doi: 10.3934/ipi.2021057
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Weighted area constraints-based breast lesion segmentation in ultrasound image analysis

1. 

School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Jiangsu 210044, China

2. 

Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, China

3. 

School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China

* Corresponding author: Qianting Ma

Received  November 2020 Revised  June 2021 Early access September 2021

Fund Project: The work of Qianting Ma is supported by the National Natural Science Foundation of China (Grant No. 61902192), the High-Level Innovative and entrepreneurial project in Jiangsu Province, China (Jiangsu Personnel Office Document, No. [2019]20), and the Startup Foundation for Introducing Talent of NUIST (Grant No. 1131111901015). The work of Tieyong Zeng is supported by the National Key R&D Program of China under Grant 2021YFE0203700, Grant NSFC/RGC N_CUHK 415/19, Grant RGC 14300219, 14302920, 14301121, and CUHK Direct Grant for Research under Grant 4053405, 4053460. The work of Dexing Kong is supported by the National Natural Science Foundation of China (Grant Nos. 12090020 and 12090025)

Breast ultrasound segmentation is a challenging task in practice due to speckle noise, low contrast and blurry boundaries. Although numerous methods have been developed to solve this problem, most of them can not produce a satisfying result due to uncertainty of the segmented region without specialized domain knowledge. In this paper, we propose a novel breast ultrasound image segmentation method that incorporates weighted area constraints using level set representations. Specifically, we first use speckle reducing anisotropic diffusion filter to suppress speckle noise, and apply the Grabcut on them to provide an initial segmentation result. In order to refine the resulting image mask, we propose a weighted area constraints-based level set formulation (WACLSF) to extract a more accurate tumor boundary. The major contribution of this paper is the introduction of a simple nonlinear constraint for the regularization of probability scores from a classifier, which can speed up the motion of zero level set to move to a desired boundary. Comparisons with other state-of-the-art methods, such as FCN-AlexNet and U-Net, show the advantages of our proposed WACLSF-based strategy in terms of visual view and accuracy.

Citation: Qianting Ma, Tieyong Zeng, Dexing Kong, Jianwei Zhang. Weighted area constraints-based breast lesion segmentation in ultrasound image analysis. Inverse Problems & Imaging, doi: 10.3934/ipi.2021057
References:
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Y. Chen and M. Wu, A level set method for brain MR image segmentation under asymmetric distributions, Signal, Image and Video Processing, 13 (2019), 1421-1429.  doi: 10.1007/s11760-019-01491-8.  Google Scholar

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M. I. DaoudA. A. AtallahF. AwwadM. AI-Najjar and R. Alazrai, Automatic superpixel-based segmentation method for breast ultrasound images, Expert Systems with Applications, 121 (2019), 78-96.  doi: 10.1016/j.eswa.2018.11.024.  Google Scholar

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M. Elawady, I. Sadek, A. E. R. Shabayek, G. Pons and S. Ganau, Automatic nonlinear filtering and segmentation for breast ultrasound images, International Conference on Image Analysis and Recognition, Springer, Cham, (2016), 206–213. doi: 10.1007/978-3-319-41501-7_24.  Google Scholar

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W. GomezL. LeijaA. V. AlvarengaA. F. C. Infantosi and W. C. A. Pereira, Computerized lesion segmentation of breast ultrasound based on marker-controlled watershed transformation, Medical Physics, 37 (2010), 82-95.  doi: 10.1118/1.3265959.  Google Scholar

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W. Gómez-Flores and W. Pereira, A comparative study of pre-trained convolutional neural networks for semantic segmentation of breast tumors in ultrasound, Computers in Biology and Medicine, 126 (2020), 104036.  doi: 10.1016/j.compbiomed.2020.104036.  Google Scholar

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W. Gómez-Flores and B. A. Ruiz-Ortega, New fully automated method for segmentation of breast lesions on ultrasound based on texture analysis, Ultrasound in Medicine and Biology, 42 (2016), 1637-1650.  doi: 10.1016/j.ultrasmedbio.2016.02.016.  Google Scholar

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Y.-C. Lin, Y.-L. Huang and D.-R. Chen, Breast tumor segmentation based on level-set method in 3D sonography, In 2013 Seventh International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing. IEEE, (2013), 637–640. doi: 10.1109/IMIS.2013.114.  Google Scholar

[20]

Y. LiuY. ChenB. HanY. ZhangX. Zhang and Y. Su, Fully automatic breast ultrasound image segmentation based on fuzzy cellular automata framework, Biomedical Signal Processing and Control, 40 (2018), 433-442.  doi: 10.1016/j.bspc.2017.09.014.  Google Scholar

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Q. Ma, Image denoising via time-delay regularization coupled nonlinear diffusion equations, Journal of Computational Mathematics, 38 (2020), 417-436.  doi: 10.4208/jcm.1811-m2016-0763.  Google Scholar

[22]

Q. MaF. Dong and D. Kong, A fractional differential fidelity-based PDE model for image denoising, Machine Vision and Applications, 28 (2017), 635-647.  doi: 10.1007/s00138-017-0857-z.  Google Scholar

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J. MaF. WuT. JiangQ. Zhao and D. Kong, Ultrasound image-based thyroid nodule automatic segmentation using convolutional neural networks, International Journal of Computer Assisted Radiology and Surgery, 12 (2017), 1895-1910.  doi: 10.1007/s11548-017-1649-7.  Google Scholar

[24]

W. K. MoonY.-W. LeeH.-H. KeS. H. LeeC.-S. Huang and R.-F. Chang, Computer-aided diagnosis of breast ultrasound images using ensemble learning from convolutional neural networks, Computer Methods and Programs in Biomedicine, 190 (2020), 105361.  doi: 10.1016/j.cmpb.2020.105361.  Google Scholar

[25]

N. I. NizamS. R. Ara and M. K. Hasan, Classification of breast lesions using quantitative ultrasound biomarkers, Biomedical Signal Processing and Control, 57 (2020), 101786.  doi: 10.1016/j.bspc.2019.101786.  Google Scholar

[26]

Z.-F. PangH.-L. ZhangS. Luo and T. Zeng, Image denoising based on the adaptive weighted $TV^{p}$ regularization, Signal Processing, 167 (2020), 107325.  doi: 10.1016/j.sigpro.2019.107325.  Google Scholar

[27]

P. Perona and J. Malik, Scale-space and edge detection using anisotropic diffusion, IEEE Transactions on Pattern Analysis Machine Intelligence, 12 (1990), 629-639.  doi: 10.1109/34.56205.  Google Scholar

[28]

A. PratondoC.-K. Chui and S.-H. Ong, Robust edge-stop functions for edge-based active contour models in medical image segmentation, IEEE Signal Processing Letters, 23 (2016), 222-226.  doi: 10.1109/LSP.2015.2508039.  Google Scholar

[29]

A. PratondoC.-K. Chui and S.-H. Ong, Integrating machine learning with region-based active contour models in medical image segmentation, Journal of Visual Communication and Image Representation, 43 (2017), 1-9.  doi: 10.1016/j.jvcir.2016.11.019.  Google Scholar

[30]

R. RodriguesR. BrazM. PereiraJ. Moutinho and A. M. G. Pinheiro, A two-step segmentation method for breast ultrasound masses based on multi-resolution analysis, Ultrasound in Medicine and Biology, 41 (2015), 1737-1748.  doi: 10.1016/j.ultrasmedbio.2015.01.012.  Google Scholar

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[32]

C. RotherV. Kolmogorov and A. Blake, "GrabCut" interactive foreground extraction using iterated graph cuts, ACM Transactions on Graphics, 23 (2004), 309-314.  doi: 10.1145/1015706.1015720.  Google Scholar

[33]

I. Sadek, M. Elawady and V. Stefanovski, Automated breast lesion segmentation in ultrasound images, arXiv preprint, arXiv: 1609.08364, (2016). Google Scholar

[34]

J. ShanH. D. Cheng and Y. Wang, Completely automated segmentation approach for breast ultrasound images using multiple-domain features, Ultrasound in Medicine and Biology, 38 (2012), 262-275.  doi: 10.1016/j.ultrasmedbio.2011.10.022.  Google Scholar

[35]

E. ShelhamerJ. Long and T. Darrell, Fully convolutional networks for semantic segmentation, IEEE Transactions on Pattern Analysis and Machine Intelligence, 39 (2017), 640-651.  doi: 10.1109/TPAMI.2016.2572683.  Google Scholar

[36]

M. TanF. WuD. Kong and X. Mao, Automatic liver segmentation using 3D convolutional neural networks with a hybrid loss function, Medical Physics, 48 (2021), 1707-1719.  doi: 10.1002/mp.14732.  Google Scholar

[37]

F. Torres, Z. Fanti and F. A. Cosío, 3D freehand ultrasound for medical assistance in diagnosis and treatment of breast cancer: Preliminary results, IX International Seminar on Medical Information Processing and Analysis, International Society for Optics and Photonics, 8922 (2013), 89220K. doi: 10.1117/12.2041806.  Google Scholar

[38]

L. WangL. HeMishra Arabinda and C. Li, Active contours driven by local Gaussian distribution fitting energy, Signal Processing, 89 (2009), 2435-2447.  doi: 10.1016/j.sigpro.2009.03.014.  Google Scholar

[39]

Y. XuY. WangJ. YuanQ. ChengX. Wang and P. L. Carson, Medical breast ultrasound image segmentation by machine learning, Ultrasonics, 91 (2019), 1-9.  doi: 10.1016/j.ultras.2018.07.006.  Google Scholar

[40]

M. YapM. GoyalF. OsmanR. MartíE. DentonA. Juette and R. Zwiggelaar, Breast ultrasound lesions recognition: End-to-end deep learning approaches, Journal of Medical Imaging, 6 (2018), 1-8.   Google Scholar

[41]

J. YangC. LouJ. Fu and C. Feng, Vessel segmentation using multiscale vessel enhancement and a region based level set model, Computerized Medical Imaging and Graphics, 85 (2020), 101783.  doi: 10.1016/j.compmedimag.2020.101783.  Google Scholar

[42]

W. YangY. ShiS. H. ParkM. YangY. Gao and D. Shen, An effective MR-Guided CT network training for segmenting prostate in CT images, IEEE Journal of Biomedical and Health Informatics, 24 (2020), 2278-2291.  doi: 10.1109/JBHI.2019.2960153.  Google Scholar

[43]

Y. YangR. Wang and C. Feng, Level set formulation for automatic medical image segmentation based on fuzzy clustering, Signal Processing: Image Communication, 87 (2020), 115907.  doi: 10.1016/j.image.2020.115907.  Google Scholar

[44]

Y. Yu and S. T. Acton, Speckle reducing anisotropic diffusion, IEEE Transactions on Image Processing, 11 (2002), 1260-1270.  doi: 10.1109/TIP.2002.804276.  Google Scholar

show all references

References:
[1]

T. F. Chan and L. A. Vese, Active contours without edges, IEEE Transactions on Image Processing, 10 (2001), 266-277.  doi: 10.1109/83.902291.  Google Scholar

[2]

Y. Chen and M. Wu, A level set method for brain MR image segmentation under asymmetric distributions, Signal, Image and Video Processing, 13 (2019), 1421-1429.  doi: 10.1007/s11760-019-01491-8.  Google Scholar

[3]

M. I. DaoudA. A. AtallahF. AwwadM. AI-Najjar and R. Alazrai, Automatic superpixel-based segmentation method for breast ultrasound images, Expert Systems with Applications, 121 (2019), 78-96.  doi: 10.1016/j.eswa.2018.11.024.  Google Scholar

[4]

M. Elawady, I. Sadek, A. E. R. Shabayek, G. Pons and S. Ganau, Automatic nonlinear filtering and segmentation for breast ultrasound images, International Conference on Image Analysis and Recognition, Springer, Cham, (2016), 206–213. doi: 10.1007/978-3-319-41501-7_24.  Google Scholar

[5]

Y. Fang and T. Zeng, Learning deep edge prior for image denoising, Computer Vision and Image Understanding, 200 (2020), 103044.  doi: 10.1016/j.cviu.2020.103044.  Google Scholar

[6]

W. GomezL. LeijaA. V. AlvarengaA. F. C. Infantosi and W. C. A. Pereira, Computerized lesion segmentation of breast ultrasound based on marker-controlled watershed transformation, Medical Physics, 37 (2010), 82-95.  doi: 10.1118/1.3265959.  Google Scholar

[7]

W. Gómez-Flores and W. Pereira, A comparative study of pre-trained convolutional neural networks for semantic segmentation of breast tumors in ultrasound, Computers in Biology and Medicine, 126 (2020), 104036.  doi: 10.1016/j.compbiomed.2020.104036.  Google Scholar

[8]

W. Gómez-Flores and B. A. Ruiz-Ortega, New fully automated method for segmentation of breast lesions on ultrasound based on texture analysis, Ultrasound in Medicine and Biology, 42 (2016), 1637-1650.  doi: 10.1016/j.ultrasmedbio.2016.02.016.  Google Scholar

[9]

L. GuiC. Li and X. Yang, Medical image segmentation based on level set and isoperimetric constraint, Physica Medica, 42 (2017), 162-173.  doi: 10.1016/j.ejmp.2017.09.123.  Google Scholar

[10]

L. HanY. HuangH. DouS. WangS. AhamadH. LuoQ. LiuJ. Fan and J. Zhang, Semi-supervised segmentation of lesion from breast ultrasound images with attentional generative adversarial network, Computer Methods and Programs in Biomedicine, 189 (2020), 105275.  doi: 10.1016/j.cmpb.2019.105275.  Google Scholar

[11]

Y.-M. HuangL. MoisanM. K. Ng and T. Zeng, Multiplicative noise removal via a learned dictionary, IEEE Transactions on Image Processing, 21 (2012), 4534-4543.  doi: 10.1109/TIP.2012.2205007.  Google Scholar

[12]

F. JiaX.-C. Tai and J. Liu, Nonlocal regularized CNN for image segmentation, Inverse Problems and Imaging, 14 (2020), 891-911.  doi: 10.3934/ipi.2020041.  Google Scholar

[13]

J. M. KellerM. R. Gray and J. A. Givens, A fuzzy k-nearest neighbor algorithm, IEEE Transactions on Systems, Man, and Cybernetics, 4 (1985), 580-585.  doi: 10.1109/TSMC.1985.6313426.  Google Scholar

[14]

A. KrizhevskyI. Sutskever and G. E. Hinton, ImageNet classification with deep convolutional neural networks, Communications of the ACM, 60 (2017), 84-90.  doi: 10.1145/3065386.  Google Scholar

[15]

C. LiC. XuC. Gui and M. D. Fox, Distance regularized level set evolution and its application to image segmentation, IEEE Transactions on Image Processing, 19 (2010), 3243-3254.  doi: 10.1109/TIP.2010.2069690.  Google Scholar

[16]

L. LiS. LuoX.-C. Tai and J. Yang, A new variational approach based on level-set function for convex hull problem with outliers, Inverse Problems and Imaging, 15 (2021), 315-338.  doi: 10.3934/ipi.2020070.  Google Scholar

[17]

L. Liu, W. Qin, R. Yang, C. Yu, L. Li, T. Wen and J. Gu, Segmentation of breast ultrasound image using graph cuts and level set, IET International Conference on Biomedical Image and Signal Processing, (2015), 1–4. doi: 10.1049/cp.2015.0773.  Google Scholar

[18]

X. Li, C. Yang and S. Wu, Automatic segmentation algorithm of breast ultrasound image based on improved level set algorithm, IEEE International Conference on Signal and Image Processing, (2016), 319–322. doi: 10.1109/SIPROCESS.2016.7888276.  Google Scholar

[19]

Y.-C. Lin, Y.-L. Huang and D.-R. Chen, Breast tumor segmentation based on level-set method in 3D sonography, In 2013 Seventh International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing. IEEE, (2013), 637–640. doi: 10.1109/IMIS.2013.114.  Google Scholar

[20]

Y. LiuY. ChenB. HanY. ZhangX. Zhang and Y. Su, Fully automatic breast ultrasound image segmentation based on fuzzy cellular automata framework, Biomedical Signal Processing and Control, 40 (2018), 433-442.  doi: 10.1016/j.bspc.2017.09.014.  Google Scholar

[21]

Q. Ma, Image denoising via time-delay regularization coupled nonlinear diffusion equations, Journal of Computational Mathematics, 38 (2020), 417-436.  doi: 10.4208/jcm.1811-m2016-0763.  Google Scholar

[22]

Q. MaF. Dong and D. Kong, A fractional differential fidelity-based PDE model for image denoising, Machine Vision and Applications, 28 (2017), 635-647.  doi: 10.1007/s00138-017-0857-z.  Google Scholar

[23]

J. MaF. WuT. JiangQ. Zhao and D. Kong, Ultrasound image-based thyroid nodule automatic segmentation using convolutional neural networks, International Journal of Computer Assisted Radiology and Surgery, 12 (2017), 1895-1910.  doi: 10.1007/s11548-017-1649-7.  Google Scholar

[24]

W. K. MoonY.-W. LeeH.-H. KeS. H. LeeC.-S. Huang and R.-F. Chang, Computer-aided diagnosis of breast ultrasound images using ensemble learning from convolutional neural networks, Computer Methods and Programs in Biomedicine, 190 (2020), 105361.  doi: 10.1016/j.cmpb.2020.105361.  Google Scholar

[25]

N. I. NizamS. R. Ara and M. K. Hasan, Classification of breast lesions using quantitative ultrasound biomarkers, Biomedical Signal Processing and Control, 57 (2020), 101786.  doi: 10.1016/j.bspc.2019.101786.  Google Scholar

[26]

Z.-F. PangH.-L. ZhangS. Luo and T. Zeng, Image denoising based on the adaptive weighted $TV^{p}$ regularization, Signal Processing, 167 (2020), 107325.  doi: 10.1016/j.sigpro.2019.107325.  Google Scholar

[27]

P. Perona and J. Malik, Scale-space and edge detection using anisotropic diffusion, IEEE Transactions on Pattern Analysis Machine Intelligence, 12 (1990), 629-639.  doi: 10.1109/34.56205.  Google Scholar

[28]

A. PratondoC.-K. Chui and S.-H. Ong, Robust edge-stop functions for edge-based active contour models in medical image segmentation, IEEE Signal Processing Letters, 23 (2016), 222-226.  doi: 10.1109/LSP.2015.2508039.  Google Scholar

[29]

A. PratondoC.-K. Chui and S.-H. Ong, Integrating machine learning with region-based active contour models in medical image segmentation, Journal of Visual Communication and Image Representation, 43 (2017), 1-9.  doi: 10.1016/j.jvcir.2016.11.019.  Google Scholar

[30]

R. RodriguesR. BrazM. PereiraJ. Moutinho and A. M. G. Pinheiro, A two-step segmentation method for breast ultrasound masses based on multi-resolution analysis, Ultrasound in Medicine and Biology, 41 (2015), 1737-1748.  doi: 10.1016/j.ultrasmedbio.2015.01.012.  Google Scholar

[31]

O. Ronneberger, P. Fischer and T. Brox, U-net: Convolutional networks for biomedical image segmentation, International Conference on Medical Image Computing and Computer-assisted Intervention, Springer, Cham, (2015), 234–241. doi: 10.1007/978-3-319-24574-4_28.  Google Scholar

[32]

C. RotherV. Kolmogorov and A. Blake, "GrabCut" interactive foreground extraction using iterated graph cuts, ACM Transactions on Graphics, 23 (2004), 309-314.  doi: 10.1145/1015706.1015720.  Google Scholar

[33]

I. Sadek, M. Elawady and V. Stefanovski, Automated breast lesion segmentation in ultrasound images, arXiv preprint, arXiv: 1609.08364, (2016). Google Scholar

[34]

J. ShanH. D. Cheng and Y. Wang, Completely automated segmentation approach for breast ultrasound images using multiple-domain features, Ultrasound in Medicine and Biology, 38 (2012), 262-275.  doi: 10.1016/j.ultrasmedbio.2011.10.022.  Google Scholar

[35]

E. ShelhamerJ. Long and T. Darrell, Fully convolutional networks for semantic segmentation, IEEE Transactions on Pattern Analysis and Machine Intelligence, 39 (2017), 640-651.  doi: 10.1109/TPAMI.2016.2572683.  Google Scholar

[36]

M. TanF. WuD. Kong and X. Mao, Automatic liver segmentation using 3D convolutional neural networks with a hybrid loss function, Medical Physics, 48 (2021), 1707-1719.  doi: 10.1002/mp.14732.  Google Scholar

[37]

F. Torres, Z. Fanti and F. A. Cosío, 3D freehand ultrasound for medical assistance in diagnosis and treatment of breast cancer: Preliminary results, IX International Seminar on Medical Information Processing and Analysis, International Society for Optics and Photonics, 8922 (2013), 89220K. doi: 10.1117/12.2041806.  Google Scholar

[38]

L. WangL. HeMishra Arabinda and C. Li, Active contours driven by local Gaussian distribution fitting energy, Signal Processing, 89 (2009), 2435-2447.  doi: 10.1016/j.sigpro.2009.03.014.  Google Scholar

[39]

Y. XuY. WangJ. YuanQ. ChengX. Wang and P. L. Carson, Medical breast ultrasound image segmentation by machine learning, Ultrasonics, 91 (2019), 1-9.  doi: 10.1016/j.ultras.2018.07.006.  Google Scholar

[40]

M. YapM. GoyalF. OsmanR. MartíE. DentonA. Juette and R. Zwiggelaar, Breast ultrasound lesions recognition: End-to-end deep learning approaches, Journal of Medical Imaging, 6 (2018), 1-8.   Google Scholar

[41]

J. YangC. LouJ. Fu and C. Feng, Vessel segmentation using multiscale vessel enhancement and a region based level set model, Computerized Medical Imaging and Graphics, 85 (2020), 101783.  doi: 10.1016/j.compmedimag.2020.101783.  Google Scholar

[42]

W. YangY. ShiS. H. ParkM. YangY. Gao and D. Shen, An effective MR-Guided CT network training for segmenting prostate in CT images, IEEE Journal of Biomedical and Health Informatics, 24 (2020), 2278-2291.  doi: 10.1109/JBHI.2019.2960153.  Google Scholar

[43]

Y. YangR. Wang and C. Feng, Level set formulation for automatic medical image segmentation based on fuzzy clustering, Signal Processing: Image Communication, 87 (2020), 115907.  doi: 10.1016/j.image.2020.115907.  Google Scholar

[44]

Y. Yu and S. T. Acton, Speckle reducing anisotropic diffusion, IEEE Transactions on Image Processing, 11 (2002), 1260-1270.  doi: 10.1109/TIP.2002.804276.  Google Scholar

Figure 1.  The basic idea of our proposed method. (a) Original image; (b) Red regions and green regions are denoted as the definitely foreground and unknown regions, respectively; (c) Blue regions are denoted as pixels belonging to foreground that are picked from unknown regions (green regions); (d) A result achieved by our proposed method
Figure 2.  The plot of function $ \cos^{\mathbf{p}}(\pi s) $
Figure 3.  Steps involved in segmenting breast tumors using our proposed method. (a) Input image, (b) smoothed image, (c) foreground extracted image using Grabcut, (d) clusters formed using k-means, (e) marked image, (f) initial contour constructed from (d), (g) regularization for classifier probability scores, pixels with high confidence of being foreground are in white, and those with low confidence are in black, gray regions refers to pixels whose scores are close to $ 0.5 $, (h) segmented breast tumor region overlapped with original image
Figure 4.  The dependence of $ JI $ and $ DS $ on the value of $ \nu $ and K
6], (d) Torres et al [37], (e) Wilfrido et al [8], (f) Sadek et al [33], (g) Elawady et al [4], (h) Ours, (i) Initial contour, (j) Marked image">Figure 5.  Comparisons of different methods on breast ultrasound images.(a) Input image, (b) Ground truth, (c) Gomez et al [6], (d) Torres et al [37], (e) Wilfrido et al [8], (f) Sadek et al [33], (g) Elawady et al [4], (h) Ours, (i) Initial contour, (j) Marked image
6], (d) Torres et al [37], (e) Wilfrido et al [8], (f) Sadek et al [33], (g) Elawady et al [4], (h) Ours, (i) Initial contour, (j) Marked image">Figure 6.  Comparisons of different methods on breast ultrasound images. (a) Input image, (b) Ground truth, (c) Gomez et al [6], (d) Torres et al [37], (e) Wilfrido et al [8], (f) Sadek et al [33], (g) Elawady et al [4], (h) Ours, (i) Initial contour, (j) Marked image
38], (d) FCN-AlexNet[7], (e) U-Net[31], (f) Ours">Figure 7.  The comparison of different methods on breast ultrasound images. (a) Original image, (b) Ground Truth, (c) LGD[38], (d) FCN-AlexNet[7], (e) U-Net[31], (f) Ours
6], (d) Wilfrido et al [8], (e) Elawady et al [4], (f) Ours">Figure 8.  The comparison of different methods on breast ultrasound images. (a) Input image, (b) Ground truth, (c) Gomez et al [6], (d) Wilfrido et al [8], (e) Elawady et al [4], (f) Ours
Figure 9.  Box plot of the (a) $ JI $ for segmentation algorithms, (b) $ DS $ for segmentation algorithms
Figure 10.  Bar chart of the computional time for different algorithms
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