活动轮廓模型在医学图像分割的综述
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摘要
医学图像分割作为图像处理领域的一个研究热点,长期受到广大科研工作者的关注。活动轮廓模型作为医学图像分割的一个重要工具,在近30年的研究中得到了长足的发展。根据活动轮廓模型的表达方式不同,将活动轮廓模型分为参数活动轮廓模型、几何活动轮廓模型;相对于参数活动轮廓模型,几何活动轮廓模型中曲线的运动过程是基于曲线的几何度量,如曲线的法线、曲率等;又由于水平集方法在几何活动轮廓模型的成功应用,使得几何活动轮廓模型在曲线的拓扑变化、数值求解等方面有不少优势。为了全面展示活动轮廓模型的发展历程及其在医学图像领域的应用,首先简述活动轮廓模型的发展历程及一些偏微分方程的基础知识;然后,详细分析几种较为经典活动轮廓模型;接着,对两种类型的活动轮廓模型进行对比分析;最后,对全文进行总结,并对活动轮廓模型的发展与未来进行展望。
Medical image segmentation is a research hotspot of image processing,concerned by the majority of researchers. As one of important tools for medical image segmentation,the active contour model has been developed in the past three decades. According to the different expressions of the active contour model,the active contour model is divided into the parametric active contour model and the geometric active contour model. Compared with the parametric active contour model,the motion of the curve in the geometric active contour model is based on the geometric measures of the curve,such as the normal and curvature of the curve,and the Level set method is applied to the geometric active contour model which makes the geometric active contour model has many advantages in the aspect of topological change and numerical solution of the curve. In order to fully demonstrate the development of the active contour model and its application in the field of medical imaging,first,the development of the active contour model and the basic knowledge of some partial differential equations were described. Second,several classical active contour models were analyzed. Third,the two types of active contours compared were and analyzed. Finally,a summary and outlook of the active contour model at the conclusion of the full text were given.
Medical image segmentation is a research hotspot of image processing,concerned by the majority of researchers. As one of important tools for medical image segmentation,the active contour model has been developed in the past three decades. According to the different expressions of the active contour model,the active contour model is divided into the parametric active contour model and the geometric active contour model. Compared with the parametric active contour model,the motion of the curve in the geometric active contour model is based on the geometric measures of the curve,such as the normal and curvature of the curve,and the Level set method is applied to the geometric active contour model which makes the geometric active contour model has many advantages in the aspect of topological change and numerical solution of the curve. In order to fully demonstrate the development of the active contour model and its application in the field of medical imaging,first,the development of the active contour model and the basic knowledge of some partial differential equations were described. Second,several classical active contour models were analyzed. Third,the two types of active contours compared were and analyzed. Finally,a summary and outlook of the active contour model at the conclusion of the full text were given.
引文
1章毓晋.《中国图象图形学报》创刊20年出版情况统计分析.中国图象图形学报,2017;22(4):415-421Zhang Yujin.Statistical analysis of the publication of Journal of Image and Graphics founded 20 years.Journal of Image and Graphics,2017;22(4):415-421
2 Latifi-Navid M,Bilen M,Konukseven E 6)I,et al.Fast and accurate semiautomatic haptic segmentation of brain tumor in 3D MRI images.Turkish Journal of Electrical Engineering&Computer Sciences,2016;24(3):1397-1411
3 Menze B H,Jakab A,Bauer S,et al.The multimodal brain tumor image segmentation benchmark(BRAT-S).IEEE Transactions on Medical Imaging,2015;34(10):1993-2024
4 Brun E,Grandl S,Sztrókaygaul A,et al.Breast tumor segmentation in high resolution X-ray phase contrast analyzer based computed tomography.Medical Physics,2014;41(11):111902
5 Ni B,He F,Yuan Z.Segmentation of uterine fibroid ultrasound images using a dynamic statistical shape model in HIFU therapy.The Official Journal of the Computerized Medical Imaging Society,2015;46(3):302-314
6张石,董建威,佘黎煌.医学图像分割算法的评价方法.中国图象图形学报,2009;14(9):1872-1880Zhang Shi,Dong Jianwei,She Lihuang.The method ology of evaluating segmentation algorithms on medical image.Journal of Image and Graphics,2009;14(9):1872-1880
7 Kass M,Witk in A,Terzopoulos D.Snakes:Active contour models.International Journal of Computer Vision,1987;1(4):321-331
8 Marr D.Vision:A computational investigation into the human representation and processing of visual information.San Francisco:W.H.Freeman and Company,1982
9 Zhao Y,Rada L,Chen K,et al.Automated vessel segmentation using infinite perimeter active contour model with hybrid region information with application to retinal images.IEEE Transactions on Medical Imaging,2015;34(9):1797-1807
10 Zhou S,Wang J,Zhang S,et al.Active contour model based on local and global intensity information for medical image segmentation.Neurocomputing,2016;186(C):107-118
11 Zhuang M,Dierckx R A J O,Zaidi H.Generic and robust method for automatic segmentation of PET images using an active contour model.Medical Physics,2016;43(8):4483-4494
12 Zheng Q,Dong E,Cao Z,et al.Active contour model driven by linear speed function for local segmentation with robust initialization and applications in MR brain images.Signal Processing,2014;97(7):117-133
13兰红,张璐.分水岭优化的Snake模型肝脏图像分割.中国图象图形学报,2012;17(7):873-879Lan Hong,Zhang Lu.Liver image segmentation algorithm based on the Snake model and optimized by watershed transformation.Journal of Image and Graphics,2012;17(7):873-879
14 Fu Z L,Ye M,Su Y L,et al.A novel active contour model for medical image segmentation.Journal of Shanghai Jiaotong University,2010;15(5):549-555
15 Dervieux A,Thomasset F.A finite element method for the simulation of Rayleigh-Taylor instability.Approximation Methods for Navier-Stokes Problems.Berlin:Springer.1979:145-158
16 Dervieux A,Thomasset F.Multifluid incompressible flows by a finite element method.Seventh International Conference on Numerical Methods in Fluid Dynamics.Berlin:Springer,1981:158-163
17 Osher S,Sethian J A.Fronts propagating with curvature-dependent speed:Algorithms based on Hamilton-Jacobi formulations.Journal of Computational Physics,1987;79(1):12-49
18周飞飞.基于活动轮廓模型的图像分割方法.南昌:南昌航空大学,2015Zhou Feifei.Image segmentation method based on active contour model.Nanchang:Nanchang Hangkong University,2015
19 Aubert G,Kornprobst P.Mathematical problem in image processing.New York:Springer New York,2006
20 Moreno J C,Prasath V B S,Proenca H,et al.Fast and globally convex multiphase active contours for brain MRI segmentation.Computer Vision and Image Understanding,2014;125:237-250
21 Lestari D P,Madenda S,Massich J.A segmentation algorithm for breast lesion based on active contour model and morphological operations.Advanced Science,Engineering and Medicine,2015;7(10):920-924
22杨新.图像偏微分方程的原理与应用.上海:上海交通大学出版社,2003Yang xin.The principle and application of image partial differential equation.Shanghai:Shanghai Jiao Tong University Press,2003
23王大凯,侯榆青,彭进业.图像处理的偏微分方程方法.北京:科学出版社,2008Wang Dakai,Hou Yuqing,Peng Jinye.Partial differential equation method for image processing.Beijing:Science Press,2008
24老大中.变分法基础.北京:国防工业出版社,2007Lao Dazhong.The basis of the variational method.Beijing:National Defend Industry Press,2007
25 Cohen L D.On active contour models and balloons.CVGIP:Image Understanding,1991;53(2):211-218
26 Xu C,Prince J L.Snakes,shapes,and gradient vector flow.IEEETransactions on Image Processing A Publication of the IEEE Signal Processing Society,1998;7(3):359-369
27 Cohen L D,Cohen I.Finite-element methods for active contour models and balloons for 2-D and 3-D images.IEEE Transactions on Pattern Analysis and Machine Intelligence,1993;15(11):1131-1147
28 Caselles V,Kimmel R,Sapiro G.Geodesic active contours.Fifth International Conference on.Computer Vision.New York:IEEE,1995:694-699
29 Malladi R,Sethian J A,Vemuri B C.Shape modeling with front propagation:A level set approach.IEEE Transactions on Pattern Analysis and Machine Intelligence,1995;17(2):158-175
30 Chan T F,Vese L A.Active contours without edges.IEEE Transactions on Image Processing,2001;10(2):266-277
31 Mumford D,Shan J.Optimal approximation by piecewise smooth function and associated variational problems.Communication on Pure and Applied Mathematics,1989;42(5):577-685
32 Chang R F,Wu W J,Moon W K,et al.Segmentation of breast tumor in three-dimensional ultrasound images using three-dimensional discrete active contour model.Ultrasound in Medicine&Biology,2003;29(11):1571-81
33 Aldiri B,Hunter A,Steel D.An active contour model for segmenting and measuring retinal vessels.IEEE Transactions on Medical Imaging,2009;28(9):1488-1497
34 Pratondo A,Chui C K,Ong S H.Integrating machine learning with region-based active contour models in medical image segmentation.Journal of Visual Communication&Image Representation,2016;43:1-9
35 Zhuang M,Dierckx R A J O,Zaidi H.Generic and robust method for automatic segmentation of PET images using an active contour model.Medical Physics,2016;43(8):4483-4494
36赵文超,万韬阮,武桐,等.基于三维形变曲面模型的脊椎分割方法.西安工程大学学报,2015;(3):341-345Zhao Wenchao,Wan Taoruan,Wu Tong,et al.Vertebral segmentation method based on three-dimensional deformable model.Journal of Xi'an Polytechnic University,2015;(3):341-345
37武玉伟,梁佳,王元全.一种基于广义梯度矢量流Snake模型的心脏MR图像分割方法.中国图象图形学报,2010;15(4):598-606Wu Yuwei,Liang Jia,Wang Yuanquan.A method for segmentation of the cardiac MR images based on GGVF snake.Journal of Image and Graphics,2010;15(4):598-606
38张麒,汪源源,王威琪,等.基于梯度矢量流snake与多尺度分析的血管内超声图像轮廓提取.生命科学仪器,2007;5(8):32-36Zhang Lin,Wang Yuanyuan,Wang Weiqi,et al.Contour detection from IVUS images based on gradient vector flow snakes and multiscale analysis.Life Science Instruments,2007;5(8):32-36
39张静林,高红,马宝英.一种改进的梯度矢量流Snake侧脑室分割算法.中国医学物理学杂志,2015;32(5):711-716Zhang Jinglin,Gao Hong,Ma Baoying.Improved gradient vector flow snake algorithm for lateral ventricle segmentation.Chinese Journal of Medical Physics,2015;32(5):711-716
40 Sharif S M S A,Deriche M,Maalej N,et al.A fast geodesic active contour model for medical image segmentation using prior analysis and wavelets.Arabian Journal for Science&Engineering,2014;39(2):1017-1037
41 Kasmi R,Mokrani K,Rader R K,et al.Biologically inspired skin lesion segmentation using a geodesic active contour technique.Skin Research&Technology,2016;22(2):208-222
42杨红喆,赵立辉.融合高斯混合模型的测地线脑肿瘤分割方法.计算机工程,2014;40(2):256-259Yang Hongzhe,Zhao Lihui.Brain tumor segmentation method using geodesic combined with Gaussian mixed model.Computer Engineering,2014;40(2):256-259
43 Vese L A,Chan T F.A multiphase level set framework for image segmentation using the mumford and shah model.International Journal of Computer Vision,2002;50(3):271-293
44 Tsai A,Yezzi A J,Willsky A S.Curve evolution implementation of the Mumford-Shah functional for image segmentation,denoising,interpolation,and magnification.IEEE Trans Image Process,2001;10(8):1169-86
45 Li C,Kao C Y,Gore J C,et al.Implicit active contours driven by local binary fitting energy.CVPR'07.Computer Vision and Pattern Recognition.Piscataway:IEEE,2007:1-7
46 Xu C,Yezzi A,Prince J L.On the relationship between parametric and geometric active contours.Conference Record of the ThirtyFourth Asilomar Conference on Signals,Systems and Computers.Piscataway:IEEE,2000:483-489
2 Latifi-Navid M,Bilen M,Konukseven E 6)I,et al.Fast and accurate semiautomatic haptic segmentation of brain tumor in 3D MRI images.Turkish Journal of Electrical Engineering&Computer Sciences,2016;24(3):1397-1411
3 Menze B H,Jakab A,Bauer S,et al.The multimodal brain tumor image segmentation benchmark(BRAT-S).IEEE Transactions on Medical Imaging,2015;34(10):1993-2024
4 Brun E,Grandl S,Sztrókaygaul A,et al.Breast tumor segmentation in high resolution X-ray phase contrast analyzer based computed tomography.Medical Physics,2014;41(11):111902
5 Ni B,He F,Yuan Z.Segmentation of uterine fibroid ultrasound images using a dynamic statistical shape model in HIFU therapy.The Official Journal of the Computerized Medical Imaging Society,2015;46(3):302-314
6张石,董建威,佘黎煌.医学图像分割算法的评价方法.中国图象图形学报,2009;14(9):1872-1880Zhang Shi,Dong Jianwei,She Lihuang.The method ology of evaluating segmentation algorithms on medical image.Journal of Image and Graphics,2009;14(9):1872-1880
7 Kass M,Witk in A,Terzopoulos D.Snakes:Active contour models.International Journal of Computer Vision,1987;1(4):321-331
8 Marr D.Vision:A computational investigation into the human representation and processing of visual information.San Francisco:W.H.Freeman and Company,1982
9 Zhao Y,Rada L,Chen K,et al.Automated vessel segmentation using infinite perimeter active contour model with hybrid region information with application to retinal images.IEEE Transactions on Medical Imaging,2015;34(9):1797-1807
10 Zhou S,Wang J,Zhang S,et al.Active contour model based on local and global intensity information for medical image segmentation.Neurocomputing,2016;186(C):107-118
11 Zhuang M,Dierckx R A J O,Zaidi H.Generic and robust method for automatic segmentation of PET images using an active contour model.Medical Physics,2016;43(8):4483-4494
12 Zheng Q,Dong E,Cao Z,et al.Active contour model driven by linear speed function for local segmentation with robust initialization and applications in MR brain images.Signal Processing,2014;97(7):117-133
13兰红,张璐.分水岭优化的Snake模型肝脏图像分割.中国图象图形学报,2012;17(7):873-879Lan Hong,Zhang Lu.Liver image segmentation algorithm based on the Snake model and optimized by watershed transformation.Journal of Image and Graphics,2012;17(7):873-879
14 Fu Z L,Ye M,Su Y L,et al.A novel active contour model for medical image segmentation.Journal of Shanghai Jiaotong University,2010;15(5):549-555
15 Dervieux A,Thomasset F.A finite element method for the simulation of Rayleigh-Taylor instability.Approximation Methods for Navier-Stokes Problems.Berlin:Springer.1979:145-158
16 Dervieux A,Thomasset F.Multifluid incompressible flows by a finite element method.Seventh International Conference on Numerical Methods in Fluid Dynamics.Berlin:Springer,1981:158-163
17 Osher S,Sethian J A.Fronts propagating with curvature-dependent speed:Algorithms based on Hamilton-Jacobi formulations.Journal of Computational Physics,1987;79(1):12-49
18周飞飞.基于活动轮廓模型的图像分割方法.南昌:南昌航空大学,2015Zhou Feifei.Image segmentation method based on active contour model.Nanchang:Nanchang Hangkong University,2015
19 Aubert G,Kornprobst P.Mathematical problem in image processing.New York:Springer New York,2006
20 Moreno J C,Prasath V B S,Proenca H,et al.Fast and globally convex multiphase active contours for brain MRI segmentation.Computer Vision and Image Understanding,2014;125:237-250
21 Lestari D P,Madenda S,Massich J.A segmentation algorithm for breast lesion based on active contour model and morphological operations.Advanced Science,Engineering and Medicine,2015;7(10):920-924
22杨新.图像偏微分方程的原理与应用.上海:上海交通大学出版社,2003Yang xin.The principle and application of image partial differential equation.Shanghai:Shanghai Jiao Tong University Press,2003
23王大凯,侯榆青,彭进业.图像处理的偏微分方程方法.北京:科学出版社,2008Wang Dakai,Hou Yuqing,Peng Jinye.Partial differential equation method for image processing.Beijing:Science Press,2008
24老大中.变分法基础.北京:国防工业出版社,2007Lao Dazhong.The basis of the variational method.Beijing:National Defend Industry Press,2007
25 Cohen L D.On active contour models and balloons.CVGIP:Image Understanding,1991;53(2):211-218
26 Xu C,Prince J L.Snakes,shapes,and gradient vector flow.IEEETransactions on Image Processing A Publication of the IEEE Signal Processing Society,1998;7(3):359-369
27 Cohen L D,Cohen I.Finite-element methods for active contour models and balloons for 2-D and 3-D images.IEEE Transactions on Pattern Analysis and Machine Intelligence,1993;15(11):1131-1147
28 Caselles V,Kimmel R,Sapiro G.Geodesic active contours.Fifth International Conference on.Computer Vision.New York:IEEE,1995:694-699
29 Malladi R,Sethian J A,Vemuri B C.Shape modeling with front propagation:A level set approach.IEEE Transactions on Pattern Analysis and Machine Intelligence,1995;17(2):158-175
30 Chan T F,Vese L A.Active contours without edges.IEEE Transactions on Image Processing,2001;10(2):266-277
31 Mumford D,Shan J.Optimal approximation by piecewise smooth function and associated variational problems.Communication on Pure and Applied Mathematics,1989;42(5):577-685
32 Chang R F,Wu W J,Moon W K,et al.Segmentation of breast tumor in three-dimensional ultrasound images using three-dimensional discrete active contour model.Ultrasound in Medicine&Biology,2003;29(11):1571-81
33 Aldiri B,Hunter A,Steel D.An active contour model for segmenting and measuring retinal vessels.IEEE Transactions on Medical Imaging,2009;28(9):1488-1497
34 Pratondo A,Chui C K,Ong S H.Integrating machine learning with region-based active contour models in medical image segmentation.Journal of Visual Communication&Image Representation,2016;43:1-9
35 Zhuang M,Dierckx R A J O,Zaidi H.Generic and robust method for automatic segmentation of PET images using an active contour model.Medical Physics,2016;43(8):4483-4494
36赵文超,万韬阮,武桐,等.基于三维形变曲面模型的脊椎分割方法.西安工程大学学报,2015;(3):341-345Zhao Wenchao,Wan Taoruan,Wu Tong,et al.Vertebral segmentation method based on three-dimensional deformable model.Journal of Xi'an Polytechnic University,2015;(3):341-345
37武玉伟,梁佳,王元全.一种基于广义梯度矢量流Snake模型的心脏MR图像分割方法.中国图象图形学报,2010;15(4):598-606Wu Yuwei,Liang Jia,Wang Yuanquan.A method for segmentation of the cardiac MR images based on GGVF snake.Journal of Image and Graphics,2010;15(4):598-606
38张麒,汪源源,王威琪,等.基于梯度矢量流snake与多尺度分析的血管内超声图像轮廓提取.生命科学仪器,2007;5(8):32-36Zhang Lin,Wang Yuanyuan,Wang Weiqi,et al.Contour detection from IVUS images based on gradient vector flow snakes and multiscale analysis.Life Science Instruments,2007;5(8):32-36
39张静林,高红,马宝英.一种改进的梯度矢量流Snake侧脑室分割算法.中国医学物理学杂志,2015;32(5):711-716Zhang Jinglin,Gao Hong,Ma Baoying.Improved gradient vector flow snake algorithm for lateral ventricle segmentation.Chinese Journal of Medical Physics,2015;32(5):711-716
40 Sharif S M S A,Deriche M,Maalej N,et al.A fast geodesic active contour model for medical image segmentation using prior analysis and wavelets.Arabian Journal for Science&Engineering,2014;39(2):1017-1037
41 Kasmi R,Mokrani K,Rader R K,et al.Biologically inspired skin lesion segmentation using a geodesic active contour technique.Skin Research&Technology,2016;22(2):208-222
42杨红喆,赵立辉.融合高斯混合模型的测地线脑肿瘤分割方法.计算机工程,2014;40(2):256-259Yang Hongzhe,Zhao Lihui.Brain tumor segmentation method using geodesic combined with Gaussian mixed model.Computer Engineering,2014;40(2):256-259
43 Vese L A,Chan T F.A multiphase level set framework for image segmentation using the mumford and shah model.International Journal of Computer Vision,2002;50(3):271-293
44 Tsai A,Yezzi A J,Willsky A S.Curve evolution implementation of the Mumford-Shah functional for image segmentation,denoising,interpolation,and magnification.IEEE Trans Image Process,2001;10(8):1169-86
45 Li C,Kao C Y,Gore J C,et al.Implicit active contours driven by local binary fitting energy.CVPR'07.Computer Vision and Pattern Recognition.Piscataway:IEEE,2007:1-7
46 Xu C,Yezzi A,Prince J L.On the relationship between parametric and geometric active contours.Conference Record of the ThirtyFourth Asilomar Conference on Signals,Systems and Computers.Piscataway:IEEE,2000:483-489
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