一種基於熵加權局部強度聚類的不均勻影像分割模型

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姓名

廖唯廷(Wei-Ting Liao) 查詢紙本館藏

畢業系所

數學系

論文名稱

一種基於熵加權局部強度聚類的不均勻影像分割模型
(An entropy-weighted local intensity clustering-based model for inhomogeneous image segmentation)

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摘要(中)

本文研究一種以熵加權局部強度聚類為基礎的不均勻影像分割模型，用於分割因為採集過程偏置場所產生的強度不均勻影像。該模型最小化一個由分割區域邊界總長度的正則化項和局部熵加權的數據擬合項所組成的能量泛函，其中分割邊界的長度由熱核與分割區域的特徵函數進行卷積來近似，而數據擬合項由偏置場模型與局部強度聚類性質相結合後，再進一步由局部熵加權所產生。最終所得出的熵加權模型可以同時分割影像並估計用於校正強度不均勻影像的偏置場。此外，所考慮的熵加權模型可以應用迭代卷積閾值法有效地實現。最後，我們進行一系列數值實驗以展示所提出方法的有效性與穩健性。

摘要(英)

In this thesis, we study an entropy-weighted local intensity clustering-based model for inhomogeneous image segmentation. The intensity inhomogeneity mainly arises from the bias field in improper image acquisition. The considered model minimizes an energy functional consisting of a regularization term for the total length of the segmentation boundary and a data fitting term weighted by local entropy. The total length is approximated by the convolution of the heat kernel and the characteristic functions of the segmentation regions. The data fitting term is generated by combining the bias field model and the local intensity clustering property, further weighted by the local entropy. The model can simultaneously segment the inhomogeneous image and estimate the bias field for image correction. Furthermore, we can efficiently realize the model using an iterative convolution-thresholding scheme. Finally, we conduct many numerical experiments to demonstrate the effectiveness and robustness of the method.

關鍵字(中)

★ 影像分割
★ 強度不均勻影像
★ 偏置校正
★ 強度聚類
★ 局部熵
★ 迭代卷積閾值法

關鍵字(英)

★ image segmentation
★ intensity inhomogeneity
★ bias correction
★ intensity clustering
★ local entropy
★ iterative convolution-thresholding scheme

論文目次

摘要 i
Abstract ii
1 前言 1
2 Mumford-Shah模型和Chan-Vese模型 4
2.1 Mumford-Shah模型 4
2.2 水平集函數 4
2.3 Chan-Vese模型 5
3 熵加權局部強度聚類為基礎的影像分割模型 8
3.1 局部聚類性質 8
3.2 局部熵 9
3.3 迭代卷積閾值法 10
4 數值實驗 16
4.1 實驗1 (二相分割) 16
4.2 實驗2 (三相分割) 16
4.3 實驗3 (初始特徵函數選取的穩健性) 19
4.4 實驗4 (對噪聲的穩健性) 19
4.5 實驗參數 22
5 結語 23
參考文獻 25

參考文獻

[1] G. Alberti and G. Bellettini, A non-local anisotropic model for phase transitions: asymptotic behaviour of rescaled energies, European Journal of Applied Mathematics, 9 (1998), pp. 261-284.
[2] G. Aubert and P. Kornprobst, Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations, Second Edition, Springer-Verlag, New York, 2006.
[3] V. Caselles, R. Kimmel, and G. Sapiro, Geodesic active contours, International Journal of Computer Vision, 22 (1997), pp. 61-79.
[4] T. F. Chan and J. Shen, Image Processing and Analysis: Variational, PDE, Wavelet and Stochastic Methods, Society for Industrial and Applied Mathematics, Philadelphia, 2005.
[5] T. F. Chan and L. A. Vese, An active contour model without edges, Lecture Notes in Computer Science, 1682 (1999), pp. 141-151.
[6] T. F. Chan and L. A. Vese, Active contours without edges, IEEE Transactions on Image Processing, 10 (2001), pp. 266-277.
[7] S. Esedog ̅lu and F. Otto, Threshold dynamics for networks with arbitrary surface tensions, Communications on Pure and Applied Mathematics, 68 (2015), pp. 808-864.
[8] P. Getreuer, Chan-Vese segmentation, Image Processing On Line, 2 (2012), pp. 214-224.
[9] R. C. Gonzalez and R. E. Woods, Digital Image Processing, Fourth Edition, Pearson Education Limited, New York, 2018.
[10] C. He, Y. Wang, and Q. Chen, Active contours driven by weighted region-scalable fitting energy based on local entropy, Signal Processing, 92 (2012), pp. 587-600.
[11] P.-W. Hsieh, P.-C. Shao, and S.-Y. Yang, Advection-enhanced gradient vector flow for active-contour image segmentation, Communications in Computational Physics, 26 (2019), pp. 206-232.
[12] M. Kass, A.Witkin, and D.Terzopoulos, Snakes: active contour models, International Journal of Computer Vision, 1 (1987), pp. 321-331.
[13] C. Li, R. Huang, Z. Ding, J. C. Gatenby, D. N. Metaxas, and J. C. Gore, A level set method for image segmentation in the presence of intensity inhomogeneities with application to MRI, IEEE Transactions on Image Processing, 20 (2011), pp. 2007-2016.
[14] C. Li, C. Kao, J. C. Gore, and Z. Ding, Minimization of region-scalable fitting energy for image segmentation, IEEE Transactions on Image Processing, 17 (2008), pp. 1940-1949.
[15] W.-T. Liao, S.-Y. Yang, and C.-S. You, An entropy-weighted local intensity clustering-based model for intensity inhomogeneous image segmentation, Preprint, 2021.
[16] A. Mitiche and I. B. Ayed, Variational and Level Set Methods in Image Segmentation, Vol. 5, Springer-Verlag, Berlin & Heidelberg, 2010.
[17] D. Mumford and J. Shah, Optimal approximations by piecewise smooth functions and associated variational problems, Communications on Pure and Applied Mathematics, 42 (1989), pp. 577-685.
[18] S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, 79 (1988), pp. 12-49.
[19] A. P. S. Pharwaha and B. Singh, Shannon and non-Shannon measures of entropy for statistical texture feature extraction in digitized mammograms, Proceedings of the World Congress on Engineering and Computer Science, 2 (2009), 6 pages.
[20] L. I. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D, 60 (1992), pp. 259-268.
[21] S. Song, Y. Zheng, and Y. He, A review of methods for bias correction in medical images, Biomedical Engineering Review, 1 (2017), 10 pages.
[22] J. Tang and X. Jiang, A variational level set approach based on local entropy for image segmentation and bias field correction, Computational and Mathematical Methods in Medicine, (2017), Article ID 9174275, 15 pages.
[23] D. Wang and X.-P. Wang, The iterative convolution-thresholding method (ICTM) for image segmentation, arXiv:1904.10917v1 [cs.CV], 24 April 2019.
[24] D. Wang, H. Li, X. Wei, and X.-P. Wang, An efficient iterative thresholding method for image segmentation, Journal of Computational Physics, 350 (2017), pp. 657-667.
[25] R. Wojcik and D. Krapf, Solid-state nanopore recognition and measurement using Shannon entropy, IEEE Photonics Journal, 3 (2011), pp. 337-343.
[26] C. Xu and J. L. Prince, Snakes, shapes, and gradient vector flow, IEEE Transactions on Image Processing, 7 (1998), pp. 359-369.
[27] K. Zhang, L. Zhang, K.-M. Lam, and D. Zhang, A level set approach to image segmentation with intensity inhomogeneity, IEEE Transactions on Cybernetics, 46 (2016), pp. 546-557.

指導教授

楊肅煜(Suh-Yuh Yang)

審核日期

2022-7-13

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