Multimedia Tools and Applications

, Volume 78, Issue 24, pp 34839–34865 | Cite as

Blood vessel segmentation of retinal image using Clifford matched filter and Clifford convolution

  • Somasis Roy
  • Anirban Mitra
  • Sudipta RoyEmail author
  • Sanjit Kumar Setua


The appearance and structure of blood vessels in retinal fundus image is a fundamental part of diagnosing different issues related with such as diabetes and hypertension. The proposed blood vessel segmentation in fundus image using Clifford Algebra approach is divided into three steps. Image vectorization as a first step helps to convert the image space into Clifford space. Next step introduces Clifford matched filter as a proposed mask which works for retinal blood vessel extraction. The third and final step of this method is Clifford convolution operation with the help of Clifford convolution. This mask generates edge points along the boundaries of the blood vessels. The edge points are represented as a Grade-0 vector or scalar unit. Discrete edge points along the boundary of blood vessels are the edge pixels instead of continuous edges. The output of this method differs in the representation of vessel tree compare to other existing methods. The output image can be defined as the edge point set. This method achieves blood vessel segmentation accuracy of 94.88% and 92.95% on two publicly available datasets STARE and DRIVE respectively in less than 0.5 s per image. The proposed matched filter and the segmentation technique opens many windows of reliable and faster processing for further image processing steps on retinal fundus images.


Blood vessel segmentation Clifford algebra Clifford convolution Fundus images Multi-vector RGB color model 



The authors extend sincere thanks to the Department of Computer Science and Engineering, University of Calcutta West Bengal, India and Academy Of Technology, Hooghly, West Bengal, India for using the infrastructure facilities for developing the technique.


  1. 1.
    Armande N, Montesinos P, Monga O (1997) Thin Nets Extraction using a Multi-Scale Approach. SCALE-SPACE ‟97: Proceedings of the First International Conference on Scale-Space Theory in Computer Vision, Springer-Verlag, pp. 361–364Google Scholar
  2. 2.
    Azzopardi G et al (2015) Trainable COSFIRE filters for vessel delineation with application to retinal images. Med Image Anal 19(1):46–57CrossRefGoogle Scholar
  3. 3.
    Batard T, Berthier M (2010) Clifford algebra bundles to multidimensional image segmentation. AACA 20(3–4):489–516MathSciNetCrossRefGoogle Scholar
  4. 4.
    Batard T, Saint-Jean C, Berthier M (2009) A metric approach to nD images edge detection with Clifford algebras. Journal of Mathematical Imaging and Vision 33(3):296–312MathSciNetCrossRefGoogle Scholar
  5. 5.
    Bhalerao A, Wilson R (2001) Estimating Local and Global Image Structure using a Gaussian Intensity Model. Medical Image Understanding and AnalysisGoogle Scholar
  6. 6.
    Carré P, Denis P, Fernandez-Maloigne C (2014) Spatial color image processing using Clifford algebras: application to color active contour. SIViP 8(7):1357–1372CrossRefGoogle Scholar
  7. 7.
    Chanwimaluang T, Fan G (2003) An Efficient Blood Vessel Detection Algorithm for Retinal Images using Local Entropy Thresholding. In: Proc. of the IEEE International Symposium on Circuits and Systems, Bangkok, vol.5, pp.21–24Google Scholar
  8. 8.
    Chaudhuri S, Chatterjee S, Katz N, Nelson M, Goldbaum M (1989) Detection of blood vessels in retinal images using two-dimensional matched filters. IEEE Trans Med Imaging 8(3):263–269CrossRefGoogle Scholar
  9. 9.
    Dash J, Bhoi N (2016) A method for blood vessel segmentation in retinal images using morphological reconstruction. Computer, Electrical & Communication Engineering (ICCECE), 2016 International Conference on. IEEEGoogle Scholar
  10. 10.
    Denis P, Carré P (2007) Colour gradient using geometric algebra." Signal Processing Conference, 2007 15th European. IEEEGoogle Scholar
  11. 11.
    Dian Tunjung N, Arifin AZ, Soelaiman R. Medical image segmentation using generalized gradient vector flow and Clifford geometric algebraGoogle Scholar
  12. 12.
    Dorst L, Mann S (2002) Geometric Algebra: A Computational Framework for Geometrical Applications(I). IEEE Comput Graph ApplGoogle Scholar
  13. 13.
    Ebling J, Scheuermann G (2003) Clifford Convolution and Pattern Matching On Vector Fields. Proceedings of IEEE Visualization:193–200, 2003Google Scholar
  14. 14.
    Ell TA (2007) Multi-vector color-image filters. 2007 IEEE International Conference on Image Processing. Vol. 5. IEEEGoogle Scholar
  15. 15.
    Fang B, Hsu W, Lee M (2003) Reconstruction of Vascular Structures in Retinal Images. Proc. ICIP‟03, pp. 157–160Google Scholar
  16. 16.
    Fathi A, Naghsh-Nilchi AR (2012) Automatic wavelet-based retinal blood vessels segmentation and vessel diameter estimation. Biomedical Signal Pro-cessing and Control 8(1):71–80CrossRefGoogle Scholar
  17. 17.
    Frame A, McCree M, Olson J, McHardy K, Sharp P, Forrester JV (1997) Structural Analysis of Retinal Vessels. Proceedings of the Sixth International Conference on Image Processing and its Applications, IEEE, vol.2, pp. 824–827Google Scholar
  18. 18.
    Franchini S, et al (2012) Clifford Algebra Based Edge Detector for Color Images. Complex, Intelligent and Software Intensive Systems (CISIS), 2012 Sixth International Conference on. IEEEGoogle Scholar
  19. 19.
    Fraz MM, Remagnino P, Hoppe A, Uyyanonvara B, Rudnicka A, Owen C, Barman S (2012) Blood vessel segmentation methodologies in retinal images – A survey. Comput Methods Prog Biomed 108:407–433CrossRefGoogle Scholar
  20. 20.
    Gonzalez RC, Woods RE (2001) Digital Image Processing, 2nd editionGoogle Scholar
  21. 21.
    Grass SHM, Rasche V, O S, Haehnel S, Sartor K (2002) An X-Ray-Based Method for the Determination of the Contrast Agent Propagation in 3-D Vessel Structures. IEEE Trans Med Imaging 21:251–262CrossRefGoogle Scholar
  22. 22.
    Hart WE, Goldbaum M, Cote B, Kube P, Nelson MR (1997) Automated measurement of retinal vascular tortuosity. In: Proceedings of the AMIA Fall ConferenceGoogle Scholar
  23. 23.
    Hoover A, Kouznetsova V, Goldbaum M (2000) Locating blood vessels in retinal images by piecewise threshold probing of a matched filter response. IEEE Transactions onMedical Imaging 19(3):203–210CrossRefGoogle Scholar
  24. 24.
    J¨ahne B (2002) Digitale Bildverarbeitung. Springer Verlag, BerlinCrossRefGoogle Scholar
  25. 25.
    Jiang X, Mojon D (2003) Adaptive local thresholding by verification-based multithreshold probing with application to vessel detection in retinal images. IEEE Trans Pattern Anal Mach Intell 25(1):131–137CrossRefGoogle Scholar
  26. 26.
    (2009) Learning Geometric Algebra with CLUCalc. In: Geometric Algebra with Applications in Engineering. Geometry and Computing, vol 4. Springer, Berlin, HeidelbergGoogle Scholar
  27. 27.
    Li H, Hsu W, Lee ML, Wang H (2005) Automatic Grading of Retinal Vessel Calibre. IEEE Trans Biomed Eng 52:1352–1355CrossRefGoogle Scholar
  28. 28.
    Maharjan A (2016) Blood Vessel Segmentation from Retinal Images. Comput Therm SciGoogle Scholar
  29. 29.
    Maitra IK, Nag S, Bandyopadhyay SK (2011) Automated Digital Mammogram Segmentation for Detection of Abnormal Masses Using Binary Homogeneity Enhancement Algorithm. IJCSE, ISSN No. 0976–5166 2(3):415–427Google Scholar
  30. 30.
    Mann S, Dorst L, Bouma T (2001) The Making of GABLE: A Geometric Algebra Learning Environment in Matlab. In: Corrochano EB, Sobczyk G (eds) Geometric Algebra with Applications in Science and Engineering. Birkhäuser, BostonGoogle Scholar
  31. 31.
    Mishra B, Wilson P, Al-Hashimi BM (2008) Advancement in color image processing using Geometric Algebra. Signal Processing Conference, 2008 16th European. IEEEGoogle Scholar
  32. 32.
    Mishra B, Wilson P, Wilcock R (2015) A geometric algebra co-processor for color edge detection. Electronics 4(1):94–117CrossRefGoogle Scholar
  33. 33.
    Mitra A, Roy S, Roy S, Setua SK (2018) Enhancement and Restoration of non-uniform illuminated Fundus Image of Retina obtained through thin layer of Cataract. Comput Methods Prog Biomed, ELSEVIER 156:169–178CrossRefGoogle Scholar
  34. 34.
    Mitra A, Roy S, Setua SK (2014) Morphologically contour extraction of decisive objects from image. Automation, Control, Energy and Systems (ACES), 2014 First International Conference on. IEEEGoogle Scholar
  35. 35.
    Mittal M, Verma A, Kaur B, Sharma M, Goyal LM, Kaur I, Roy S, Kim T (2019) An Efficient Edge Detection Approach to Provide Better Edge Connectivity for Image Analysis. IEEE ACCESS 7(1):33240–33255CrossRefGoogle Scholar
  36. 36.
    Mudassar AA, Butt S (2013) Extraction of blood vessels in retinal images using four different techniques. Journal of Medical Engineering 2013Google Scholar
  37. 37.
    Nguyen UT, Bhuiyan A, Park LA, Ramamohanarao K (2013) An effective retinal blood vessel segmentation method using multi-scale line detection. Pattern Recogn 46:703–715CrossRefGoogle Scholar
  38. 38.
    Pizer SM et al (1987) Adaptive histogram equalization and its variations. Computer Vision, Graphics, and Image Processing 39(3):355–368CrossRefGoogle Scholar
  39. 39.
    Rani P, Priyadarshini N, Rajkumar ER, Rajamani K (2016) Retinal vessel segmentation under pathological conditions using supervised machine learning. In 2016 International Conference on, Systems in Medicine and Biology (ICSMB), pp. 62–66Google Scholar
  40. 40.
    Reich, Wieland, and Gerik Scheuermann. (2010) Analyzing Real Vector Fields with Clifford Convolution and Clifford-Fourier Transform. pp. 121–133Google Scholar
  41. 41.
    Ricci E, Perfetti R (2007) Retinal Blood Vessel Segmentation Using Line Operators and Support Vector Classification. IEEE Trans Med Imaging 26(2007):1357–1365CrossRefGoogle Scholar
  42. 42.
    Rivera-Rovelo J, Bayro-Corrochano E (2006) Medical image segmentation using a self-organizing neural network and Clifford geometric algebra. The 2006 IEEE International Joint Conference on Neural Network Proceedings. IEEEGoogle Scholar
  43. 43.
    Roy S, Mitra A, Setua SK (2014) Color Image Representation Using Multivector. Intelligent Systems, Modelling and Simulation (ISMS), 2014 5th International Conference on. IEEEGoogle Scholar
  44. 44.
    Roychowdhury S, Koozekanani DD, Parhi KK (2015) Blood vessel segmentation of fundus images by major vessel extraction and subimage classification. IEEE Journal of Biomedical and Health Informatics 19(3):1118–1128Google Scholar
  45. 45.
    Schlemmer M, et al (2006) Clifford pattern matching for color image edge detection. Visualization of Large and Unstructured Data Sets, GI-Edition Lecture Notes in Informatics (LNI) 4, pp. 47–58Google Scholar
  46. 46.
    Shah SAA, Tang TB, Faye I, Laude A (2017) Blood vessel segmentation in color fundus images based on regional and Hessian features. Graefes Arch Clin Exp Ophthalmol:1–9Google Scholar
  47. 47.
    Soares JV, Leandro JJ, Cesar RM, Jelinek HF, Cree MJ (2006) Retinal vessel segmentation using the 2-D Gabor wavelet and supervised classification. IEEE Transaction of Medical Imaging 25:1214–1222CrossRefGoogle Scholar
  48. 48.
    Staal J, Abr’amoff MD, Niemeijer M, Viergever MA, Van Ginneken B (2004) Ridge-based vessel segmentation in color images of the retina. IEEE Trans Med Imaging 23(4):501–509CrossRefGoogle Scholar
  49. 49.
    Sun K, Chen Z, Jiang S, Wang Y (2011) Morphological multiscale enhance-ment, fuzzy filter and watershed for vascular tree extraction in angiogram. J Med Syst 35(5):811–824CrossRefGoogle Scholar
  50. 50.
    Wang L, Bhalerao A, Wilson R (2007) Analysis of Retinal Vasculature using a Multiresolution Hermite Model. IEEE Trans Med Imaging 26:137–152CrossRefGoogle Scholar
  51. 51.
    Xu L, Luo S (2010) A novel method for blood vessel detection from retinal images. Biomed Eng Online 9(1):14CrossRefGoogle Scholar
  52. 52.
    Yavuz Z, Köse C (2017) Blood Vessel Extraction in Color Retinal Fundus Images with Enhancement Filtering and Unsupervised Classification. Journal of Healthcare Engineering 2017Google Scholar
  53. 53.
    Yin X-X, Hadjiloucas S, Zhang Y (2017) Outlook for Clifford Algebra Based Feature and Deep Learning AI Architectures. Pattern Classification of Medical Images: Computer Aided Diagnosis. Springer, Cham, pp. 165–177CrossRefGoogle Scholar
  54. 54.
    Zana F, Klein J (2001) Segmentation of Vessel-Like Patterns using Mathematical Morphology and Curvature Evaluation. IEEE Trans Image Process:1010–1019CrossRefGoogle Scholar
  55. 55.
    Zhang Y, Hsu Mong W, Lee L (2007) Segmentation of Retinal Vessels Using Nonlinear Projections. IEEE International Conference on Image Processing 5:541–544Google Scholar
  56. 56.
    Zhang B, Zhang L, Karray F (2010) Retinal vessel extraction by matched filter with first-order derivative of Gaussian. Comput Biol Med 40:438–445CrossRefGoogle Scholar
  57. 57.
    Zhao YQ et al (2014) Retinal vessels segmentation based on level set and region growing. Pattern Recogn 47(7):2437–2446CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Computer Science & EngineeringCalcutta University Technology CampusKolkataIndia
  2. 2.Department of Computer Science & EngineeringAcademy of TechnologyAdisaptagramIndia
  3. 3.Mallinckrodt Institute of RadiologyWashington University in Saint LouisSaint LouisUSA

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