine breast tissues are well-preserved because the image output through the low-frequency filter has approximate values of the input image. 3. Design Of Deep Learning Network For Segmentation 3.1. Overview This paper proposed a multi-class semantic segmentation method for breast tissues to reconstruct breast shape in a standing position using U-Net based on Haar wavelet pooling. To train deep learning networks, labeled breast tissue data are necessary. MRI images, which are essential for breast cancer screening, have higher resolution and lower noise than CT or ultrasound images. Moreover, MRI images are effective for representing and segmenting micro-soft tissues such as fat and fibrous granular variants in the breast. Figure 1 shows breast tissue segmentation process based on deep learning network for breast shape reconstruction. In the first step, MRI images in Digital Imaging Communication in Medicine (DICOM) format were collected. In the second step, breast tissues from collected MRI breast images were labelled to build a dataset for training the deep learning network. Labeling steps included removing noise from the MRI image with a median filter using Otsu's threshold algorithm, expanding to all MRI images through the template-based segmentation method based on the segmented tissues, and verifying labels by a radiologist. In the third step, U-Net based on Haar wavelet pooling was designed to segment breast tissues for breast shape reconstruction. To improve the multi-class semantic segmentation performance for MRI breast images, this study combined U-Net with Haar wavelet pooling. The U-Net based on Haar wavelet pooling uses the LL sub-band, which holds approximate value of the input image, and three distinct frequency sub-bands (LH, HL, and HH), which have detailed edge features. Therefore, breast tissue features could be effectively extracted by reducing the loss of image information in the subsampling. The U-Net based on Haar wavelet pooling was trained with constructed datasets and its performance was then tested. 3.2. Building an MRI dataset for breast tissue segmentation A set of data including labels for every pixel of the MRI data is required for breast tissue segmentation with deep learning. In this study, an MRI dataset was collected from the breast-diagnosis database 22 of The Cancer Imaging Archive (TCIA), an open access database for medical images for cancer research. The breast-diagnosis database contains medical images of breast cancer patients as well as cases of breast diagnosis such as high-risk normal, DCIS, fibroids, and lobular carcinomas. Each image was captured with three pulses (T2, STIR, BLISS) using a Phillips 1.5 T MRI system. Breast MRI images of 89 breast cancer patients were obtained at 2 mm intervals at resolutions of 500 to 600 DPI, with 80 to 90 MRI slices per person. This study used MRI slice images of T2-weighted pulse sequences data. Figure 2 shows a step-by-step process of labeling breast tissues from MRI slice images. The breast tissue should be segmented into skin, fat, fibroglandular tissue, and background because the upper part of the pectoral muscle is incised in a mastectomy. As shown Fig. 2 (a), the noise of the slice image was removed using a median filter. Otsu's threshold algorithm was used to segment breast tissues from denoised MRI images. This algorithm could separate the foreground and background by a threshold based on the distribution of pixels in the image. Multiple thresholds were utilized to separate breast tissues with the same pixel distribution value. Figure 2 (b) shows the result of segmenting fibroglandular tissues (yellow region) and the background (light blue region) using Otsu’s threshold algorithm by setting the background and the foreground (fibroglandular tissues). Figure 2 (c) shows result of segmenting fat (green region) and the rest of the breast tissues (red region) through Otsu’s threshold algorithm by setting the background and the foreground (fat, muscle, and chest wall). Figure 2 (d) shows that the background (brown region) and the inside of the human body (green region) are separated through Otsu’s threshold algorithm. Skin data are lost during T2-weighted pulse sequence images. Hence, boundary lines between green and brown regions were offset by pixels with a thickness of 2 mm that matched the thickness of the human body's skin and the result was used as skin data. These segmented skin data were validated through BLISS MRI images of breast cancer patients. In this process, breast-diagnosis cases such as fibroma and breast cancer were recognized and segmented as fibroglandular tissues because they were diseases expanded by the action of hormones on mammary glands. As shown in Fig. 2 (f), breast tissues obtained in the previous step were integrated. Light blue, blue, green, and yellow regions represented the background, skin, fat, and fibroglandular tissues, respectively. In order to reduce the manual labeling of breast tissues, we used template-based segmentation. Template-based segmentation expands with a single MRI slice as a reference template for the remaining other MRI slices. It can extract individual breast tissue features after analyzing each tissue's location, size, shape, and pixel distribution values with MRI slice of a cross-section into which breast tissues are segmented and set as a reference template. The full MRI image in which breast tissues are finally segmented can be obtained by extracting breast tissues with similar characteristics from consecutive MRI slices. Figure 3 shows the process of segmenting the entire MRI slice image through template-based segmentation. T2-weighted pulse sequence data that were input for breast tissue segmentation and the segmented breast tissue are output at 800 × 800 DPI resolution. These labeled data with template-based segmentation were validated by a radiologist. 3.3. Designing U-Net based on Haar wavelet pooling This study proposed a U-Net based on Haar wavelet pooling in the subsampling stage. The wavelet transform, which has information on the spatial domain and the frequency domain, is expressed as a vibration with an average of zero that vibrates while repeating increase and decrease within a preset time. Wavelet transform can effectively detect sudden signal changes because it describes regional features and provides signal analysis at different scales and levels. The wavelet transform for a signal \(x\left(t\right)\) is defined by Eq. (1) 23 : $${W}_{a}x\left(b\right)= \frac{1}{\sqrt{a}}\underset{-{\infty }}{\overset{+{\infty }}{\int }}x\left(t\right){\varPsi }^{*}\left(\frac{t-b}{a}\right)dt a>0$$ 1 where \(a\) is the parameter for scale change, \(b\) is the displacement rate, and \({\varPsi }^{\text{*}}\left(t\right)\) is a continuous basis function called mother wavelet. In this study, a two-dimensional (2D) discrete Haar wavelet transform that could minimize the amount of computation when converting MRI breast images in the deep learning network was used. The 2D-wavelet transform presents the input image as a matrix of two-dimensional signals based on the brightness of pixels. Data passing through the 2D-wavelet transform were divided into four bands according to the applied filter. Figure 4 shows the structure of wavelet pooling. Wavelet pooling passed through two steps. Input data were decomposed through a high pass filter and a low pass filter at each step. The size of the input data was reduced because down-sampling was performed in each step. In the first step of wavelet pooling, the input image was horizontally separated into low (L), which was a low-frequency component, and high (H), which was a high-frequency component by applying the horizontal filter. In this process, the approximate value of the input image was decomposed for the low-frequency component and the detailed value was decomposed for the high-frequency component. In the second step where the vertical filter was applied, images of low- and high-frequency components were vertically separated again and decomposed into four sets of data: LL, LH, HL, and HH bands. Resolutions of data in all bands were reduced to half the resolution of the input data. Data of the LL band had a low-frequency component, indicating the overall trend data of the input data. Data of LH, HL, and HH bands had edge features for vertical, horizontal, and diagonal components, respectively. The segmentation performance can be improved because decomposed data can represent various features such as micro breast tissues. U-Net consists of a contracting path that extracts features from the training data and an expansive path for restoring the original resolution. The contracting path performs down-sampling by setting the stride size of the convolution to two in each step, whereas the expansive path performs up-sampling using transposed convolution. The max pooling in the subsampling stage used in previous studies was difficult to generalize because it was sensitive to overfitting of the dataset 24 . Although some studies have attempted to solve the vanishing gradient problem by passing the information in the contraction path to the expansive path through a skip connection, overfitting still occurs 25 . Breast tissues are delicate data linked by small pixels. Therefore, if max pooling is used, information on the breast tissues might be lost. This study designed a deep learning network of the U-Net architecture based on Haar wavelet pooling for subsampling to segment breast tissues. Figure 5 shows the deep learning network architecture that combines Haar wavelet pooling with U-Net. The deep learning network was composed of 12 convolution layers, 5 Haar wavelet pooling layers, and 5 inverse wavelet-based up-sampling layers. Input breast image data were converted into LL, LH, HL, and HH band data by Haar wavelet pooling. These converted data were then transmitted to the convolution layer. The resolution was restored using an inverse wavelet, which could reconstruct data using the output value of wavelet pooling. In the proposed architecture, a batch normalization function and a ReLU activation function were used with each convolution layer. The amount of computation for the network was reduced compared with previous studies by applying the Haar wavelet pooling. The number of existing channels was maintained because the pooling result did not affect the number of channels in the deep learning network. However, the number of input channels of the convolution layer was increased by a factor of four because the U-Net based on Haar wavelet pooling simultaneously used LL, LH, HL, and HH bands. 4. System Implementation And Experimental Evaluation 4.1. Implementation environment Table 3 shows the implementation environment for building the U-Net based on wavelet pooling. The U-Net was executed on Ubuntu Linux. It was implemented in Python using Anaconda, a math and science library, PyTorch, a deep learning library, and CUDA and CuDNN for GPU operation. Table 3 Implementation environment. Item Usage Version Ubuntu Operating system 16.04.5 LTS-64bit Python Development language 3.8.12 Anaconda Math and science library 4.10.1 PyTorch Deep learning library 1.10.0 CUDA GPU parallel computing library 11.3 CuDNN GPU-accelerated library 8.2.4 Two units of NVIDIA Quadro RTX 5000 16G were interconnected for distributed data parallel processing for deep learning operations. The interface module was implemented with the DistributedDataParallel library provided by PyTorch to synchronize IDs of GPU operation processes performed on two graphic cards. 4.2. Experiment and evaluation Segmentation accuracies for background, skin, fat, and fibroglandular tissues were analyzed to evaluate the performance of the U-Net based on Haar wavelet pooling. The dataset of 5,202 images was divided into a training dataset, a validation dataset, and a test dataset at a ratio of 8:1:1. These data were rotated at a random angle for augmentation of the dataset in the deep learning network training process. Multi-class semantic segmentation was performed using the U-Net based on Haar wavelet pooling. The resolution of the training data was set to be 800 × 800 DPI, with batch size of 8, epoch of 200, and learning rate of 0.002. Furthermore, focal loss and adaptive moment estimation optimizer (Adam) were applied. The loss function was compared with cross entropy, dice loss, and focal loss to find the optimal parameter. Max pooling, average pooling, and Haar wavelet pooling were applied in this experiment to prove the effectiveness of Haar wavelet pooling with subsampling. The segmentation performance was measured using Intersection over Union (IoU) commonly used as a performance evaluation index for segmentation, mIoU (the average of all IoU values), and pixel accuracy. Equations for IoU (2), mIoU (3), and pixel accuracy (4) are shown as follows: \(IOU= \frac{TP}{TP+FP+FN}\) (2) \(mIOU= \frac{1}{k}{\sum }_{i=0}^{k}\frac{TP}{TP+FP+FN}\) (3) \(pixel accuracy= \frac{TP+TN}{TP+TN+FP+FN}\) (4) where TP, TN, FP, FN, and k represent true positive, true negative, false positive, false negative, and the number of classes, respectively. Table 4 shows IoU, mIoU, and pixel accuracy results for background, skin, fat, and fibroglandular tissues of the test dataset. Haar wavelet pooling showed higher breast tissue segmentation performance than max pooling and average pooling in the same experimental environment. Furthermore, the deep learning network using focal loss and Haar wavelet pooling showed the highest mIoU and pixel accuracy values. The deep learning network using focal loss and Haar wavelet pooling confirmed that segmentation accuracies for skin and fibroglandular tissues were relatively high. This is because deep learning networks can be trained effectively because Haar wavelet pooling can reduce the influence of easy negative examples such as background and fat while focusing on training hard negative examples such as skin and fibroglandular tissues. By contrast, the deep learning network using both dice loss and average pooling showed low segmentation performance. Table 4 Experimental results obtained with a combination of training parameters of the deep learning network for breast tissue segmentation. Pooling method Loss function Background IoU (%) Skin IoU (%) Fat IoU (%) Fibroglandular tissue IoU (%) mIoU (%) Pixel accuracy (%) Max pooling Cross entropy 98.78 75.44 94.62 76.28 86.28 99.29 Average pooling Cross entropy 98.39 70.03 93.88 73.15 83.86 99.12 Haar wavelet Pooling Cross entropy 98.80 75.37 94.70 77.66 86.63 99.31 Max pooling Dice loss 98.62 72.07 94.17 75.52 85.09 99.20 Average pooling Dice loss 98.40 74.65 93.84 63.94 82.71 98.78 Haar wavelet pooling Dice loss 98.77 73.63 94.79 76.20 85.85 99.29 Max pooling Focal loss 98.90 76.57 94.78 78.58 87.21 99.34 Average pooling Focal loss 98.85 75.47 94.38 73.79 85.62 99.29 Haar wavelet pooling Focal loss 98.90 77.14 94.81 79.06 87.48 99.35 Table 5 Comparison of complexity, segmentation accuracy, and pixel accuracy values of deep learning networks. Method # of params (million) Background IoU (%) Skin IoU (%) Fat IoU (%) Fibroglandular tissue IoU (%) mIoU (%) Pixel accuracy (%) U-Net 31.04 98.85 74.34 94.20 76.46 85.96 99.28 End-to-End U-Net 27.91 98.85 74.16 93.66 71.99 84.67 99.23 RDA-U-Net 18.85 98.61 75.71 93.89 68.90 84.28 99.19 VEU-Net 14.22 98.63 74.43 94.03 69.77 84.21 99.04 nnU-Net 47.88 98.86 73.00 94.78 78.65 86.32 99.31 LL wavelet U-Net 21.98 97.00 68.30 90.75 43.67 74.95 98.54 Ours 24.28 98.90 77.14 94.81 79.06 87.48 99.35 Table 5 compares results of breast tissue segmentation accuracy between the proposed network and previous studies. The IoU, mIoU, and pixel accuracy values for background, skin, fat, and fibroglandular tissues were measured in this experiment. The U-Net based on Haar wavelet pooling achieved an mIoU of 87.48 and a pixel accuracy of 99.35% for breast tissue segmentation. The segmentation accuracy for these breast tissues showed a significant performance improvement of 1–2%p compared to a previous study 26 . In particular, the U-Net based on Haar wavelet pooling achieved a very high segmentation accuracy for skin and fibroglandular tissues with a small number of parameters. 4.3. Verification of segmentation results through visualization Figure 6 shows original MRI images of three patients (A, B, and C) with different breast shapes and fibroglandular tissue densities in the test dataset and images of breast tissues segmented by the proposed network. The top of Fig. 6 depicts the original MRI images and the bottom shows breast tissue images segmented using the proposed network. Black, blue, green, and yellow indicates the background, skin, fat, fibroglandular tissues, respectively. For Patient A, a small breast shape and a high density of fibroglandular tissues were observed. Patient B was characterized by a medium-sized breast shape and low-density fibroglandular tissues close to the chest wall muscle. Patient C, with a large breast shape, was characterized by moderately dense fibroglandular tissues. These results showed that the proposed network could effectively segment skin, fat, and fibroglandular tissues even when MRI images with different breast shapes and fibroglandular tissue densities were used as input. Figure 7 shows MRI images and segmentation results for two patients. Figure 7 (A) shows the 69th patient out of 89 patients, with an mIoU of 90.28. Figure 7 (B) shows an MRI image of the 58th patient with an mIoU of 77.94. In rectangle areas of Fig. 7 (A3) and Fig. 7 (B3), the fibroglandular tissue of Patient A had a higher density than that of Patient B. As for Patient B with a low density of fibroglandular tissues, the mIoU of the segmented breast tissue was lower than that of Patient A with a high density of fibroglandular tissues. This observation indicated that the U-Net based on Haar wavelet pooling could effectively segment breast images of women with a high density of fibroglandular tissues. Figure 8 visualizes the ground truth image and the segmented breast tissue image with U-Net, nnU-Net, and U-Net based on Haar wavelet pooling. The rectangle area indicated that the U-Net based on Haar wavelet pooling segmented breast tissues more accurately than U-Net and nnU-Net. By contrast, in Fig. 8 (b), the outside of the background was misrecognized as skin tissue and the inside as fibroglandular tissue and fat owing to the noise of the background. When Fig. 8 (b) showing an image of breast tissue segmented through nnU-Net was compared with the ground truth, the background was incorrectly segmented into fibroglandular tissue, skin, and fat because of the noise inside the background. These results showed that the proposed network could distinguish the noise of the input image and the breast tissue more accurately than methods described in previous studies and accurately segment delicate soft tissues and skin of the mammary gland. 5. Conclusion Recently, deep learning networks with excellent performance have been introduced in various studies for medical image segmentation. Many methods have been proposed for segmenting breast tissues using binary-image segmentation to diagnose breast diseases such as breast cancer and breast tumors. However, conventional methods are time-consuming and labor-intensive because the ROI for breast tissues is manually set and the quality of the segmented tissue varies depending on the skill level of the worker. To address this issue, we proposed a U-Net based on Haar wavelet pooling for multi-class semantic segmentation of breast tissues from MRI images. In addition, a labeled dataset was built to train network for breast shape reconstruction. The proposed network achieved an mIoU of 87.48 and a pixel accuracy of 99.35%. In particular, the network accurately segmented breast tissues of women with a high density of fine mammary glands. In the future, additional construction of datasets for MRI breast images taken with other equipment such as STIR pulse sequences and BLISS pulse sequences is required. Furthermore, the performance for medical image segmentation can be improved by applying various wavelet transforms such as the Daubechies wavelet transform and the dual-tree complex wavelet transform. Declarations Funding This work was supported by a grant (grant number 2018R1D1A1B07050199) of the Basic Science Research Program through the National Research Foundation (NRF) funded by the Ministry of Education, Republic of Korea. Conflicts of interest/Competing interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. Availability of data and material The datasets used and/or analysed during the current study available from the corresponding author on reasonable request. Code availability Not applicable Authors' contributions KwangBin Yang: Data preparation, Software, Methodology, Writing—Original draft preparation. Jinwon Lee: Methodology, Writing—Reviewing and Editing. Jeongsam Yang: Methodology, Supervision, Writing—Reviewing and Editing. Ethics approval Not applicable Consent to participate All authors consent for participation. Consent for publication All authors consent for publication. References Cancer, I. A. for R. on & others. IARC Biennial Report 2020-2021. Lyon: International Agency for Research on Cancer (2021). Danch-Wierzchowska, M., Borys, D. & Swierniak, A. 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Wavefuse: A unified deep framework for image fusion with discrete wavelet transform. arXiv preprint arXiv:2007.14110 (2020). Liu, P., Zhang, H., Zhang, K., Lin, L. & Zuo, W. Multi-level wavelet-CNN for image restoration. in Proceedings of the IEEE conference on computer vision and pattern recognition workshops 773–782 (2018). Li, Q., Shen, L., Guo, S. & Lai, Z. Wavelet integrated CNNs for noise-robust image classification. in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition 7245–7254 (2020). Suryanarayana, G. et al. Accurate magnetic resonance image super-resolution using deep networks and Gaussian filtering in the stationary wavelet domain. IEEE Access 9 , 71406–71417 (2021). Alijamaat, A., NikravanShalmani, A. & Bayat, P. Multiple sclerosis lesion segmentation from brain MRI using U-Net based on wavelet pooling. International journal of computer assisted radiology and surgery 16 , 1459–1467 (2021). Zhao, C. et al. Multi-scale wavelet network algorithm for pediatric echocardiographic segmentation via hierarchical feature guided fusion. Applied Soft Computing 107 , 107386 (2021). Bloch, B. N., Jain, A. & Jaffe, C. C. Data from breast-diagnosis. The Cancer Imaging Archive 10 , K9 (2015). Nielsen, M. A. Neural networks and deep learning . vol. 25 (Determination press San Francisco, CA, USA, 2015). Williams, T. & Li, R. Wavelet pooling for convolutional neural networks. in International Conference on Learning Representations (2018). Zhou, Z., Rahman Siddiquee, M. M., Tajbakhsh, N. & Liang, J. Unet++: A nested u-net architecture for medical image segmentation. in Deep learning in medical image analysis and multimodal learning for clinical decision support 3–11 (Springer, 2018). Gare, G. R. et al. W-Net: Dense and diagnostic semantic segmentation of subcutaneous and breast tissue in ultrasound images by incorporating ultrasound RF waveform data. Medical Image Analysis 76 , 102326 (2022). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 20 Jul, 2023 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Major revision 13 Mar, 2023 Reviews received at journal 18 Feb, 2023 Reviewers agreed at journal 08 Feb, 2023 Reviews received at journal 05 Feb, 2023 Reviewers agreed at journal 28 Jan, 2023 Reviewers agreed at journal 26 Jan, 2023 Reviewers invited by journal 24 Jan, 2023 Editor assigned by journal 24 Jan, 2023 Editor invited by journal 16 Jan, 2023 Submission checks completed at journal 16 Jan, 2023 First submitted to journal 11 Jan, 2023 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-2465906","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":168119358,"identity":"ceefdbb8-6184-4bd4-8e9a-488ea8aaa90c","order_by":0,"name":"Kwang Bin Yang","email":"","orcid":"","institution":"Samsung (South Korea)","correspondingAuthor":false,"prefix":"","firstName":"Kwang","middleName":"Bin","lastName":"Yang","suffix":""},{"id":168119359,"identity":"a4e125f1-abf0-4b95-bd12-37309d608194","order_by":1,"name":"Jinwon Lee","email":"","orcid":"","institution":"Gangneung–Wonju National University","correspondingAuthor":false,"prefix":"","firstName":"Jinwon","middleName":"","lastName":"Lee","suffix":""},{"id":168119360,"identity":"623f0baf-d6e1-4acd-a96e-e37f5f7bbcbe","order_by":2,"name":"Jeongsam Yang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAxklEQVRIiWNgGAWjYBACxgYQWcHADOUnEKvlDClaIPra4EwitDDPSH728Os8O3Z+iQTGDz8Y0vIJWzAjzdxYdlsys+SMBGbJHoYcywbCWhLMpCW3MTMb3EhgkAYGhAERtqR/k5acUw/SwvybSC05ZpIfGw6DtLABbckhQkvPmzJphmPHgf542GbZY5BGWIthe/o2yR811cn87MmHb/yoSCZCy4QEBmYeBoZkSKwS1sDAIM9/gIHxBwODHRFqR8EoGAWjYKQCANXONZfmF1R6AAAAAElFTkSuQmCC","orcid":"","institution":"Ajou University","correspondingAuthor":true,"prefix":"","firstName":"Jeongsam","middleName":"","lastName":"Yang","suffix":""}],"badges":[],"createdAt":"2023-01-11 07:29:23","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2465906/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2465906/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-023-38557-0","type":"published","date":"2023-07-20T21:40:14+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":31756228,"identity":"9a452247-2f71-4f0f-9b2f-616533bcf8d3","added_by":"auto","created_at":"2023-01-18 15:38:54","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":188410,"visible":true,"origin":"","legend":"\u003cp\u003eBreast tissue segmentation process based on deep learning network.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-2465906/v1/e0abef1e745bbf027443059b.png"},{"id":31756978,"identity":"c5b02e66-c362-450e-b665-5fb25eeae1bc","added_by":"auto","created_at":"2023-01-18 15:46:54","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":337994,"visible":true,"origin":"","legend":"\u003cp\u003eStep-by-step process for breast tissue labeling.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-2465906/v1/9ccb993036bcb5f30ad2b8fd.png"},{"id":31757448,"identity":"6865719b-3a05-427e-a1a6-1d6d3db6e656","added_by":"auto","created_at":"2023-01-18 15:54:54","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":309825,"visible":true,"origin":"","legend":"\u003cp\u003eSegmentation of full MRI slice images through template-based segmentation.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-2465906/v1/742e31fc4c9c3ecd83c7a78f.png"},{"id":31756221,"identity":"670dbedb-8299-4105-945a-0ec3de8c4c83","added_by":"auto","created_at":"2023-01-18 15:38:54","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":279236,"visible":true,"origin":"","legend":"\u003cp\u003eTwo-dimensional wavelet pooling structure.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-2465906/v1/a56597bc4f72161a072c62e8.png"},{"id":31756227,"identity":"c061bb72-40ec-4130-b636-6b6d7044964e","added_by":"auto","created_at":"2023-01-18 15:38:54","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":141011,"visible":true,"origin":"","legend":"\u003cp\u003eU-Net based on Haar wavelet pooling.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-2465906/v1/6317ae79d5da13d89fb7a446.png"},{"id":31756224,"identity":"130328de-7696-4c5b-a24c-90a26f9347a5","added_by":"auto","created_at":"2023-01-18 15:38:54","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":554955,"visible":true,"origin":"","legend":"\u003cp\u003eOriginal MRI images (top) and breast tissue images segmented through the U-Net based on Haar wavelet pooling (bottom) for three female patients.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-2465906/v1/e41b8e351e43bb7ddfce45af.png"},{"id":31756977,"identity":"68c72f8d-a4e2-4429-abc0-344ed9f24823","added_by":"auto","created_at":"2023-01-18 15:46:54","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":713342,"visible":true,"origin":"","legend":"\u003cp\u003eMRI images and breast tissue segmentation images of Patient A with a high segmentation accuracy (mIoU: 90.28) and Patient B with a low segmentation accuracy (mIoU: 77.94).\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-2465906/v1/fe8d6a8ce5f3bafca8e0b1ab.png"},{"id":31759283,"identity":"846d0670-70cc-4e0c-a712-e2741333b8d0","added_by":"auto","created_at":"2023-01-18 16:02:54","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":439275,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of breast tissue images segmented by three deep learning networks with the highest mIoU values.\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-2465906/v1/7cc14da24f49ba59137c82f4.png"},{"id":44734942,"identity":"647728f9-85bb-4fd4-8acc-4742849c3b48","added_by":"auto","created_at":"2023-10-16 22:22:37","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3063079,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2465906/v1/0c5e9c94-1833-41a9-8a59-9b004786d342.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Multi-class semantic segmentation of breast tissues from MRI images using U-Net based on Haar wavelet pooling","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe International Agency for Research on Cancer has reported that breast cancer is one of the most prevalent cancers worldwide, accounting for 11.7% of all cancer cases\u003csup\u003e1\u003c/sup\u003e. Due to increasing incidence of breast cancer, the demand for breast reconstruction surgery is also continuously increasing owing to breast removal. In the preparation stage for breast reconstruction surgery, a natural breast shape in a standing position is necessary before mastectomy. However, plastic surgeons can access only magnetic resonance imaging (MRI) or computed tomography (CT) images taken with patient lying in a prone position during the examination process. Consequently, they are limited in producing a natural-shaped breast implant in the standing position solely from images in a prone position. To overcome this limitation, studies have been conducted on reconstructing breast shapes in the standing position from prone-position MRI images by obtaining an approximate solution through ordinary differential equation of the finite element method for deformations caused by the center of gravity acting on the breast\u003csup\u003e2,3\u003c/sup\u003e. However, it is difficult to obtain meaningful results from these studies for the natural breast shape in a standing position because elastic moduli of breast tissues such as skin, fat, and fibroglandular tissue affected by gravity are different from every other.\u003c/p\u003e\n\u003cp\u003eTo address this issue, this study proposed a deep learning network using U-Net based on Haar wavelet pooling to segment breast tissues for reconstructing the breast shape in the standing. To train the deep learning network, we constructed a dataset consisting of background, skin, fat, and fibroglandular tissues from MRI breast images. For labeling of the dataset, the median filter, Otsu\u0026rsquo;s threshold algorithm, and a template-based segmentation method were utilized. In the subsampling stage of the conventional U-Net, the max pooling is sensitive to overfitting. It may cause a significant error during data segmentation because weak information about the breast tissue is lost. To improve the segmentation accuracy of breast tissues, we utilized the Haar wavelet pooling instead of the max pooling to robust for overfitting. The U-Net based on Haar wavelet pooling simultaneously uses a low-low (LL) sub-band that holds approximate values of the input image and three distinct frequency sub-bands (low-high (LH), high-low (HL), and high-high (HH)) with detailed edge feature information. Therefore, it can effectively extract features of breast tissues by reducing the loss of image information in the subsampling stage. It also implements a deep learning network that is robust to overfitting.\u003c/p\u003e\n\u003cp\u003eTo compare performances of the proposed network and other networks described in previous studies for segmenting breast tissues, various experiments with max pooling and average pooling were conducted. The proposed U-Net based on Haar wavelet pooling achieved a mean intersection over union (mIoU) of 87.48, which was higher than those of other methods.\u003c/p\u003e"},{"header":"2. Literature Review","content":"\u003ch2\u003e2.1. Deep learning-based breast tissue segmentation method\u003c/h2\u003e\n\u003cp\u003ePrevious studies on breast image analysis have used binary segmentation methods to diagnose breast diseases such as breast cancer and breast tumors\u003csup\u003e4\u0026ndash;6\u003c/sup\u003e. However, such methods were time-consuming and labor-intensive because the region of interest (ROI) for the breast tissue was manually set. Moreover, these methods had a disadvantage in that the quality of segmented tissues varied depending on the skill level of the worker and the algorithm used. Recently, various deep learning-based algorithms have been introduced for medical image processing to overcome such disadvantages.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTable 1. Comparison of deep learning-based segmentation methods for breast tissues in existing studies.\u003c/p\u003e\n\u003cdiv align=\"\"\u003e\n \u003ctable border=\"1\" cellpadding=\"0\" cellspacing=\"0\" width=\"595\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"20.168067226890756%\"\u003e\n \u003cp\u003e\u003cstrong\u003eRelated study\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.15126050420168%\"\u003e\n \u003cp\u003e\u003cstrong\u003eBackbone model\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"16.470588235294116%\"\u003e\n \u003cp\u003e\u003cstrong\u003eInput\u0026nbsp;\u003cbr\u003e\u0026nbsp;images\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"22.18487394957983%\"\u003e\n \u003cp\u003e\u003cstrong\u003e# of segment classes including background\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.025210084033613%\"\u003e\n \u003cp\u003e\u003cstrong\u003eSegmented tissue\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"20.168067226890756%\"\u003e\n \u003cp\u003eSoulami et al. \u0026nbsp;(2021)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.15126050420168%\"\u003e\n \u003cp\u003eEnd-to-End\u003c/p\u003e\n \u003cp\u003eU-Net\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"16.470588235294116%\"\u003e\n \u003cp\u003eMammogram\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"22.18487394957983%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.025210084033613%\"\u003e\n \u003cp\u003eBreast cancer\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"20.168067226890756%\"\u003e\n \u003cp\u003eNegi et al. (2020)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.15126050420168%\"\u003e\n \u003cp\u003eRDA-U-Net\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"2\" width=\"16.470588235294116%\"\u003e\n \u003cp\u003eUltrasound\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"22.18487394957983%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.025210084033613%\"\u003e\n \u003cp\u003eBreast tumor\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"24.14486921529175%\"\u003e\n \u003cp\u003eIlesanmi et al. (2021)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"21.730382293762574%\"\u003e\n \u003cp\u003eVEU-Net\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"26.559356136820927%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"27.56539235412475%\"\u003e\n \u003cp\u003eBreast tumor\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"20.168067226890756%\"\u003e\n \u003cp\u003eZhang et al. (2019)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.15126050420168%\"\u003e\n \u003cp\u003eU-Net\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"3\" width=\"16.470588235294116%\"\u003e\n \u003cp\u003eMRI\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"22.18487394957983%\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.025210084033613%\"\u003e\n \u003cp\u003eFat, Fibroglandular tissue\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"24.14486921529175%\"\u003e\n \u003cp\u003eZhang et al. (2021)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"21.730382293762574%\"\u003e\n \u003cp\u003eU-Net\u003c/p\u003e\n \u003cp\u003e(Transfer learning)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"26.559356136820927%\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"27.56539235412475%\"\u003e\n \u003cp\u003eFat, Fibroglandular tissue\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"24.14486921529175%\"\u003e\n \u003cp\u003eHuo et al. (2021)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"21.730382293762574%\"\u003e\n \u003cp\u003ennU-Net\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"26.559356136820927%\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"27.56539235412475%\"\u003e\n \u003cp\u003eFat, Fibroglandular tissue\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"20.168067226890756%\"\u003e\n \u003cp\u003eOurs\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.15126050420168%\"\u003e\n \u003cp\u003eHaar wavelet pooling U-Net\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"16.470588235294116%\"\u003e\n \u003cp\u003eMRI\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"22.18487394957983%\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.025210084033613%\"\u003e\n \u003cp\u003eSkin, Fat, Fibroglandular tissue\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eTable 1 summarizes segmentation methods for breast tissues based on deep learning with MRI breast images used in previous studies. Most deep learning-based networks that segment breast tissues modified the U-Net\u003csup\u003e7\u003c/sup\u003e to perform segmentation for a single class, such as breast cancer, breast tumor, and breast density. To detect breast cancer in digital mammography, Soulami et al. have improved the segmentation performance by proposing a deep learning network based on the end-to-end U-Net method\u003csup\u003e8\u003c/sup\u003e. Further, to segment tumors in breast ultrasound images, Negi et al. have used a deep learning network called RDA-U-Net and the Wasserstein GAN algorithm and reported remarkable performance\u003csup\u003e9\u003c/sup\u003e. Ilesanmi et al. have proposed a variant-enhanced block that combines max pooling and average pooling to segment tumors in breast ultrasound images, consequently improving the accuracy of semantic segmentation for tumors by using the VEU-Net network\u003csup\u003e10\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eMany studies have been conducted to segment fibroglandular tissues known to account for a large proportion of breast tissues using deep learning. Zhang et al. have segmented fat and fibroglandular tissues from MRI breast images using a U-Net\u003csup\u003e11\u003c/sup\u003e. Subsequently, Zhang et al. have improved the segmentation accuracy by performing transfer learning for fat and fibroglandular tissues in a deep learning model that segments breast density of MRI breast images\u003csup\u003e12\u003c/sup\u003e. Huo et al. have improved the segmentation accuracy of fibroglandular tissues by adopting nnU-Net to segment the entire breast and fibroglandular tissues in DCE-MRI breast images\u003csup\u003e13\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eIn contrast to most previous studies that used binary segmentation methods, our study performed multi-class semantic segmentation through U-Net based on Haar wavelet pooling to segment various types of breast tissues for breast shape reconstruction.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e2.2. Deep learning method based on wavelet pooling for images\u003c/p\u003e\n\u003cp\u003eThe wavelet pooling used in the sampling operation of deep learning algorithms has an advantage of decreasing the effect of noise on segmentation by filtering the input image before sampling. Previous studies have conducted various image segmentation tasks by combining wavelet pooling and deep learning \u003csup\u003e14,15\u003c/sup\u003e. Table 2 summarizes improved performances of image classification, segmentation, recognition, and restoration using wavelet pooling-based deep learning in previous studies.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTable 2. Comparison of deep learning methods based on wavelet pooling for images.\u003c/p\u003e\n\u003cdiv align=\"\"\u003e\n \u003ctable border=\"1\" cellpadding=\"0\" cellspacing=\"0\" width=\"595\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"15.966386554621849%\"\u003e\n \u003cp\u003e\u003cstrong\u003eRelated study\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.823529411764707%\"\u003e\n \u003cp\u003e\u003cstrong\u003eDeep learning purpose\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.81512605042017%\"\u003e\n \u003cp\u003e\u003cstrong\u003eWavelet transform\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.65546218487395%\"\u003e\n \u003cp\u003e\u003cstrong\u003eDeep learning type\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.73949579831933%\"\u003e\n \u003cp\u003e\u003cstrong\u003eImage dataset\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"15.966386554621849%\"\u003e\n \u003cp\u003e\u003csup\u003e16\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.823529411764707%\"\u003e\n \u003cp\u003eImage fusion\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.81512605042017%\"\u003e\n \u003cp\u003eDiscrete wavelet transform\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.65546218487395%\"\u003e\n \u003cp\u003eCNN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.73949579831933%\"\u003e\n \u003cp\u003eCOCO\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"15.966386554621849%\"\u003e\n \u003cp\u003e\u003csup\u003e17\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.823529411764707%\"\u003e\n \u003cp\u003eImage restoration\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.81512605042017%\"\u003e\n \u003cp\u003eMulti-level wavelet transform\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.65546218487395%\"\u003e\n \u003cp\u003eMulti-level wavelet CNN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.73949579831933%\"\u003e\n \u003cp\u003eBerkeley segmentation dataset, DIV2K, Waterloo exploration database\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"15.966386554621849%\"\u003e\n \u003cp\u003e\u003csup\u003e18\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.823529411764707%\"\u003e\n \u003cp\u003eImage classification\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.81512605042017%\"\u003e\n \u003cp\u003eDiscrete wavelet transform\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.65546218487395%\"\u003e\n \u003cp\u003eCNN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.73949579831933%\"\u003e\n \u003cp\u003eMNIST, CIFAR-10,\u0026nbsp;\u003c/p\u003e\n \u003cp\u003eSHVN, KDEF\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"15.966386554621849%\"\u003e\n \u003cp\u003e\u003csup\u003e19\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.823529411764707%\"\u003e\n \u003cp\u003eSuper resolution\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.81512605042017%\"\u003e\n \u003cp\u003eStationary wavelet transform\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.65546218487395%\"\u003e\n \u003cp\u003eVDR-Net\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.73949579831933%\"\u003e\n \u003cp\u003eBrain MRI\u003c/p\u003e\n \u003cp\u003e(IXI-MR dataset)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"15.966386554621849%\"\u003e\n \u003cp\u003e\u003csup\u003e20\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.823529411764707%\"\u003e\n \u003cp\u003eSemantic segmentation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.81512605042017%\"\u003e\n \u003cp\u003eDiscrete wavelet transform\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.65546218487395%\"\u003e\n \u003cp\u003eU-Net\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.73949579831933%\"\u003e\n \u003cp\u003eBrain MRI\u003c/p\u003e\n \u003cp\u003e(MICCAI dataset)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"15.966386554621849%\"\u003e\n \u003cp\u003e\u003csup\u003e21\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.823529411764707%\"\u003e\n \u003cp\u003eSemantic segmentation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.81512605042017%\"\u003e\n \u003cp\u003eMulti-scale wavelet transform\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.65546218487395%\"\u003e\n \u003cp\u003eWU-Net\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.73949579831933%\"\u003e\n \u003cp\u003ePediatric echocardiographic\u003c/p\u003e\n \u003cp\u003e(CAMUS dataset)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"15.966386554621849%\"\u003e\n \u003cp\u003eOurs\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.823529411764707%\"\u003e\n \u003cp\u003eSemantic segmentation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.81512605042017%\"\u003e\n \u003cp\u003eDiscrete wavelet transform\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.65546218487395%\"\u003e\n \u003cp\u003eHaar wavelet pooling U-Net\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.73949579831933%\"\u003e\n \u003cp\u003eBreast MRI\u003c/p\u003e\n \u003cp\u003e(TCIA breast-diagnosis)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003ePrevious studies have proposed an unsupervised image fusion algorithm for image restoration and classification that combines a deep learning network with a multi-scale discrete wavelet transform\u0026nbsp;\u003csup\u003e16\u0026ndash;18\u003c/sup\u003e. Suryanarayana et al. have converted low-resolution MRI images into high-resolution MRI images by combining VDR-Net with wavelet pooling that uses both low and high frequencies\u003csup\u003e19\u003c/sup\u003e. Alijamaat et al. have combined U-Net with wavelet pooling of low-frequency component (LL band) characterized by high image pixel concentration while maintaining the overall trend of images to improve the segmentation performance for multiple sclerosis of the brain\u003csup\u003e20\u003c/sup\u003e. Zhao et al. have improved the performance of congenital heart disease diagnosis in pediatric echocardiography images by combining low-frequency information of multi-scale wavelet with WU-Net\u003csup\u003e21\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eExisting studies cited above have demonstrated that the combination of wavelet pooling and deep learning algorithms can improve image performance in various applications such as classification, segmentation, recognition, and restoration. This study improve the semantic segmentation performance for breast tissues by combining Haar wavelet pooling with U-Net. In particular, the image output through the high-frequency filter of wavelet pooling can effectively express locations of breast tissues and expression of micro-soft tissues by emphasizing edge features for vertical, horizontal, and diagonal components. Furthermore, characteristics of fine breast tissues are well-preserved because the image output through the low-frequency filter has approximate values of the input image.\u0026nbsp;\u003c/p\u003e"},{"header":"3. Design Of Deep Learning Network For Segmentation","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1. Overview\u003c/h2\u003e \u003cp\u003eThis paper proposed a multi-class semantic segmentation method for breast tissues to reconstruct breast shape in a standing position using U-Net based on Haar wavelet pooling. To train deep learning networks, labeled breast tissue data are necessary. MRI images, which are essential for breast cancer screening, have higher resolution and lower noise than CT or ultrasound images. Moreover, MRI images are effective for representing and segmenting micro-soft tissues such as fat and fibrous granular variants in the breast.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows breast tissue segmentation process based on deep learning network for breast shape reconstruction. In the first step, MRI images in Digital Imaging Communication in Medicine (DICOM) format were collected. In the second step, breast tissues from collected MRI breast images were labelled to build a dataset for training the deep learning network. Labeling steps included removing noise from the MRI image with a median filter using Otsu's threshold algorithm, expanding to all MRI images through the template-based segmentation method based on the segmented tissues, and verifying labels by a radiologist. In the third step, U-Net based on Haar wavelet pooling was designed to segment breast tissues for breast shape reconstruction. To improve the multi-class semantic segmentation performance for MRI breast images, this study combined U-Net with Haar wavelet pooling. The U-Net based on Haar wavelet pooling uses the LL sub-band, which holds approximate value of the input image, and three distinct frequency sub-bands (LH, HL, and HH), which have detailed edge features. Therefore, breast tissue features could be effectively extracted by reducing the loss of image information in the subsampling. The U-Net based on Haar wavelet pooling was trained with constructed datasets and its performance was then tested.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.2. Building an MRI dataset for breast tissue segmentation\u003c/h2\u003e \u003cp\u003eA set of data including labels for every pixel of the MRI data is required for breast tissue segmentation with deep learning. In this study, an MRI dataset was collected from the breast-diagnosis database \u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e of The Cancer Imaging Archive (TCIA), an open access database for medical images for cancer research. The breast-diagnosis database contains medical images of breast cancer patients as well as cases of breast diagnosis such as high-risk normal, DCIS, fibroids, and lobular carcinomas. Each image was captured with three pulses (T2, STIR, BLISS) using a Phillips 1.5 T MRI system. Breast MRI images of 89 breast cancer patients were obtained at 2 mm intervals at resolutions of 500 to 600 DPI, with 80 to 90 MRI slices per person. This study used MRI slice images of T2-weighted pulse sequences data.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e shows a step-by-step process of labeling breast tissues from MRI slice images. The breast tissue should be segmented into skin, fat, fibroglandular tissue, and background because the upper part of the pectoral muscle is incised in a mastectomy. As shown Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e (a), the noise of the slice image was removed using a median filter. Otsu's threshold algorithm was used to segment breast tissues from denoised MRI images. This algorithm could separate the foreground and background by a threshold based on the distribution of pixels in the image. Multiple thresholds were utilized to separate breast tissues with the same pixel distribution value.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e (b) shows the result of segmenting fibroglandular tissues (yellow region) and the background (light blue region) using Otsu\u0026rsquo;s threshold algorithm by setting the background and the foreground (fibroglandular tissues). Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e (c) shows result of segmenting fat (green region) and the rest of the breast tissues (red region) through Otsu\u0026rsquo;s threshold algorithm by setting the background and the foreground (fat, muscle, and chest wall). Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e (d) shows that the background (brown region) and the inside of the human body (green region) are separated through Otsu\u0026rsquo;s threshold algorithm. Skin data are lost during T2-weighted pulse sequence images. Hence, boundary lines between green and brown regions were offset by pixels with a thickness of 2 mm that matched the thickness of the human body's skin and the result was used as skin data. These segmented skin data were validated through BLISS MRI images of breast cancer patients. In this process, breast-diagnosis cases such as fibroma and breast cancer were recognized and segmented as fibroglandular tissues because they were diseases expanded by the action of hormones on mammary glands. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e (f), breast tissues obtained in the previous step were integrated. Light blue, blue, green, and yellow regions represented the background, skin, fat, and fibroglandular tissues, respectively.\u003c/p\u003e \u003cp\u003eIn order to reduce the manual labeling of breast tissues, we used template-based segmentation. Template-based segmentation expands with a single MRI slice as a reference template for the remaining other MRI slices. It can extract individual breast tissue features after analyzing each tissue's location, size, shape, and pixel distribution values with MRI slice of a cross-section into which breast tissues are segmented and set as a reference template. The full MRI image in which breast tissues are finally segmented can be obtained by extracting breast tissues with similar characteristics from consecutive MRI slices. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows the process of segmenting the entire MRI slice image through template-based segmentation. T2-weighted pulse sequence data that were input for breast tissue segmentation and the segmented breast tissue are output at 800 \u0026times; 800 DPI resolution. These labeled data with template-based segmentation were validated by a radiologist.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.3. Designing U-Net based on Haar wavelet pooling\u003c/h2\u003e \u003cp\u003eThis study proposed a U-Net based on Haar wavelet pooling in the subsampling stage. The wavelet transform, which has information on the spatial domain and the frequency domain, is expressed as a vibration with an average of zero that vibrates while repeating increase and decrease within a preset time. Wavelet transform can effectively detect sudden signal changes because it describes regional features and provides signal analysis at different scales and levels. The wavelet transform for a signal \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(x\\left(t\\right)\\)\u003c/span\u003e\u003c/span\u003e is defined by Eq.\u0026nbsp;(1) \u003csup\u003e23\u003c/sup\u003e:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$${W}_{a}x\\left(b\\right)= \\frac{1}{\\sqrt{a}}\\underset{-{\\infty }}{\\overset{+{\\infty }}{\\int }}x\\left(t\\right){\\varPsi }^{*}\\left(\\frac{t-b}{a}\\right)dt a\u0026gt;0$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(a\\)\u003c/span\u003e\u003c/span\u003e is the parameter for scale change, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(b\\)\u003c/span\u003e\u003c/span\u003e is the displacement rate, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varPsi }^{\\text{*}}\\left(t\\right)\\)\u003c/span\u003e\u003c/span\u003e is a continuous basis function called mother wavelet. In this study, a two-dimensional (2D) discrete Haar wavelet transform that could minimize the amount of computation when converting MRI breast images in the deep learning network was used.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe 2D-wavelet transform presents the input image as a matrix of two-dimensional signals based on the brightness of pixels. Data passing through the 2D-wavelet transform were divided into four bands according to the applied filter. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows the structure of wavelet pooling. Wavelet pooling passed through two steps. Input data were decomposed through a high pass filter and a low pass filter at each step. The size of the input data was reduced because down-sampling was performed in each step. In the first step of wavelet pooling, the input image was horizontally separated into low (L), which was a low-frequency component, and high (H), which was a high-frequency component by applying the horizontal filter. In this process, the approximate value of the input image was decomposed for the low-frequency component and the detailed value was decomposed for the high-frequency component. In the second step where the vertical filter was applied, images of low- and high-frequency components were vertically separated again and decomposed into four sets of data: LL, LH, HL, and HH bands. Resolutions of data in all bands were reduced to half the resolution of the input data. Data of the LL band had a low-frequency component, indicating the overall trend data of the input data. Data of LH, HL, and HH bands had edge features for vertical, horizontal, and diagonal components, respectively. The segmentation performance can be improved because decomposed data can represent various features such as micro breast tissues.\u003c/p\u003e \u003cp\u003eU-Net consists of a contracting path that extracts features from the training data and an expansive path for restoring the original resolution. The contracting path performs down-sampling by setting the stride size of the convolution to two in each step, whereas the expansive path performs up-sampling using transposed convolution. The max pooling in the subsampling stage used in previous studies was difficult to generalize because it was sensitive to overfitting of the dataset \u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e. Although some studies have attempted to solve the vanishing gradient problem by passing the information in the contraction path to the expansive path through a skip connection, overfitting still occurs \u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e. Breast tissues are delicate data linked by small pixels. Therefore, if max pooling is used, information on the breast tissues might be lost. This study designed a deep learning network of the U-Net architecture based on Haar wavelet pooling for subsampling to segment breast tissues.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e shows the deep learning network architecture that combines Haar wavelet pooling with U-Net. The deep learning network was composed of 12 convolution layers, 5 Haar wavelet pooling layers, and 5 inverse wavelet-based up-sampling layers. Input breast image data were converted into LL, LH, HL, and HH band data by Haar wavelet pooling. These converted data were then transmitted to the convolution layer. The resolution was restored using an inverse wavelet, which could reconstruct data using the output value of wavelet pooling. In the proposed architecture, a batch normalization function and a ReLU activation function were used with each convolution layer. The amount of computation for the network was reduced compared with previous studies by applying the Haar wavelet pooling. The number of existing channels was maintained because the pooling result did not affect the number of channels in the deep learning network. However, the number of input channels of the convolution layer was increased by a factor of four because the U-Net based on Haar wavelet pooling simultaneously used LL, LH, HL, and HH bands.\u003c/p\u003e \u003c/div\u003e"},{"header":"4. System Implementation And Experimental Evaluation","content":"\u003cdiv class=\"Section2\" id=\"Sec8\"\u003e\n \u003ch2\u003e4.1. Implementation environment\u003c/h2\u003e\n \u003cp\u003eTable \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e shows the implementation environment for building the U-Net based on wavelet pooling. The U-Net was executed on Ubuntu Linux. It was implemented in Python using Anaconda, a math and science library, PyTorch, a deep learning library, and CUDA and CuDNN for GPU operation.\u003c/p\u003e\u003ctable border=\"1\" id=\"Tab3\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eImplementation environment.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eItem\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eUsage\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eVersion\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eUbuntu\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eOperating system\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e16.04.5 LTS-64bit\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ePython\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDevelopment language\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.8.12\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAnaconda\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMath and science library\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.10.1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ePyTorch\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDeep learning library\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.10.0\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCUDA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGPU parallel computing library\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11.3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCuDNN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGPU-accelerated library\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8.2.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003eTwo units of NVIDIA Quadro RTX 5000 16G were interconnected for distributed data parallel processing for deep learning operations. The interface module was implemented with the DistributedDataParallel library provided by PyTorch to synchronize IDs of GPU operation processes performed on two graphic cards.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv class=\"Section2\" id=\"Sec9\"\u003e\n \u003ch2\u003e4.2. Experiment and evaluation\u003c/h2\u003e\n \u003cp\u003eSegmentation accuracies for background, skin, fat, and fibroglandular tissues were analyzed to evaluate the performance of the U-Net based on Haar wavelet pooling. The dataset of 5,202 images was divided into a training dataset, a validation dataset, and a test dataset at a ratio of 8:1:1. These data were rotated at a random angle for augmentation of the dataset in the deep learning network training process.\u003c/p\u003e\n \u003cp\u003eMulti-class semantic segmentation was performed using the U-Net based on Haar wavelet pooling. The resolution of the training data was set to be 800 \u0026times; 800 DPI, with batch size of 8, epoch of 200, and learning rate of 0.002. Furthermore, focal loss and adaptive moment estimation optimizer (Adam) were applied. The loss function was compared with cross entropy, dice loss, and focal loss to find the optimal parameter. Max pooling, average pooling, and Haar wavelet pooling were applied in this experiment to prove the effectiveness of Haar wavelet pooling with subsampling. The segmentation performance was measured using Intersection over Union (IoU) commonly used as a performance evaluation index for segmentation, mIoU (the average of all IoU values), and pixel accuracy. Equations for IoU (2), mIoU (3), and pixel accuracy (4) are shown as follows:\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003cdiv align=\"left\" class=\"colspec\"\u003e\u003cbr\u003e\u003c/div\u003e\u0026nbsp;\u003ctable border=\"1\" id=\"Taba\"\u003e\n \u003ccolgroup cols=\"2\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(IOU= \\frac{TP}{TP+FP+FN}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e(2)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(mIOU= \\frac{1}{k}{\\sum }_{i=0}^{k}\\frac{TP}{TP+FP+FN}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e(3)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(pixel accuracy= \\frac{TP+TN}{TP+TN+FP+FN}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e(4)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003ewhere TP, TN, FP, FN, and k represent true positive, true negative, false positive, false negative, and the number of classes, respectively.\u003c/p\u003e\n \u003cp\u003eTable \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e shows IoU, mIoU, and pixel accuracy results for background, skin, fat, and fibroglandular tissues of the test dataset. Haar wavelet pooling showed higher breast tissue segmentation performance than max pooling and average pooling in the same experimental environment. Furthermore, the deep learning network using focal loss and Haar wavelet pooling showed the highest mIoU and pixel accuracy values. The deep learning network using focal loss and Haar wavelet pooling confirmed that segmentation accuracies for skin and fibroglandular tissues were relatively high. This is because deep learning networks can be trained effectively because Haar wavelet pooling can reduce the influence of easy negative examples such as background and fat while focusing on training hard negative examples such as skin and fibroglandular tissues. By contrast, the deep learning network using both dice loss and average pooling showed low segmentation performance.\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\u0026nbsp;\u003ctable border=\"1\" id=\"Tab4\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eExperimental results obtained with a combination of training parameters of the deep learning network for breast tissue segmentation.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ePooling method\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eLoss function\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eBackground IoU (%)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSkin IoU (%)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eFat IoU (%)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eFibroglandular tissue IoU (%)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003emIoU (%)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ePixel accuracy (%)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMax pooling\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCross entropy\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e98.78\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e75.44\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e94.62\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e76.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e86.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e99.29\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAverage pooling\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCross entropy\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e98.39\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e70.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e93.88\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e73.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e83.86\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e99.12\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eHaar wavelet Pooling\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCross entropy\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e98.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e75.37\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e94.70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e77.66\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e86.63\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e99.31\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMax pooling\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDice loss\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e98.62\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e72.07\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e94.17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e75.52\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e85.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e99.20\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAverage pooling\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDice loss\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e98.40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e74.65\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e93.84\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e63.94\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e82.71\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e98.78\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eHaar wavelet pooling\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDice loss\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e98.77\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e73.63\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cspan class=\"BoldUnderline\" name=\"Emphasis\" type=\"BoldUnderline\"\u003e94.79\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e76.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e85.85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e99.29\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMax pooling\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eFocal loss\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cspan class=\"BoldUnderline\" name=\"Emphasis\" type=\"BoldUnderline\"\u003e98.90\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cspan class=\"BoldUnderline\" name=\"Emphasis\" type=\"BoldUnderline\"\u003e76.57\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e94.78\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cspan class=\"BoldUnderline\" name=\"Emphasis\" type=\"BoldUnderline\"\u003e78.58\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cspan class=\"BoldUnderline\" name=\"Emphasis\" type=\"BoldUnderline\"\u003e87.21\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cspan class=\"BoldUnderline\" name=\"Emphasis\" type=\"BoldUnderline\"\u003e99.34\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAverage pooling\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eFocal loss\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e98.85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e75.47\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e94.38\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e73.79\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e85.62\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e99.29\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eHaar wavelet pooling\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eFocal loss\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cspan class=\"BoldUnderline\" name=\"Emphasis\" type=\"BoldUnderline\"\u003e98.90\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cspan class=\"BoldUnderline\" name=\"Emphasis\" type=\"BoldUnderline\"\u003e77.14\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cspan class=\"BoldUnderline\" name=\"Emphasis\" type=\"BoldUnderline\"\u003e94.81\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cspan class=\"BoldUnderline\" name=\"Emphasis\" type=\"BoldUnderline\"\u003e79.06\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cspan class=\"BoldUnderline\" name=\"Emphasis\" type=\"BoldUnderline\"\u003e87.48\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cspan class=\"BoldUnderline\" name=\"Emphasis\" type=\"BoldUnderline\"\u003e99.35\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\u0026nbsp;\u003ctable border=\"1\" id=\"Tab5\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eComparison of complexity, segmentation accuracy, and pixel accuracy values of deep learning networks.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMethod\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e# of params (million)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eBackground IoU (%)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSkin IoU (%)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eFat IoU (%)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eFibroglandular tissue IoU (%)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003emIoU (%)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ePixel accuracy (%)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eU-Net\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e31.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e98.85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cspan class=\"BoldUnderline\" name=\"Emphasis\" type=\"BoldUnderline\"\u003e74.34\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e94.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e76.46\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e85.96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e99.28\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eEnd-to-End\u003c/p\u003e\n \u003cp\u003eU-Net\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e27.91\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e98.85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e74.16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e93.66\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e71.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e84.67\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e99.23\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRDA-U-Net\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e18.85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e98.61\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e75.71\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e93.89\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e68.90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e84.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e99.19\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eVEU-Net\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e14.22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e98.63\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e74.43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e94.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e69.77\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e84.21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e99.04\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ennU-Net\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e47.88\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cspan class=\"BoldUnderline\" name=\"Emphasis\" type=\"BoldUnderline\"\u003e98.86\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e73.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cspan class=\"BoldUnderline\" name=\"Emphasis\" type=\"BoldUnderline\"\u003e94.78\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cspan class=\"BoldUnderline\" name=\"Emphasis\" type=\"BoldUnderline\"\u003e78.65\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cspan class=\"BoldUnderline\" name=\"Emphasis\" type=\"BoldUnderline\"\u003e86.32\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cspan class=\"BoldUnderline\" name=\"Emphasis\" type=\"BoldUnderline\"\u003e99.31\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eLL wavelet\u003c/p\u003e\n \u003cp\u003eU-Net\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e21.98\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e97.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e68.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e90.75\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e43.67\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e74.95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e98.54\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eOurs\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e24.28\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cspan class=\"BoldUnderline\" name=\"Emphasis\" type=\"BoldUnderline\"\u003e98.90\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cspan class=\"BoldUnderline\" name=\"Emphasis\" type=\"BoldUnderline\"\u003e77.14\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cspan class=\"BoldUnderline\" name=\"Emphasis\" type=\"BoldUnderline\"\u003e94.81\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cspan class=\"BoldUnderline\" name=\"Emphasis\" type=\"BoldUnderline\"\u003e79.06\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cspan class=\"BoldUnderline\" name=\"Emphasis\" type=\"BoldUnderline\"\u003e87.48\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cspan class=\"BoldUnderline\" name=\"Emphasis\" type=\"BoldUnderline\"\u003e99.35\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003eTable \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e compares results of breast tissue segmentation accuracy between the proposed network and previous studies. The IoU, mIoU, and pixel accuracy values for background, skin, fat, and fibroglandular tissues were measured in this experiment. The U-Net based on Haar wavelet pooling achieved an mIoU of 87.48 and a pixel accuracy of 99.35% for breast tissue segmentation. The segmentation accuracy for these breast tissues showed a significant performance improvement of 1\u0026ndash;2%p compared to a previous study \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e. In particular, the U-Net based on Haar wavelet pooling achieved a very high segmentation accuracy for skin and fibroglandular tissues with a small number of parameters.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv class=\"Section2\" id=\"Sec10\"\u003e\n \u003ch2\u003e4.3. Verification of segmentation results through visualization\u003c/h2\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e shows original MRI images of three patients (A, B, and C) with different breast shapes and fibroglandular tissue densities in the test dataset and images of breast tissues segmented by the proposed network. The top of Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e depicts the original MRI images and the bottom shows breast tissue images segmented using the proposed network. Black, blue, green, and yellow indicates the background, skin, fat, fibroglandular tissues, respectively. For Patient A, a small breast shape and a high density of fibroglandular tissues were observed. Patient B was characterized by a medium-sized breast shape and low-density fibroglandular tissues close to the chest wall muscle. Patient C, with a large breast shape, was characterized by moderately dense fibroglandular tissues. These results showed that the proposed network could effectively segment skin, fat, and fibroglandular tissues even when MRI images with different breast shapes and fibroglandular tissue densities were used as input.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e shows MRI images and segmentation results for two patients. Figure \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e (A) shows the 69th patient out of 89 patients, with an mIoU of 90.28. Figure \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e (B) shows an MRI image of the 58th patient with an mIoU of 77.94. In rectangle areas of Fig. \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e (A3) and Fig. \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e (B3), the fibroglandular tissue of Patient A had a higher density than that of Patient B. As for Patient B with a low density of fibroglandular tissues, the mIoU of the segmented breast tissue was lower than that of Patient A with a high density of fibroglandular tissues. This observation indicated that the U-Net based on Haar wavelet pooling could effectively segment breast images of women with a high density of fibroglandular tissues.\u003c/p\u003e\n \u003cp\u003eFigure 8 visualizes the ground truth image and the segmented breast tissue image with U-Net, nnU-Net, and U-Net based on Haar wavelet pooling. The rectangle area indicated that the U-Net based on Haar wavelet pooling segmented breast tissues more accurately than U-Net and nnU-Net. By contrast, in Fig. 8 (b), the outside of the background was misrecognized as skin tissue and the inside as fibroglandular tissue and fat owing to the noise of the background. When Fig. 8 (b) showing an image of breast tissue segmented through nnU-Net was compared with the ground truth, the background was incorrectly segmented into fibroglandular tissue, skin, and fat because of the noise inside the background. These results showed that the proposed network could distinguish the noise of the input image and the breast tissue more accurately than methods described in previous studies and accurately segment delicate soft tissues and skin of the mammary gland.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eRecently, deep learning networks with excellent performance have been introduced in various studies for medical image segmentation. Many methods have been proposed for segmenting breast tissues using binary-image segmentation to diagnose breast diseases such as breast cancer and breast tumors. However, conventional methods are time-consuming and labor-intensive because the ROI for breast tissues is manually set and the quality of the segmented tissue varies depending on the skill level of the worker. To address this issue, we proposed a U-Net based on Haar wavelet pooling for multi-class semantic segmentation of breast tissues from MRI images. In addition, a labeled dataset was built to train network for breast shape reconstruction. The proposed network achieved an mIoU of 87.48 and a pixel accuracy of 99.35%. In particular, the network accurately segmented breast tissues of women with a high density of fine mammary glands.\u003c/p\u003e \u003cp\u003eIn the future, additional construction of datasets for MRI breast images taken with other equipment such as STIR pulse sequences and BLISS pulse sequences is required. Furthermore, the performance for medical image segmentation can be improved by applying various wavelet transforms such as the Daubechies wavelet transform and the dual-tree complex wavelet transform.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was supported by a grant (grant number 2018R1D1A1B07050199) of the Basic Science Research Program through the National Research Foundation (NRF) funded by the Ministry of Education, Republic of Korea.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflicts of interest/Competing interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and material\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe datasets used and/or analysed during the current study available from the corresponding author on reasonable request.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCode availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors\u0026apos; contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eKwangBin Yang: Data preparation, Software, Methodology, Writing\u0026mdash;Original draft preparation. Jinwon Lee: Methodology, Writing\u0026mdash;Reviewing and Editing. Jeongsam Yang: Methodology, Supervision, Writing\u0026mdash;Reviewing and Editing. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics approval\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent to participate\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll authors consent for participation.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for publication\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll authors consent for publication.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eCancer, I. A. for R. on \u0026amp; others. IARC Biennial Report 2020-2021. \u003cem\u003eLyon: International Agency for Research on Cancer\u003c/em\u003e (2021).\u003c/li\u003e\n\u003cli\u003eDanch-Wierzchowska, M., Borys, D. \u0026amp; Swierniak, A. 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R. \u003cem\u003eet al.\u003c/em\u003e W-Net: Dense and diagnostic semantic segmentation of subcutaneous and breast tissue in ultrasound images by incorporating ultrasound RF waveform data. \u003cem\u003eMedical Image Analysis\u003c/em\u003e \u003cstrong\u003e76\u003c/strong\u003e, 102326 (2022).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Breast shape reconstruction, Multi-class semantic segmentation, Discrete wavelet transform, U-Net semantic segmentation, Wavelet U-Net","lastPublishedDoi":"10.21203/rs.3.rs-2465906/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2465906/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eMRI images for breast cancer diagnosis are inappropriate for reconstructing the natural breast shape in a standing position because they are taken in a lying position. Some studies have proposed methods to present the breast shape in a standing position using ordinary differential equation of the finite element method. However, it is difficult to obtain meaningful results because breast tissues have different elastic moduli. This study proposed a multi-class semantic segmentation method for breast tissues to reconstruct breast shape using U-Net based on Haar wavelet pooling. First, a dataset was constructed by labeling the skin, fat, and fibro-glandular tissues and the background from MRI images taken in a lying position. Next, multi-class semantic segmentation was performed using U-Net based on Haar wavelet pooling to improve the segmentation accuracy for breast tissues. The U-Net based on Haar wavelet pooling effectively extracted breast tissue features while reducing information loss of the image in a subsampling stage using multiple sub-bands. In addition, the proposed network is robust to overfitting. The proposed network showed an mIOU of 87.48 for segmenting breast tissues. The proposed networks showed high-accuracy segmentation for breast tissue with different elastic moduli to reconstruct the natural breast shape.\u003c/p\u003e","manuscriptTitle":"Multi-class semantic segmentation of breast tissues from MRI images using U-Net based on Haar wavelet pooling","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-01-18 15:38:49","doi":"10.21203/rs.3.rs-2465906/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Major revision","date":"2023-03-13T16:22:14+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2023-02-18T22:34:45+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"515bf2d1-6eeb-4389-aff2-3de0025b1125","date":"2023-02-08T12:43:39+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2023-02-05T13:09:09+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"4cdd91b6-0d67-4410-84b4-ea8cc0f1716f","date":"2023-01-28T06:32:42+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"87147799-cec2-4684-81dc-337b675ec8ed","date":"2023-01-26T08:11:41+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2023-01-24T15:16:43+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2023-01-24T15:12:38+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2023-01-16T13:38:39+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2023-01-16T13:28:48+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2023-01-11T07:25:24+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"29a8f74d-2446-47b6-884e-0b3be8adf2d1","owner":[],"postedDate":"January 18th, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":18443477,"name":"Biological sciences/Cancer/Breast cancer"},{"id":18443478,"name":"Biological sciences/Cancer/Cancer imaging"},{"id":18443479,"name":"Physical sciences/Engineering/Electrical and electronic engineering"}],"tags":[],"updatedAt":"2023-10-16T22:05:37+00:00","versionOfRecord":{"articleIdentity":"rs-2465906","link":"https://doi.org/10.1038/s41598-023-38557-0","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2023-07-20 21:40:14","publishedOnDateReadable":"July 20th, 2023"},"versionCreatedAt":"2023-01-18 15:38:49","video":"","vorDoi":"10.1038/s41598-023-38557-0","vorDoiUrl":"https://doi.org/10.1038/s41598-023-38557-0","workflowStages":[]},"version":"v1","identity":"rs-2465906","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2465906","identity":"rs-2465906","version":["v1"]},"buildId":"_2-kVJe1T_tPrBINL-cwx","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}