Retinal vessel segmentation using a finite element based binary level set method

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May 2014, 8(2): 459-473. doi: 10.3934/ipi.2014.8.459

Retinal vessel segmentation using a finite element based binary level set method

Zhenlin Guo ^1, , Ping Lin ^2, , Guangrong Ji ^3, and Yangfan Wang ^4,

1.	Department of Mathematics and Mechanics, University of Science and Technology Beijing (USTB), Beijing, 100083, China
2.	Division of Mathematics, University of Dundee, Dundee, DD1 4HN, United Kingdom
3.	College of Information Science and Engineering, Ocean University of China, Qingdao, 266071, China
4.	College of Marine Life Science, Ocean University of China, Qingdao, 266071, China

Received July 2012 Revised October 2013 Published May 2014

Abstract
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In this paper we combine a few techniques to label blood vessels in the matched filter (MF) response image by using a finite element based binary level set method. An operator-splitting method is applied to numerically solve the Euler-Lagrange equation from minimizing an energy functional. Unlike the traditional MF methods, where a threshold is difficult to be selected, our method can automatically get more precise blood vessel segmentation using an enhanced edge information. In order to demonstrate the good performance, we compare our method with a few other methods when they are applied to a publicly available standard database of coloured images (with manual segmentations available too).

Keywords: operator-splitting., Retinal vessel segmentation, binary level set method.

Mathematics Subject Classification: Primary: 65M60, 65J22; Secondary: 94A08, 53C3.

Citation: Zhenlin Guo, Ping Lin, Guangrong Ji, Yangfan Wang. Retinal vessel segmentation using a finite element based binary level set method. Inverse Problems and Imaging, 2014, 8 (2) : 459-473. doi: 10.3934/ipi.2014.8.459

References:

[1]	X. Cai, R. Chan, S. Morigi and F. Sgallari, Framelet-based algorithm for segmentation of tubular structures, Lecture Notes in Computer Science, 6667 (2012), 411-422. doi: 10.1007/978-3-642-24785-9_35.
[2]	A. Can, H. Shen, J. N. Turner, H. L. Tanenbaum and B. Roysam, Rapid automated tracing and feature extraction from retinal fundus images using direct exploratory algorithms, IEEE Trans. Inform. Technol. Biomed., 3 (1999), 125-138.
[3]	V. Caselles, F. Catte, T. Coll and F. Dibos, A geometric model for active contours in image processing, Numer. Math., 66 (1993), 1-31. doi: 10.1007/BF01385685.
[4]	T. Chan and L. Vese, Active contours without edges, IEEE Image Proc., 10 (2001), 266-277. doi: 10.1109/83.902291.
[5]	S. Chaudhuri, S. Chatterjee, N. Katz, M. Nelson and M. Goldbaum, Detection of blood vessel in retinal images using two-dimensional matched filter, IEEE Trans. Med. Imag., 8 (1989), 263-269. doi: 10.1109/42.34715.
[6]	N. Cheung, K. Donaghue, G. Liew, L. Rogers, J. Wang, S. Lim, A. Jenkins, W. Hsu, L. Lee and T. Wong, Quantitative Assessment of Early Diabetic Retinopathy Using Fractal Analysis, Diabetes Care, 32 (2009), 106-110.
[7]	J. Chen and A. Amini, Quantifying 3D vascular structures in MRA images using hybrid PDE and geometric deformable models, IEEE Trans. Med. Imag., 10 (2004), 1251-1262.
[8]	O. Chutatape, L. Zheng and S. Krishman, Retinal blood vessel detection and tracking by matched Gaussian and Kalman filters, in Proc. IEEE Int. Conf. Eng. Biol. Soc., 6 (1998), 3144-3149. doi: 10.1109/IEMBS.1998.746160.
[9]	B. Dong, A. Chien and Z. Shen, Frame based segmentation for medical images, Commun.Math. Sci., 9 (2011), 551-559. doi: 10.4310/CMS.2011.v9.n2.a10.
[10]	A. F. Frangi, W. J. Niessen, R. M. Hoogeveen, T. van Walsum and M. A. Viergever, Model-based quantitation of 3-D magnetic resonance angiographic images, IEEE Trans. Med. Imag. , 18 (1999), 946-956. doi: 10.1109/42.811279.
[11]	L. Gang, O. Chutatape and S. M. Krishnan, Detection and measurement of retinal vessels in fundus images using amplitude modified second-order Gaussian filter, IEEE. Trans. Biomed. Eng., 49 (2002), 168-172.
[12]	R. Glowinski, P. Lin and X. Pan, An operator-splitting method for a liquid crystal model, Comp Phys. Comm., 152 (2003), 242-252. doi: 10.1016/S0010-4655(02)00823-8.
[13]	R. Glowinski, P. Lin and X. Pan, A three-stage operator-splitting/finite element method for the numerical simulation of liquid crystal flow, Int. J. Numer. Anal. Mod., 6 (2009), 440-454.
[14]	R. Glowinski and P. Tallec, Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics, SIAM, Philadelphia, PA, 1989. doi: 10.1137/1.9781611970838.
[15]	A. Hoover, V. Kouznetsova and M. Goldbaum, Locating blood vessels in retinal images by piecewise threshold probing of a matched filter response, IEEE Trans. Med. Imag., 19 (2000), 203-210.
[16]	J. Hua, P. Lin, C. Liu and Q. Wang, Energy law preserving C0 finite element schemes for phase field models in two-phase flow computations, J. Comput. Phys., 230 (2011), 7115-7131. doi: 10.1016/j.jcp.2011.05.013.
[17]	X. Jiang and D. Mojon, Adaptive local thresholding by verification based multithreshold probing with application to vessel detection in retinal images, IEEE Trans. Pattern Anal. Mach. Intell., 25 (2003), 131-137.
[18]	M. Kass, A. Witkin and D. Terzopoulos, Snakes: Active contour models, Int. J. Comput. Vis., 1 (1987), 321-331. doi: 10.1007/BF00133570.
[19]	C. Kirbas and F. K. H. Quek, A review of vessel extraction techniques and algorithms, ACM Comput. Surv., 36 (2004), 81-121. doi: 10.1145/1031120.1031121.
[20]	J. Lie, M. Lysaker and X. Tai, A variant of the levelset method and applications to image segmentation, UCLA CAM 03- 50, (2003).
[21]	J. Lie, M. Lysaker and X. Tai, A binary level set metod and some application to image processing, UCLA CAM 04-31, (2004).
[22]	J. Lie, M. Lysaker and X. Tai, Piecewise constant level set methods and image segmentation. In Scale Space and PDE Methods in Computer Vision, Lectures notes in Computer Sciences, 3459 (2005), 573-584. Springer.
[23]	P. Lin and C. Liu, Simulation of singularity dynamics in liquid crystal flows: a C0 finite element approach, J. Comp. Phys., 215 (2006), 348-362. doi: 10.1016/j.jcp.2005.10.027.
[24]	C. Liu and J. Shen, A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-Spectral method, Phys. D, 179 (2003), 211-228. doi: 10.1016/S0167-2789(03)00030-7.
[25]	L. M. Lorigo, O. Faugeras, W. E. L. Grimson, R. Keriven, R. Kikins, A. Nabavi and C.-F. Westin, CURVES: Curve evolution for vessel segmentation, Med. Image. Anal., 5 (2001), 195-206. doi: 10.1016/S1361-8415(01)00040-8.
[26]	C. Lupascu, D. Tegolo and E. Trucco, FABC: Retinal vessel segmentation using adaBoost, IEEE Trans. Inf. Technol. Biomed., 14 (2010), 1267-1274. doi: 10.1109/TITB.2010.2052282.
[27]	T. McInerney and D. Terzopoulos, T-snakes: Topology adaptive snakes, Med. Imag. Anal. , 4 (2000), 73-91. doi: 10.1016/S1361-8415(00)00008-6.
[28]	T. McInerney and D. Terzopoulos, Deformable models in medical image analysis: A survey, Med. Image Anal., 1 (1996), 91-108. doi: 10.1016/S1361-8415(96)80007-7.
[29]	A. M. Mendonca and A. Campilho, Segmentation of Retinal Blood Vessels by Combining the Detection of Centerlines and Morphological Reconstruction, IEEE Trans. Med. Imag., 25 (2006), 1200-1213. doi: 10.1109/TMI.2006.879955.
[30]	C. E. Metz, Basic principles of ROC analysis, Seminars Nucl. Med., 8 (1978), 283-298. doi: 10.1016/S0001-2998(78)80014-2.
[31]	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.
[32]	M. Niemeijer, J. Staal, B. Ginneken, M. Long and M. D. Abramoff, Comparative study of retinal vessel segmentation methods on a new publicly available database, Proc. SPIE Med. Imag., 5370 (2004), 648-656. doi: 10.1117/12.535349.
[33]	S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi Formulation, J. Comput. Phys., 79 (1988), 12-49. doi: 10.1016/0021-9991(88)90002-2.
[34]	Q. Sheng, Recent trends in splitting, adaptive and hybrid numerical methods for differential equations, Neural, Parallel and Sci. Comput., 16 (2008), 283-301.
[35]	C. Sinthanayothin, J. F. Boyce, T. H. Williamson, H. L. Cook, E. Mensah, S. Lal and D. Usher, Automated detection of diabetic retinopathy on digital fundus images, Diabetic Med., 19 (2002), 105-112. doi: 10.1046/j.1464-5491.2002.00613.x.
[36]	J. Soares, J. Leandro, J. Cesar, H. Jelinek and M. Cree, Retinal vessel segmentation using the 2-d gabor wavelet and supervised classification, IEEE Trans. Med. Imag., 25 (2006), 1214-1222. doi: 10.1109/TMI.2006.879967.
[37]	J. Staal, M. Abramoff, M. Viergever and B. Ginneken, Ridge based vessel segmentation in color images of the retina, IEEE Trans. Med. Imag., 23 (2004), 501-509. doi: 10.1109/TMI.2004.825627.
[38]	K. Sum and P. Cheung, Vessel extraction under non-uniform illumination: A level set approach, IEEE Trans. Biomed. Eng., 55 (2008), 358-360. doi: 10.1109/TBME.2007.896587.
[39]	X. Tai, O. Christiansen, P. Lin and I. Skjaelaaen, A remark on the MBO scheme and some piecewise constant level set methods, Int. J. Comput. Vis., 73 (2007), 61-76.
[40]	T. Walter and J. C. Klein, Segmentation of color fundus images of the human retina: Detection of the optic disc and the vascular tree using morphological techniques, in Medical Data Analysis, J. Crespo, V. Maojo, and F. Martin, Eds. Berlin, Germany: Springer-Verlag, 2199 (2001), 282-287. ser. Lecture Notes in Computer Science. doi: 10.1007/3-540-45497-7_43.
[41]	L. Wang, A. Bhalerao and R. Wilson, Analysis of retinal vasculature using a multiresolution hermite model, IEEE Trans. Med. Imag., 26 (2007), 137-152. doi: 10.1109/TMI.2006.889732.
[42]	Y. Wang, G. Ji, P. Lin and E. Trucco, Retinal vessel segmentation using matched filter with multiwavelet kernels and multiscale hierachical decomposition, Pattern Recog., 46 (2013), 2117-2133.
[43]	C. Wu and X. Tai, Augmented Lagrangian method, Dual methods and Split-Bregman Iterations for ROF, vectorial TV and higher order models, SIAM J. Imag. Sci., 3 (2010), 300-339. doi: 10.1137/090767558.
[44]	F. Zana and J. C. Klein, Segmentation of vessel-like patterns using mathematical morphology and curvature evaluation, IEEE Trans. Imag. Proc., 10 (2001), 1010-1019. doi: 10.1109/83.931095.
[45]	D. Zonoobi, A. Kassim and W. Shen, Vasculature segmentation in MRA images using gradient compensated geodesic active contours, J. Sign. Process. Syst., 54 (2009), 171-181. doi: 10.1007/s11265-008-0216-4.

show all references

References:

[1]	X. Cai, R. Chan, S. Morigi and F. Sgallari, Framelet-based algorithm for segmentation of tubular structures, Lecture Notes in Computer Science, 6667 (2012), 411-422. doi: 10.1007/978-3-642-24785-9_35.
[2]	A. Can, H. Shen, J. N. Turner, H. L. Tanenbaum and B. Roysam, Rapid automated tracing and feature extraction from retinal fundus images using direct exploratory algorithms, IEEE Trans. Inform. Technol. Biomed., 3 (1999), 125-138.
[3]	V. Caselles, F. Catte, T. Coll and F. Dibos, A geometric model for active contours in image processing, Numer. Math., 66 (1993), 1-31. doi: 10.1007/BF01385685.
[4]	T. Chan and L. Vese, Active contours without edges, IEEE Image Proc., 10 (2001), 266-277. doi: 10.1109/83.902291.
[5]	S. Chaudhuri, S. Chatterjee, N. Katz, M. Nelson and M. Goldbaum, Detection of blood vessel in retinal images using two-dimensional matched filter, IEEE Trans. Med. Imag., 8 (1989), 263-269. doi: 10.1109/42.34715.
[6]	N. Cheung, K. Donaghue, G. Liew, L. Rogers, J. Wang, S. Lim, A. Jenkins, W. Hsu, L. Lee and T. Wong, Quantitative Assessment of Early Diabetic Retinopathy Using Fractal Analysis, Diabetes Care, 32 (2009), 106-110.
[7]	J. Chen and A. Amini, Quantifying 3D vascular structures in MRA images using hybrid PDE and geometric deformable models, IEEE Trans. Med. Imag., 10 (2004), 1251-1262.
[8]	O. Chutatape, L. Zheng and S. Krishman, Retinal blood vessel detection and tracking by matched Gaussian and Kalman filters, in Proc. IEEE Int. Conf. Eng. Biol. Soc., 6 (1998), 3144-3149. doi: 10.1109/IEMBS.1998.746160.
[9]	B. Dong, A. Chien and Z. Shen, Frame based segmentation for medical images, Commun.Math. Sci., 9 (2011), 551-559. doi: 10.4310/CMS.2011.v9.n2.a10.
[10]	A. F. Frangi, W. J. Niessen, R. M. Hoogeveen, T. van Walsum and M. A. Viergever, Model-based quantitation of 3-D magnetic resonance angiographic images, IEEE Trans. Med. Imag. , 18 (1999), 946-956. doi: 10.1109/42.811279.
[11]	L. Gang, O. Chutatape and S. M. Krishnan, Detection and measurement of retinal vessels in fundus images using amplitude modified second-order Gaussian filter, IEEE. Trans. Biomed. Eng., 49 (2002), 168-172.
[12]	R. Glowinski, P. Lin and X. Pan, An operator-splitting method for a liquid crystal model, Comp Phys. Comm., 152 (2003), 242-252. doi: 10.1016/S0010-4655(02)00823-8.
[13]	R. Glowinski, P. Lin and X. Pan, A three-stage operator-splitting/finite element method for the numerical simulation of liquid crystal flow, Int. J. Numer. Anal. Mod., 6 (2009), 440-454.
[14]	R. Glowinski and P. Tallec, Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics, SIAM, Philadelphia, PA, 1989. doi: 10.1137/1.9781611970838.
[15]	A. Hoover, V. Kouznetsova and M. Goldbaum, Locating blood vessels in retinal images by piecewise threshold probing of a matched filter response, IEEE Trans. Med. Imag., 19 (2000), 203-210.
[16]	J. Hua, P. Lin, C. Liu and Q. Wang, Energy law preserving C0 finite element schemes for phase field models in two-phase flow computations, J. Comput. Phys., 230 (2011), 7115-7131. doi: 10.1016/j.jcp.2011.05.013.
[17]	X. Jiang and D. Mojon, Adaptive local thresholding by verification based multithreshold probing with application to vessel detection in retinal images, IEEE Trans. Pattern Anal. Mach. Intell., 25 (2003), 131-137.
[18]	M. Kass, A. Witkin and D. Terzopoulos, Snakes: Active contour models, Int. J. Comput. Vis., 1 (1987), 321-331. doi: 10.1007/BF00133570.
[19]	C. Kirbas and F. K. H. Quek, A review of vessel extraction techniques and algorithms, ACM Comput. Surv., 36 (2004), 81-121. doi: 10.1145/1031120.1031121.
[20]	J. Lie, M. Lysaker and X. Tai, A variant of the levelset method and applications to image segmentation, UCLA CAM 03- 50, (2003).
[21]	J. Lie, M. Lysaker and X. Tai, A binary level set metod and some application to image processing, UCLA CAM 04-31, (2004).
[22]	J. Lie, M. Lysaker and X. Tai, Piecewise constant level set methods and image segmentation. In Scale Space and PDE Methods in Computer Vision, Lectures notes in Computer Sciences, 3459 (2005), 573-584. Springer.
[23]	P. Lin and C. Liu, Simulation of singularity dynamics in liquid crystal flows: a C0 finite element approach, J. Comp. Phys., 215 (2006), 348-362. doi: 10.1016/j.jcp.2005.10.027.
[24]	C. Liu and J. Shen, A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-Spectral method, Phys. D, 179 (2003), 211-228. doi: 10.1016/S0167-2789(03)00030-7.
[25]	L. M. Lorigo, O. Faugeras, W. E. L. Grimson, R. Keriven, R. Kikins, A. Nabavi and C.-F. Westin, CURVES: Curve evolution for vessel segmentation, Med. Image. Anal., 5 (2001), 195-206. doi: 10.1016/S1361-8415(01)00040-8.
[26]	C. Lupascu, D. Tegolo and E. Trucco, FABC: Retinal vessel segmentation using adaBoost, IEEE Trans. Inf. Technol. Biomed., 14 (2010), 1267-1274. doi: 10.1109/TITB.2010.2052282.
[27]	T. McInerney and D. Terzopoulos, T-snakes: Topology adaptive snakes, Med. Imag. Anal. , 4 (2000), 73-91. doi: 10.1016/S1361-8415(00)00008-6.
[28]	T. McInerney and D. Terzopoulos, Deformable models in medical image analysis: A survey, Med. Image Anal., 1 (1996), 91-108. doi: 10.1016/S1361-8415(96)80007-7.
[29]	A. M. Mendonca and A. Campilho, Segmentation of Retinal Blood Vessels by Combining the Detection of Centerlines and Morphological Reconstruction, IEEE Trans. Med. Imag., 25 (2006), 1200-1213. doi: 10.1109/TMI.2006.879955.
[30]	C. E. Metz, Basic principles of ROC analysis, Seminars Nucl. Med., 8 (1978), 283-298. doi: 10.1016/S0001-2998(78)80014-2.
[31]	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.
[32]	M. Niemeijer, J. Staal, B. Ginneken, M. Long and M. D. Abramoff, Comparative study of retinal vessel segmentation methods on a new publicly available database, Proc. SPIE Med. Imag., 5370 (2004), 648-656. doi: 10.1117/12.535349.
[33]	S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi Formulation, J. Comput. Phys., 79 (1988), 12-49. doi: 10.1016/0021-9991(88)90002-2.
[34]	Q. Sheng, Recent trends in splitting, adaptive and hybrid numerical methods for differential equations, Neural, Parallel and Sci. Comput., 16 (2008), 283-301.
[35]	C. Sinthanayothin, J. F. Boyce, T. H. Williamson, H. L. Cook, E. Mensah, S. Lal and D. Usher, Automated detection of diabetic retinopathy on digital fundus images, Diabetic Med., 19 (2002), 105-112. doi: 10.1046/j.1464-5491.2002.00613.x.
[36]	J. Soares, J. Leandro, J. Cesar, H. Jelinek and M. Cree, Retinal vessel segmentation using the 2-d gabor wavelet and supervised classification, IEEE Trans. Med. Imag., 25 (2006), 1214-1222. doi: 10.1109/TMI.2006.879967.
[37]	J. Staal, M. Abramoff, M. Viergever and B. Ginneken, Ridge based vessel segmentation in color images of the retina, IEEE Trans. Med. Imag., 23 (2004), 501-509. doi: 10.1109/TMI.2004.825627.
[38]	K. Sum and P. Cheung, Vessel extraction under non-uniform illumination: A level set approach, IEEE Trans. Biomed. Eng., 55 (2008), 358-360. doi: 10.1109/TBME.2007.896587.
[39]	X. Tai, O. Christiansen, P. Lin and I. Skjaelaaen, A remark on the MBO scheme and some piecewise constant level set methods, Int. J. Comput. Vis., 73 (2007), 61-76.
[40]	T. Walter and J. C. Klein, Segmentation of color fundus images of the human retina: Detection of the optic disc and the vascular tree using morphological techniques, in Medical Data Analysis, J. Crespo, V. Maojo, and F. Martin, Eds. Berlin, Germany: Springer-Verlag, 2199 (2001), 282-287. ser. Lecture Notes in Computer Science. doi: 10.1007/3-540-45497-7_43.
[41]	L. Wang, A. Bhalerao and R. Wilson, Analysis of retinal vasculature using a multiresolution hermite model, IEEE Trans. Med. Imag., 26 (2007), 137-152. doi: 10.1109/TMI.2006.889732.
[42]	Y. Wang, G. Ji, P. Lin and E. Trucco, Retinal vessel segmentation using matched filter with multiwavelet kernels and multiscale hierachical decomposition, Pattern Recog., 46 (2013), 2117-2133.
[43]	C. Wu and X. Tai, Augmented Lagrangian method, Dual methods and Split-Bregman Iterations for ROF, vectorial TV and higher order models, SIAM J. Imag. Sci., 3 (2010), 300-339. doi: 10.1137/090767558.
[44]	F. Zana and J. C. Klein, Segmentation of vessel-like patterns using mathematical morphology and curvature evaluation, IEEE Trans. Imag. Proc., 10 (2001), 1010-1019. doi: 10.1109/83.931095.
[45]	D. Zonoobi, A. Kassim and W. Shen, Vasculature segmentation in MRA images using gradient compensated geodesic active contours, J. Sign. Process. Syst., 54 (2009), 171-181. doi: 10.1007/s11265-008-0216-4.

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