Weighted area constraints-based breast lesion segmentation in ultrasound image analysis

Qianting Ma; Tieyong Zeng; Dexing Kong; Jianwei Zhang

doi:10.3934/ipi.2021057

Article Contents

2022, Volume 16, Issue 2: 451-466. 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
^* Corresponding author: Qianting Ma

Received: November 2020

Revised: June 2021

Early access: September 2021

Published: April 2022

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)

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Abstract

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.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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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

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Figure 2. The plot of function $ \cos^{\mathbf{p}}(\pi s) $

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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

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Figure 4. The dependence of $ JI $ and $ DS $ on the value of $ \nu $ and K

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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

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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

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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

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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

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Figure 9. Box plot of the (a) $ JI $ for segmentation algorithms, (b) $ DS $ for segmentation algorithms

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Figure 10. Bar chart of the computional time for different algorithms

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