August  2011, 5(3): 645-657. doi: 10.3934/ipi.2011.5.645

A fast algorithm for global minimization of maximum likelihood based on ultrasound image segmentation

1. 

Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China, China

2. 

Department of Mathematics, University of Florida, Gainesville, FL 32611

Received  November 2010 Revised  April 2011 Published  August 2011

This paper presents a novel variational model for ultrasound image segmentation that uses a maximum likelihood estimator based on Fisher-Tippett distribution of the intensities of ultrasound images. A convex relaxation method is applied to get a convex model of the subproblem with fixed distribution parameters. The relaxed subproblem, which is convex, can be fast solved by using a primal-dual hybrid gradient algorithm. The experimental results on simulated and real ultrasound images indicate the effectiveness of the method presented.
Citation: Jie Huang, Xiaoping Yang, Yunmei Chen. A fast algorithm for global minimization of maximum likelihood based on ultrasound image segmentation. Inverse Problems and Imaging, 2011, 5 (3) : 645-657. doi: 10.3934/ipi.2011.5.645
References:
[1]

V. Caselles, R. Kimmel and G. Sapiro, On geodesic active contours, Int. J. Comput. Vis., 22 (1997), 61-79. doi: 10.1023/A:1007979827043.

[2]

D. Mumford and J. Shah, Optimal approximation by piecewise smooth functions and associated variational problems, Commun. Pure Appl. Math, 42 (1989), 577-685. doi: 10.1002/cpa.3160420503.

[3]

S. C. Zhu and A. Yuille, Region competition: Unifying snakes, region growing, and Bayes/MDL for multiband image segmentation, IEEE PAMI, 18 (1996), 884-900. doi: 10.1109/34.537343.

[4]

N. Paragios and R. Deriche, Geodesic active regions and level set methods for supervised texture segmentation, Int. J. Computer Vision, 46 (2002), 223-247. doi: 10.1023/A:1014080923068.

[5]

T. F. Chan and L. A. Vese, Active contoure without edges, IEEE Trans. Image Processing, 10 (2001), 266-277. doi: 10.1109/83.902291.

[6]

I. B. Ayed, C. Vazquez, A. Mitiche and Z. Belhadj, SAR image segmentation with active contours and level sets, Proceedings of IEEE Intl. Conf. Image Process (ICIP), 4 (2004), 2717-2720.

[7]

Zhong Tao and H. D. Tagare, Evaluation of four probability distribution models for speckle in clinical cardic ultrasound images, IEEE Trans. Medical Imaging, 25 (2006), 1483-1491. doi: 10.1109/TMI.2006.881376.

[8]

A. Sarti, C. Corsi and E. Mazzini, Maximum likelihood segmentation of ultrasound images with Rayleigh distribution, IEEE Trans. Ultrasonics Ferroelectrics and Frequency Control, 52 (2005), 947-960. doi: 10.1109/TUFFC.2005.1504017.

[9]

J. M. Thijssen, Ultrasonic speckle formation, analysis and processing applied to tissue characterization, Pattern Recognition Letters, 24 (2003), 659-675. doi: 10.1016/S0167-8655(02)00173-3.

[10]

S. Osher, J. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys., 79 (1988), 12-49. doi: 10.1016/0021-9991(88)90002-2.

[11]

T. F. Chan, S. Esedoḡlu and M. Nikolova, Algorithms for finding global minimizers of image segmentation and denoising models, SIAM J. Appl. Math, 66 (2006), 1632-1648. doi: 10.1137/040615286.

[12]

X. Bresson, S. Esedoḡlu, P. Vandergheynst, J.-P. Thiran and S. Osher, Fast global minimization of the active contour/snake model, J. Math Imaging Vis., 28 (2007), 151-167. doi: 10.1007/s10851-007-0002-0.

[13]

T. Goldstein, X. Bresson and S. Osher, Geometric application of the split Bregman method: Segmentation and surface reconstruction, Journal of Scientific Computing, 45 (2010), 272-293.

[14]

J. Yuan, E. Bae and Xue-Cheng Tai, A study on continuous max-flow and min-cut approaches, 2010 IEEE Conference on Computer Vision and Pattern Recognition, June 2010, 2217-2224.

[15]

E. S. Brown, T. F. Chan and X. Bresson, "Globally Convex Chan-Vese Image Segmentation," CAM Report, 10-44, UCLA, 2010.

[16]

E. Bae, J. Yuan and Xue-Cheng Tai, Global minimization for continuous multiphase partitioning problems using a dual approach, Int. J. Comput. Vis., 92 (2011), 112-129. doi: 10.1007/s11263-010-0406-y.

[17]

Mingqiang Zhu and T. F. Chan, "An Efficient Primal-Dual Hybrid Gradient Algorithm for TV Image Restoration," CAM Report, 8-34, UCLA, 2008.

[18]

C. B. Burckhardt, Speckle in ultrasound B-mode scans, IEEE Transaction on Sonics and Ultrasonics, 25 (1978), 1-6.

[19]

R. F. Wanger, S. W. Smith and J. M. Sandrik, Statistics of speckle in ultrasound B-scans, IEEE Transaction on Sonics and Ultrasonics, 30 (1983), 156-163. doi: 10.1109/T-SU.1983.31404.

[20]

V. Dutt and J. Greenleaf, Statistics of the log-compression envelope, Journal of Acoustical Society of America, 99 (1996), 3817-3825.

[21]

J. M. Thijssen, B. J. Oosterveld and R. F. Wanger, Gray level transforms and lesion detectabivity in echographic images, Utrason. Imag, 10 (1988), 171-195.

[22]

E. Esser, Xiaoqun Zhang and T. F. Chan, "A General Framework for a Class of First Order Primal-Dual Algorithms for TV Minimization," CAM Report, 9-67, UCLA, 2009.

[23]

Zhang Xu, A unified primal-dual algorithm based on l1 and Bregman iteration, private communication, April 2009.

[24]

J. A. Jensen, Field: A program for simulating ultrasound systems, Biological Engineering and Computing, 34 (1996), 351-353.

[25]

J. A. Jensen and N. B. Svendsen, Calculation of pressure fields from arbitrarily shaped, apodized, and excited ultrasound transducers, IEEE Trans. Ultrason., Ferroelec., Freq. Contr., 39 (1992), 262-267.

show all references

References:
[1]

V. Caselles, R. Kimmel and G. Sapiro, On geodesic active contours, Int. J. Comput. Vis., 22 (1997), 61-79. doi: 10.1023/A:1007979827043.

[2]

D. Mumford and J. Shah, Optimal approximation by piecewise smooth functions and associated variational problems, Commun. Pure Appl. Math, 42 (1989), 577-685. doi: 10.1002/cpa.3160420503.

[3]

S. C. Zhu and A. Yuille, Region competition: Unifying snakes, region growing, and Bayes/MDL for multiband image segmentation, IEEE PAMI, 18 (1996), 884-900. doi: 10.1109/34.537343.

[4]

N. Paragios and R. Deriche, Geodesic active regions and level set methods for supervised texture segmentation, Int. J. Computer Vision, 46 (2002), 223-247. doi: 10.1023/A:1014080923068.

[5]

T. F. Chan and L. A. Vese, Active contoure without edges, IEEE Trans. Image Processing, 10 (2001), 266-277. doi: 10.1109/83.902291.

[6]

I. B. Ayed, C. Vazquez, A. Mitiche and Z. Belhadj, SAR image segmentation with active contours and level sets, Proceedings of IEEE Intl. Conf. Image Process (ICIP), 4 (2004), 2717-2720.

[7]

Zhong Tao and H. D. Tagare, Evaluation of four probability distribution models for speckle in clinical cardic ultrasound images, IEEE Trans. Medical Imaging, 25 (2006), 1483-1491. doi: 10.1109/TMI.2006.881376.

[8]

A. Sarti, C. Corsi and E. Mazzini, Maximum likelihood segmentation of ultrasound images with Rayleigh distribution, IEEE Trans. Ultrasonics Ferroelectrics and Frequency Control, 52 (2005), 947-960. doi: 10.1109/TUFFC.2005.1504017.

[9]

J. M. Thijssen, Ultrasonic speckle formation, analysis and processing applied to tissue characterization, Pattern Recognition Letters, 24 (2003), 659-675. doi: 10.1016/S0167-8655(02)00173-3.

[10]

S. Osher, J. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys., 79 (1988), 12-49. doi: 10.1016/0021-9991(88)90002-2.

[11]

T. F. Chan, S. Esedoḡlu and M. Nikolova, Algorithms for finding global minimizers of image segmentation and denoising models, SIAM J. Appl. Math, 66 (2006), 1632-1648. doi: 10.1137/040615286.

[12]

X. Bresson, S. Esedoḡlu, P. Vandergheynst, J.-P. Thiran and S. Osher, Fast global minimization of the active contour/snake model, J. Math Imaging Vis., 28 (2007), 151-167. doi: 10.1007/s10851-007-0002-0.

[13]

T. Goldstein, X. Bresson and S. Osher, Geometric application of the split Bregman method: Segmentation and surface reconstruction, Journal of Scientific Computing, 45 (2010), 272-293.

[14]

J. Yuan, E. Bae and Xue-Cheng Tai, A study on continuous max-flow and min-cut approaches, 2010 IEEE Conference on Computer Vision and Pattern Recognition, June 2010, 2217-2224.

[15]

E. S. Brown, T. F. Chan and X. Bresson, "Globally Convex Chan-Vese Image Segmentation," CAM Report, 10-44, UCLA, 2010.

[16]

E. Bae, J. Yuan and Xue-Cheng Tai, Global minimization for continuous multiphase partitioning problems using a dual approach, Int. J. Comput. Vis., 92 (2011), 112-129. doi: 10.1007/s11263-010-0406-y.

[17]

Mingqiang Zhu and T. F. Chan, "An Efficient Primal-Dual Hybrid Gradient Algorithm for TV Image Restoration," CAM Report, 8-34, UCLA, 2008.

[18]

C. B. Burckhardt, Speckle in ultrasound B-mode scans, IEEE Transaction on Sonics and Ultrasonics, 25 (1978), 1-6.

[19]

R. F. Wanger, S. W. Smith and J. M. Sandrik, Statistics of speckle in ultrasound B-scans, IEEE Transaction on Sonics and Ultrasonics, 30 (1983), 156-163. doi: 10.1109/T-SU.1983.31404.

[20]

V. Dutt and J. Greenleaf, Statistics of the log-compression envelope, Journal of Acoustical Society of America, 99 (1996), 3817-3825.

[21]

J. M. Thijssen, B. J. Oosterveld and R. F. Wanger, Gray level transforms and lesion detectabivity in echographic images, Utrason. Imag, 10 (1988), 171-195.

[22]

E. Esser, Xiaoqun Zhang and T. F. Chan, "A General Framework for a Class of First Order Primal-Dual Algorithms for TV Minimization," CAM Report, 9-67, UCLA, 2009.

[23]

Zhang Xu, A unified primal-dual algorithm based on l1 and Bregman iteration, private communication, April 2009.

[24]

J. A. Jensen, Field: A program for simulating ultrasound systems, Biological Engineering and Computing, 34 (1996), 351-353.

[25]

J. A. Jensen and N. B. Svendsen, Calculation of pressure fields from arbitrarily shaped, apodized, and excited ultrasound transducers, IEEE Trans. Ultrason., Ferroelec., Freq. Contr., 39 (1992), 262-267.

[1]

Qianting Ma, Tieyong Zeng, Dexing Kong, Jianwei Zhang. Weighted area constraints-based breast lesion segmentation in ultrasound image analysis. Inverse Problems and Imaging, 2022, 16 (2) : 451-466. doi: 10.3934/ipi.2021057

[2]

Shi Yan, Jun Liu, Haiyang Huang, Xue-Cheng Tai. A dual EM algorithm for TV regularized Gaussian mixture model in image segmentation. Inverse Problems and Imaging, 2019, 13 (3) : 653-677. doi: 10.3934/ipi.2019030

[3]

Liam Burrows, Weihong Guo, Ke Chen, Francesco Torella. Reproducible kernel Hilbert space based global and local image segmentation. Inverse Problems and Imaging, 2021, 15 (1) : 1-25. doi: 10.3934/ipi.2020048

[4]

Yu-Hong Dai, Xin-Wei Liu, Jie Sun. A primal-dual interior-point method capable of rapidly detecting infeasibility for nonlinear programs. Journal of Industrial and Management Optimization, 2020, 16 (2) : 1009-1035. doi: 10.3934/jimo.2018190

[5]

Yixuan Yang, Yuchao Tang, Meng Wen, Tieyong Zeng. Preconditioned Douglas-Rachford type primal-dual method for solving composite monotone inclusion problems with applications. Inverse Problems and Imaging, 2021, 15 (4) : 787-825. doi: 10.3934/ipi.2021014

[6]

Xiayang Zhang, Yuqian Kong, Shanshan Liu, Yuan Shen. A relaxed parameter condition for the primal-dual hybrid gradient method for saddle-point problem. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022008

[7]

Xavier Bresson, Tony F. Chan. Fast dual minimization of the vectorial total variation norm and applications to color image processing. Inverse Problems and Imaging, 2008, 2 (4) : 455-484. doi: 10.3934/ipi.2008.2.455

[8]

Maika Goto, Kazunori Kuwana, Yasuhide Uegata, Shigetoshi Yazaki. A method how to determine parameters arising in a smoldering evolution equation by image segmentation for experiment's movies. Discrete and Continuous Dynamical Systems - S, 2021, 14 (3) : 881-891. doi: 10.3934/dcdss.2020233

[9]

Fan Jia, Xue-Cheng Tai, Jun Liu. Nonlocal regularized CNN for image segmentation. Inverse Problems and Imaging, 2020, 14 (5) : 891-911. doi: 10.3934/ipi.2020041

[10]

Yonggui Zhu, Yuying Shi, Bin Zhang, Xinyan Yu. Weighted-average alternating minimization method for magnetic resonance image reconstruction based on compressive sensing. Inverse Problems and Imaging, 2014, 8 (3) : 925-937. doi: 10.3934/ipi.2014.8.925

[11]

Ye Yuan, Yan Ren, Xiaodong Liu, Jing Wang. Approach to image segmentation based on interval neutrosophic set. Numerical Algebra, Control and Optimization, 2020, 10 (1) : 1-11. doi: 10.3934/naco.2019028

[12]

Dominique Zosso, Jing An, James Stevick, Nicholas Takaki, Morgan Weiss, Liane S. Slaughter, Huan H. Cao, Paul S. Weiss, Andrea L. Bertozzi. Image segmentation with dynamic artifacts detection and bias correction. Inverse Problems and Imaging, 2017, 11 (3) : 577-600. doi: 10.3934/ipi.2017027

[13]

Matthew S. Keegan, Berta Sandberg, Tony F. Chan. A multiphase logic framework for multichannel image segmentation. Inverse Problems and Imaging, 2012, 6 (1) : 95-110. doi: 10.3934/ipi.2012.6.95

[14]

Nadia Hazzam, Zakia Kebbiche. A primal-dual interior point method for $ P_{\ast }\left( \kappa \right) $-HLCP based on a class of parametric kernel functions. Numerical Algebra, Control and Optimization, 2021, 11 (4) : 513-531. doi: 10.3934/naco.2020053

[15]

Jen-Yen Lin, Hui-Ju Chen, Ruey-Lin Sheu. Augmented Lagrange primal-dual approach for generalized fractional programming problems. Journal of Industrial and Management Optimization, 2013, 9 (4) : 723-741. doi: 10.3934/jimo.2013.9.723

[16]

Gianni Di Pillo, Giampaolo Liuzzi, Stefano Lucidi. A primal-dual algorithm for nonlinear programming exploiting negative curvature directions. Numerical Algebra, Control and Optimization, 2011, 1 (3) : 509-528. doi: 10.3934/naco.2011.1.509

[17]

Kai Wang, Deren Han. On the linear convergence of the general first order primal-dual algorithm. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021134

[18]

Burak Ordin. The modified cutting angle method for global minimization of increasing positively homogeneous functions over the unit simplex. Journal of Industrial and Management Optimization, 2009, 5 (4) : 825-834. doi: 10.3934/jimo.2009.5.825

[19]

Kaifang Liu, Lunji Song, Shan Zhao. A new over-penalized weak galerkin method. Part Ⅰ: Second-order elliptic problems. Discrete and Continuous Dynamical Systems - B, 2021, 26 (5) : 2411-2428. doi: 10.3934/dcdsb.2020184

[20]

Lunji Song, Wenya Qi, Kaifang Liu, Qingxian Gu. A new over-penalized weak galerkin finite element method. Part Ⅱ: Elliptic interface problems. Discrete and Continuous Dynamical Systems - B, 2021, 26 (5) : 2581-2598. doi: 10.3934/dcdsb.2020196

2020 Impact Factor: 1.639

Metrics

  • PDF downloads (71)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]