A multi-orientation analysis approach to retinal vessel tracking. (English) Zbl 1291.92075
Summary: This paper presents a method for retinal vasculature extraction based on biologically inspired multi-orientation analysis. We apply multi-orientation analysis via so-called invertible orientation scores, modeling the cortical columns in the visual system of higher mammals. This allows us to generically deal with many hitherto complex problems inherent to vessel tracking, such as crossings, bifurcations, parallel vessels, vessels of varying widths and vessels with high curvature. Our approach applies tracking in invertible orientation scores via a novel geometrical principle for curve optimization in the Euclidean motion group \(SE(2)\). The method runs fully automatically and provides a detailed model of the retinal vasculature, which is crucial as a sound basis for further quantitative analysis of the retina, especially in screening applications.
MSC:
| 92C55 | Biomedical imaging and signal processing |
Keywords:
Gabor wavelets; oriented wavelets; orientation scores; vessel tracking; retina; retinal vasculatureReferences:
| [1] | Abramoff, M.D., Garvin, M.K., Sonka, M.: Retinal imaging and image analysis. IEEE Rev. Biomed. Eng. 3, 169-208 (2010) · doi:10.1109/RBME.2010.2084567 |
| [2] | Al-Diri, B., Hunter, A., Steel, D.: An active contour model for segmenting and measuring retinal vessels. IEEE Trans. Med. Imaging 28(9), 1488-1497 (2009) · doi:10.1109/TMI.2009.2017941 |
| [3] | Al-Diri, B., Hunter, A., Steel, D., Habib, M.: Automated analysis of retinal vascular network connectivity. Comput. Med. Imaging Graph. 34(6), 462-470 (2010). doi:10.1016/j.compmedimag.2009.12.013. http://www.ncbi.nlm.nih.gov/pubmed/20116209. · doi:10.1016/j.compmedimag.2009.12.013 |
| [4] | Aubin, T.: A Course in Differential Geometry. Graduate Studies in Mathematics, vol. 27 (2001) · Zbl 0966.53001 |
| [5] | August, J.: The curve indicator random field. Ph.D. thesis, Yale University (2001) · Zbl 0623.35006 |
| [6] | August, J., Zucker, S.: The curve indicator random field and Markov processes. IEEE Trans. Pattern Anal. Mach. Intell. 25(4), 387-400 (2003) · doi:10.1109/TPAMI.2003.1190567 |
| [7] | Bankhead, P., Scholfield, C.N., McGeown, J.G., Curtis, T.M.: Fast retinal vessel detection and measurement using wavelets and edge location refinement. PLoS ONE 7(3), e32435 (2012) · doi:10.1371/journal.pone.0032435 |
| [8] | Bekkers, E.: A new retinal vessel tracking method based on orientation scores. Master’s thesis, Department of Biomedical Engineering, Eindhoven University of Technology, the Netherlands (2012) |
| [9] | Bergholm, F.: Edge focusing. IEEE Trans. Pattern Anal. Mach. Intell. PAMI-9(6), 726-741 (1987) · doi:10.1109/TPAMI.1987.4767980 |
| [10] | Boscain, U., Charlot, G., Rossi, F.: Existence of planar curves minimizing length and curvature. Differential equations and dynamical systems, collected papers. Tr. Mat. Inst. Steklova 270, 49-61 (2010) · Zbl 1215.53006 |
| [11] | Boscain, U., Duits, R., Rossi, F., Sachkov, Y.: Curve cuspless reconstruction via sub-Riemannian geometry. ESAIM Control Optim. Calc. Var. (2014, to appear). arXiv:1203.3089v4. http://bmia.bmt.tue.nl/people/RDuits/1203.3089v2.pdf. doi:10.1051/cocv/2013082 · Zbl 1381.49003 |
| [12] | Brinchmann-Hansen, O., Heier, H.: Theoretical relations between light streak characteristics and optical properties of retinal vessels. Acta Ophthalmol. 64(S179), 33-37 (1986). doi:10.1111/j.1755-3768.1986.tb00701.x · doi:10.1111/j.1755-3768.1986.tb00701.x |
| [13] | Budai, A.: Gold Standard Database for Evaluation of Fundus Image Segmentation Algorithms (2011). http://www5.informatik.uni-erlangen.de/en/research/data/fundus-images/ |
| [14] | Budai, A., Hornegger, J., Michelson, G.: Multiscale approach for blood vessel segmentation on retinal fundus images. Investig. Ophthalmol. Vis. Sci. 50, 325 (2009) |
| [15] | Can, A., Shen, H., Turner, J.N., Tanenbaum, H.L., Roysam, B.: Rapid automated tracing and feature extraction from retinal fundus images using direct exploratory algorithms. IEEE Trans. Inf. Technol. Biomed. 3, 125-138 (1999) · doi:10.1109/4233.767088 |
| [16] | Chen, J., Sato, Y., Tamura, S.: Orientation space filtering for multiple orientation line segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 22(5), 417-429 (2000). doi:10.1109/34.857000 · doi:10.1109/34.857000 |
| [17] | Chutatape, O.; Zheng, L.; Krishnan, S., Retinal blood vessel detection and tracking by matched Gaussian and Kalman filters, No. 6, 3144-3149 (1998) |
| [18] | Citti, G., Sarti, A.: A cortical based model of perceptual completion in the roto-translation space. J. Math. Imaging Vis. 24(3), 307-326 (2006) · Zbl 1478.92100 · doi:10.1007/s10851-005-3630-2 |
| [19] | Duits, R.: Perceptual organization in image analysis. Ph.D. thesis, Department of Biomedical Engineering, Eindhoven University of Technology, the Netherlands (2005) |
| [20] | Duits, R., Franken, E.: Left-invariant stochastic evolution equations on SE(2) and its applications to contour enhancement and contour completion via invertible orientation scores. CASA-report and arXiv (2007). arXiv:0711.0951v4. http://www.win.tue.nl/casa/research/casareports/2007.html · Zbl 1202.35334 |
| [21] | Duits, R.; Franken, E. M.; Tai, X.-C. (ed.), Line enhancement and completion via linear left-invariant scale spaces on SE(2), 795-807 (2009) · doi:10.1007/978-3-642-02256-2_66 |
| [22] | Duits, R., Franken, E.: Left-invariant parabolic evolutions on SE(2) and contour enhancement via invertible orientation scores. Part II: non-linear left-invariant diffusions on invertible orientation score. Q. Appl. Math. 68, 293-331 (2010) · Zbl 1205.35326 |
| [23] | Duits, R., Franken, E.: Left-invariant parabolic evolutions on SE(2) and contour enhancement via invertible orientation scores. Part I: linear left-invariant diffusion equations on SE(2). Q. Appl. Math. 68(2), 255-292 (2010) · Zbl 1202.35334 |
| [24] | Duits, R., van Almsick, M.: The explicit solutions of linear left-invariant second order stochastic evolution equations on the 2D-Euclidean motion group. Q. Appl. Math. 66, 27-67 (2008) · Zbl 1153.60040 |
| [25] | Duits, R., Duits, M., van Almsick, M., ter Haar Romeny, B.: Invertible orientation scores as an application of generalized wavelet theory. Pattern Recognit. Image Anal. 17, 438 (2007). doi:10.1134/S105466180703011X · doi:10.1134/S105466180703011X |
| [26] | Duits, R., Felsberg, M., Granlund, G.H., ter Haar Romeny, B.M.: Image analysis and reconstruction using a wavelet transform constructed from a reducible representation of the Euclidean motion group. Int. J. Comput. Vis. 72(1), 79-102 (2007) · doi:10.1007/s11263-006-8894-5 |
| [27] | Duits, R., Boscain, U., Rossi, F., Sachkov, Y.: Association fields via cuspless sub-Riemannian geodesics in SE(2). J. Math. Imaging Vis. (2012, submitted). http://bmia.bmt.tue.nl/people/RDuits/cusps.pdf · Zbl 1296.49040 |
| [28] | Espona, L.; Carreira, M. J.; Ortega, M.; Penedo, M. G., A snake for retinal vessel segmentation, IbPRIA’07, Berlin · doi:10.1007/978-3-540-72849-8_23 |
| [29] | Felsberg, M., Forssen, P.E., Scharr, H.: Channel smoothing: efficient robust smoothing of low-level signal features. IEEE Trans. Pattern Anal. Mach. Intell. 28(2), 209-222 (2006) · doi:10.1109/TPAMI.2006.29 |
| [30] | Fischer, S., Šroubek, F., Perrinet, L., Redondo, R., Cristóbal, G.: Self-invertible 2D log-Gabor wavelets. Int. J. Comput. Vis. 75(2), 231-246 (2007). doi:10.1007/s11263-006-0026-8 · doi:10.1007/s11263-006-0026-8 |
| [31] | Florack, L., Kuijper, A.: The topological structure of scale-space images. J. Math. Imaging Vis. 79, 65-79 (2000). http://link.springer.com/article/10.1023/A · Zbl 0979.68585 · doi:10.1023/A:1008304909717 |
| [32] | Frangi, A. F.; Niessen, W. J.; Vincken, K. L.; Viergever, M. A., Multiscale vessel enhancement filtering, 130-137 (1998), Berlin · doi:10.1007/BFb0056195 |
| [33] | Franken, E.: Enhancement of crossing elongated structures in images. Ph.D. thesis, Department of Biomedical Engineering, Eindhoven University of Technology, the Netherlands (2008) |
| [34] | Franken, E., Duits, R.: Crossing-preserving coherence-enhancing diffusion on invertible orientation scores. Int. J. Comput. Vis. 85(3), 253-278 (2009). doi:10.1007/s11263-009-0213-5 · doi:10.1007/s11263-009-0213-5 |
| [35] | Freeman, W.T., Adelson, E.H.: The design and use of steerable filters. IEEE Trans. Pattern Anal. Mach. Intell. 13, 891-906 (1991) · doi:10.1109/34.93808 |
| [36] | Führ, H.: Abstract Harmonic Analysis of Continuous Wavelet Transforms. Springer, Berlin (2005) · Zbl 1060.43002 |
| [37] | Granlund, G.H., Knutsson, H.: Signal Processing for Computer Vision. Kluwer Academic, Norwell (1995) · doi:10.1007/978-1-4757-2377-9 |
| [38] | Gregson, P.H., Shen, Z., Scott, R.C., Kozousek, V.: Automated grading of venous beading. Comput. Biomed. Res. 28(4), 291-304 (1995) · doi:10.1006/cbmr.1995.1020 |
| [39] | Grisan, E.; Pesce, A.; Giani, A.; Foracchia, M.; Ruggeri, A., A new tracking system for the robust extraction of retinal vessel structure, IEMBS’04 |
| [40] | Hough, P.: Method and means for recognizing complex patterns. US Patent nr. 3069654, 1962 |
| [41] | Hubel, D.H., Wiesel, T.N., Hubel, D., Wiesel, T.: Republication of The Journal of Physiology (1959) 148, 574-591: Receptive fields of single neurones in the cat’s striate cortex. 1959. J. Physiol. (Lond.) 587(Pt 12), 2721-2732 (2009) |
| [42] | Johansen, P.: On the classification of toppoints in scale space. J. Math. Imaging Vis. 4(1), 57-67 (1994). doi:10.1007/BF01250004. http://link.springer.com/10.1007/BF01250004 · doi:10.1007/BF01250004 |
| [43] | Kalitzin, S.N., Romeny, B.M.T.H., Viergever, M.A.: Invertible apertured orientation filters in image analysis. Int. J. Comput. Vis. 31(2-3), 145-158 (1999). doi:10.1023/A:1008013815039 · doi:10.1023/A:1008013815039 |
| [44] | Krause, M., Alles, R., Burgeth, B., Weickert, J.: Fast retinal vessel analysis. J. Real-Time Image Process., 1-10 (2013). doi:10.1007/s11554-013-0342-5 |
| [45] | Li, Q.; You, J.; Zhang, L.; Bhattacharya, P., A multiscale approach to retinal vessel segmentation using Gabor filters and scale multiplication, SMC’06 · doi:10.1109/ICSMC.2006.384665 |
| [46] | Lowell, J., Hunter, A., Steel, D., Basu, A., Ryder, R., Kennedy, R.L.: Measurement of retinal vessel widths from fundus images based on 2-D modeling. IEEE Trans. Med. Imaging 23(10), 1196-1204 (2004) · doi:10.1109/TMI.2004.830524 |
| [47] | Mumford, D., Elastica and computer vision, 491-506 (1994), Berlin · Zbl 0798.53003 · doi:10.1007/978-1-4612-2628-4_31 |
| [48] | Odstrcilik, J.; Jan, J.; Kolar, R.; Gazarek, J., Improvement of vessel segmentation by matched filtering in colour retinal images, 327-330 (2009) |
| [49] | Patton, N., Aslam, T.M., MacGillivray, T., Deary, I.J., Dhillon, B., Eikelboom, R.H., Yogesan, K., Constable, I.J.: Retinal image analysis: concepts, applications and potential. Prog. Retin. Eye Res. 25(1), 99-127 (2006). doi:10.1016/j.preteyeres.2005.07.001 · doi:10.1016/j.preteyeres.2005.07.001 |
| [50] | Perona, P., Deformable kernels for early vision, Proceedings CVPR’91 · doi:10.1109/CVPR.1991.139691 |
| [51] | Philipsen, R.: Retinal vascular tree segmentation and classification by means of multiscale vessel filtering and fractal analysis. Master’s thesis, Department of Biomedical Engineering, Eindhoven University of Technology, the Netherlands (2012) · Zbl 1231.68272 |
| [52] | Poletti, E., Fiorin, D., Grisan, E., Ruggeri, A.: Automatic vessel segmentation in wide-field retina images of infants with retinopathy of prematurity. Conf Proc IEEE Eng Med Biol Soc 2011, 3954-3957 (2011) |
| [53] | Rudin, W.: Functional Analysis. McGraw-Hill Series in Higher Mathematics. McGraw-Hill, New York (1973). W. Rudin—Functional Analysis.djvu · Zbl 0253.46001 |
| [54] | Simoncelli, E., Design of multi-dimensional derivative filters, ICIP-94 · doi:10.1109/ICIP.1994.413423 |
| [55] | Sinthanayothin, C., Boyce, J.F., Cook, H.L., Williamson, T.H.: Automated localisation of the optic disc, fovea, and retinal blood vessels from digital colour fundus images. Br. J. Ophthalmol. 83(8), 902-910 (1999) · doi:10.1136/bjo.83.8.902 |
| [56] | Soares, J.V., Leandro, J.J., Cesar Junior, R.M., Jelinek, H.F., Cree, M.J.: Retinal vessel segmentation using the 2-D Gabor wavelet and supervised classification. IEEE Trans. Med. Imaging 25(9), 1214-1222 (2006) · doi:10.1109/TMI.2006.879967 |
| [57] | Takahashi, Y.; Watanabe, S., The probability functionals (Onsager-Machlup functions) of diffusion processes, No. 851, 433-463 (1981), Berlin · Zbl 0625.60058 |
| [58] | Tasman, W., Jaeger, E.A.: Duane’s ophthalmology. Lippincott Williams and Wilkins (2009). http://www.lww.com/product/?978-1-60547-732-9 |
| [59] | Thornber, K., Williams, L.: Analytic solution of stochastic completion fields. Biol. Cybern. 75, 141-151 (1996) · Zbl 0869.92030 · doi:10.1007/s004220050282 |
| [60] | Thornber, K., Williams, L.: Characterizing the distribution of completion shapes with corners using a mixture of random processes. Pattern Recognit. 33, 543-553 (2000) · doi:10.1016/S0031-3203(99)00071-0 |
| [61] | Weickert, J.: Coherence-enhancing diffusion filtering. Int. J. Comput. Vis. 31(2-3), 111-127 (1999). doi:10.1023/A:1008009714131 · Zbl 1505.94010 · doi:10.1023/A:1008009714131 |
| [62] | Wittich, O.: An explicit local uniform large deviation bound for Brownian bridges. Stat. Probab. Lett. 73(1), 51-56 (2005) · Zbl 1080.60503 · doi:10.1016/j.spl.2005.02.013 |
| [63] | Wloka, J.: Partial Differential Equations. Cambridge University Press, Cambridge (1987). http://books.google.nl/books?id=Eix7JA9VVy0C · Zbl 0623.35006 · doi:10.1017/CBO9781139171755 |
| [64] | Xu, X., Niemeijer, M., Song, Q., Sonka, M., Garvin, M.K., Reinhardt, J.M., Abramoff, M.D.: Vessel boundary delineation on fundus images using graph-based approach. IEEE Trans. Med. Imaging 30(6), 1184-1191 (2011) · doi:10.1109/TMI.2010.2103566 |
| [65] | Yin, Y., Adel, M., Bourennane, S.: Retinal vessel segmentation using a probabilistic tracking method. Pattern Recognit. 45(4), 1235-1244 (2012). doi:10.1016/j.patcog.2011.09.019 · Zbl 1231.68272 · doi:10.1016/j.patcog.2011.09.019 |
| [66] | Zhou, L., Rzeszotarski, M.S., Singerman, L.J., Chokreff, J.M.: The detection and quantification of retinopathy using digital angiograms. IEEE Trans. Med. Imaging 13(4), 619-626 (1994) · doi:10.1109/42.363106 |
| [67] | Zweck, J., Williams, L.R.: Euclidean group invariant computation of stochastic completion fields using shiftable-twistable functions. J. Math. Imaging Vis. 21(2), 135-154 (2004) · Zbl 1433.68525 · doi:10.1023/B:JMIV.0000035179.47895.bc |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
