Skip to main content
SpringerLink
Log in

The relationship between curvilinear structure enhancement and ridge detection methods

  • Original article
  • Published:
The Visual Computer Aims and scope Submit manuscript

Abstract

Curvilinear structure detection and quantification is a large research area with many imaging applications in fields such as biology, medicine, and engineering. Curvilinear enhancement is often used as a pre-processing stage for ridge detection, but there has been little investigation into the relationship between enhancement and ridge detection. In this paper, we thoroughly evaluate the pair-wise combinations of different curvilinear enhancement and ridge detection methods across two highly varied datasets, as well as samples of three other datasets. In particular, we present the approaches complementing one another and the gained insights, which will aid researchers in designing generic ridge detectors.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Notes

  1. For the comparison of all enhancement and ridge detectors for images from both datasets, DRIVE and GUFI-1, the reader is advised to refer to Tables 4 and 5.

  2. To see the stability of output measures of all enhancement and ridge detectors for images on both datasets, DRIVE and GUFI-1, the reader is advised to refer to Tables 6 and 7.

References

  1. Wang, D.C., Vagnucci, A.H., Li, C.: Digital image enhancement: a survey. Comput. Vis., Graph., Image Process. 24(3), 363–381 (1983)

    Article  Google Scholar 

  2. Miri, M.S., Mahloojifar, A.: A comparison study to evaluate retinal image enhancement techniques. In: IEEE International Conference on Signal and Image Processing Applications, Kuala Lumpur, Malaysia, pp. 90–94 (2009)

  3. Grün, G.: The Development of the Vertebrate Retina: A Comparative Survey. Springer, Berlin (2012)

    Google Scholar 

  4. Dash, J., Bhoi, N.: A survey on blood vessel detection methodologies in retinal images. In: IEEE International Conference on Computational Intelligence and Networks, Jabalpur, India, pp. 166–171 (2015)

  5. Saha, P.K., Borgefors, G., di Baja, G.S.: A survey on skeletonization algorithms and their applications. Pattern Recogn. Lett. 76(1), 3–12 (2016)

    Article  Google Scholar 

  6. Staal, J., Abràmoff, M.D., Niemeijer, M., Viergever, M.A., Van Ginneken, B.: Ridge-based vessel segmentation in color images of the retina. IEEE Trans. Med. Imaging 23(4), 501–509 (2004)

    Article  Google Scholar 

  7. Lopez-Molina, C., de Ulzurrun, G.V.-D., Baetens, J., Van den Bulcke, J., De Baets, B.: Unsupervised ridge detection using second order anisotropic Gaussian kernels. Sig. Process. 116(1), 55–67 (2015)

    Article  Google Scholar 

  8. Smistad, E.: GPU-based airway tree segmentation and centerline extraction. Master’s thesis, Institutt for Datateknikk Og Informasjonsvitenskap (2012)

  9. Sluimer, I., Schilham, A., Prokop, M., van Ginneken, B.: Computer analysis of computed tomography scans of the lung: a survey. IEEE Trans. Med. Imaging 25(4), 385–405 (2006)

    Article  Google Scholar 

  10. Chung, D.H., Sapiro, G.: Segmentation-free skeletonization of gray-scale images via PDEs. In: IEEE International Conference on Image Processing, Quebec City, Canada, pp. 927–930 (2000)

  11. Yim, P.J., Choyke, P.L., Summers, R.M.: Gray-scale skeletonization of small vessels in magnetic resonance angiography. IEEE Trans. Med. Imaging 19(6), 568–576 (2000)

    Article  Google Scholar 

  12. Stosic, T., Stosic, B.D.: Multifractal analysis of human retinal vessels. IEEE Trans. Med. Imaging 25(8), 1101–1107 (2006)

    Article  MATH  Google Scholar 

  13. Mendonca, A.M., Campilho, A.: Segmentation of retinal blood vessels by combining the detection of centerlines and morphological reconstruction. IEEE Trans. Med. Imaging 25(9), 1200–1213 (2006)

    Article  Google Scholar 

  14. Annunziata, R., Kheirkhah, A., Hamrah, P., Trucco, E.: Scale and curvature invariant ridge detector for tortuous and fragmented structures. In: International Conference on Medical Image Computing and Computer-Assisted Intervention, Munich, Germany, pp. 588–595 (2015)

  15. Aylward, S.R., Jomier, J., Weeks, S., Bullitt, E.: Registration and analysis of vascular images. Int. J. Comput. Vis. 55(2–3), 123–138 (2003)

    Article  Google Scholar 

  16. Zhou, Y., Kaufman, A., Toga, A.W.: Three-dimensional skeleton and centerline generation based on an approximate minimum distance field. Vis. Comput. 14(7), 303–314 (1998)

    Article  Google Scholar 

  17. Piuze, E., Kry, P.G., Siddiqi, K.: Generalized helicoids for modeling hair geometry. Comput. Graph. Forum 30(2), 247–256 (2011)

    Article  Google Scholar 

  18. Willcocks, C.G., Jackson, P.T., Nelson, C.J., Obara, B.: Extracting 3D parametric curves from 2D images of helical objects. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1757–1769 (2017)

    Article  Google Scholar 

  19. Strokina, N., Kurakina, T., Eerola, T., Lensu, L., Kälviäinen, H.: Detection of curvilinear structures by tensor voting applied to fiber characterization. In: Scandinavian Conference on Image Analysis, Espoo, Finland, pp. 22–33 (2013)

  20. Maio, D., Maltoni, D.: Direct gray-scale minutiae detection in fingerprints. IEEE Trans. Pattern Anal. Mach. Intell. 19(1), 27–40 (1997)

    Article  Google Scholar 

  21. López, A.M., Lumbreras, F., Serrat, J., Villanueva, J.J.: Evaluation of methods for ridge and valley detection. IEEE Trans. Pattern Anal. Mach. Intell. 21(4), 327–335 (1999)

    Article  Google Scholar 

  22. Bas, E., Erdogmus, D.: Principal curves as skeletons of tubular objects. Neuroinformatics 9(2–3), 181–191 (2011)

    Article  Google Scholar 

  23. Cheng, G., Wang, Y., Xu, S., Wang, H., Xiang, S., Pan, C.: Automatic road detection and centerline extraction via cascaded end-to-end convolutional neural network. IEEE Trans. Geosci. Remote Sens. 55(6), 3322–3337 (2017)

    Article  Google Scholar 

  24. Sironi, A., Lepetit, V., Fua, P.: Projection onto the manifold of elongated structures for accurate extraction. In: IEEE International Conference on Computer Vision, Santiago, Chile, pp. 316–324 (2015)

  25. Shen, W., Zhao, K., Jiang, Y., Wang, Y., Zhang, Z., Bai, X.: Object skeleton extraction in natural images by fusing scale-associated deep side outputs. In: IEEE Conference on Computer Vision and Pattern Recognition, Las Vegas, USA, pp. 222–230 (2016)

  26. Ling, Y., Yan, C., Liu, C., Wang, X., Li, H.: Adaptive tone-preserved image detail enhancement. Vis. Comput. 28(6–8), 733–742 (2012)

    Article  Google Scholar 

  27. Lindeberg, T.: Edge detection and ridge detection with automatic scale selection. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Francisco, USA, pp. 465–470 (1996)

  28. Frangi, A.F., Niessen, W.J., Vincken, K.L., Viergever, M.A.: Multiscale vessel enhancement filtering. In: International Conference on Medical Image Computing and Computer-Assisted Intervention, Cambridge, MA, USA, pp. 130–137 (1998)

  29. Perona, P.: Steerable-scalable kernels for edge detection and junction analysis. In: European Conference on Computer Vision, Santa Margherita Ligure, Italy, pp. 3–18 (1992)

  30. Meijering, E., Jacob, M., Sarria, J.-C., Steiner, P., Hirling, H., Unser, M.: Design and validation of a tool for neurite tracing and analysis in fluorescence microscopy images. Cytom. Part A 58A(2), 167–176 (2004)

    Article  Google Scholar 

  31. Pizer, S.M., Amburn, E.P., Austin, J.D., Cromartie, R., Geselowitz, A., Greer, T., ter Haar Romeny, B., Zimmerman, J.B., Zuiderveld, K.: Adaptive histogram equalization and its variations. Comput. Vis., Graph., Image Process. 39(3), 355–368 (1987)

    Article  Google Scholar 

  32. Zuiderveld, K.: Contrast limited adaptive histogram equalization. In: Graphics Gems, San Diego, CA, pp. 474–485 (1994)

  33. Zhu, H., Chan, F.H., Lam, F.K.: Image contrast enhancement by constrained local histogram equalization. Comput. Vis. Image Underst. 73(2), 281–290 (1999)

    Article  Google Scholar 

  34. Sheet, D., Garud, H., Suveer, A., Mahadevappa, M., Chatterjee, J.: Brightness preserving dynamic fuzzy histogram equalization. IEEE Trans. Consum. Electron. 56(4), 10 (2010)

    Article  Google Scholar 

  35. Joshi, P., Prakash, S.: Image enhancement with naturalness preservation. Vis. Comput. 36(1), 71–83 (2020)

    Article  Google Scholar 

  36. Freeman, W.T., Adelson, E.H., et al.: The design and use of steerable filters. IEEE Trans. Pattern Anal. Mach. Intell. 13(9), 891–906 (1991)

    Article  Google Scholar 

  37. Freeman, W.T., Adelson, E.H.: Steerable filters for early vision, image analysis, and wavelet decomposition. In: IEEE International Conference on Computer Vision, Osaka, Japan, pp. 406–415 (1990)

  38. Shui, P.-L., Zhang, W.-C.: Noise-robust edge detector combining isotropic and anisotropic Gaussian kernels. Pattern Recogn. 45(2), 806–820 (2012)

    Article  MATH  Google Scholar 

  39. Haralick, R.M., Sternberg, S.R., Zhuang, X.: Image analysis using mathematical morphology. IEEE Trans. Pattern Anal. Mach. Intell. 1(4), 532–550 (1987)

    Article  Google Scholar 

  40. Zana, F., Klein, J.-C.: Segmentation of vessel-like patterns using mathematical morphology and curvature evaluation. IEEE Trans. Image Process. 10(7), 1010–1019 (2001)

    Article  MATH  Google Scholar 

  41. Merveille, O., Naegel, B., Talbot, H., Najman, L., Passat, N.: 2D filtering of curvilinear structures by ranking the orientation responses of path operators (RORPO). Image Process. Line 7(1), 246–261 (2017)

    Article  MathSciNet  Google Scholar 

  42. Merveille, O., Talbot, H., Najman, L., Passat, N.: Curvilinear structure analysis by ranking the orientation responses of path operators. IEEE Trans. Pattern Anal. Mach. Intell. 40(2), 304–317 (2018)

    Article  MATH  Google Scholar 

  43. Sazak, Ç., Nelson, C.J., Obara, B.: The multiscale bowler-hat transform for blood vessel enhancement in retinal images. Pattern Recogn. 88, 739–750 (2019)

    Article  Google Scholar 

  44. Sato, Y., Nakajima, S., Atsumi, H., Koller, T., Gerig, G., Yoshida, S., Kikinis, R.: 3D multi-scale line filter for segmentation and visualization of curvilinear structures in medical images. In: Computer Vision, Virtual Reality and Robotics in Medicine and Medical Robotics and Computer-Assisted Surgery Grenoble, Grenoble, France, pp. 213–222 (1997)

  45. Jerman, T., Pernuš, F., Likar, B., Špiclin, Ž.: Enhancement of vascular structures in 3D and 2D angiographic images. IEEE Trans. Med. Imaging 35(9), 2107–2118 (2016)

    Article  Google Scholar 

  46. Obara, B., Fricker, M., Gavaghan, D., Grau, V.: Contrast-independent curvilinear structure detection in biomedical images. IEEE Trans. Image Process. 21(5), 2572–2581 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  47. Kovesi, P.: Phase congruency detects corners and edges. In: The Australian Pattern Recognition Society Conference, Brisbane, pp. 309–318 (2003)

  48. 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), 32435 (2012)

    Article  Google Scholar 

  49. Otsu, N.: A threshold selection method from gray-level histograms. IEEE Trans. Syst., Man, Cybern. 9(1), 62–66 (1979)

    Article  MathSciNet  Google Scholar 

  50. Vala, M.H.J., Baxi, A.: A review on Otsu image segmentation algorithm. Int. J. Adv. Res. Comput. Eng. Technol. 2(2), 387–389 (2013)

    Google Scholar 

  51. Nixon, M.S., Aguado, A.S.: Feature Extraction and Image Processing for Computer Vision. Academic Press, New York (2012)

    Google Scholar 

  52. Chang, S.G., Yu, B., Vetterli, M.: Spatially adaptive wavelet thresholding with context modeling for image denoising. IEEE Trans. Image Process. 9(9), 1522–1531 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  53. Jiang, X., Mojon, D.: Adaptive local thresholding by verification-based multithreshold probing with application to vessel detection in retinal images. IEEE Trans. Pattern Anal. Mach. Intell. 25(1), 131–137 (2003)

    Article  Google Scholar 

  54. Sezgin, M., et al.: Survey over image thresholding techniques and quantitative performance evaluation. J. Electron. Imaging 13(1), 146–168 (2004)

    Article  Google Scholar 

  55. Blum, H., Nagel, R.N.: Shape description using weighted symmetric axis features. Pattern Recogn. 10(3), 167–180 (1978)

    Article  MATH  Google Scholar 

  56. Cornea, N.D., Silver, D., Yuan, X., Balasubramanian, R.: Computing hierarchical curve-skeletons of 3D objects. Vis. Comput. 21(11), 945–955 (2005)

    Article  Google Scholar 

  57. Wade, L., Parent, R.E.: Automated generation of control skeletons for use in animation. Vis. Comput. 18(2), 97–110 (2002)

    Article  MATH  Google Scholar 

  58. Hassouna, M.S., Farag, A.A.: Robust centerline extraction framework using level sets. In: IEEE Conference on Computer Vision and Pattern Recognition, London, UK, pp. 458–465 (2005)

  59. Hassouna, M.S., Farag, A.A.: Variational curve skeletons using gradient vector flow. IEEE Trans. Pattern Anal. Mach. Intell. 31(12), 2257–2274 (2009)

    Article  Google Scholar 

  60. Siddiqi, K., Shokoufandeh, A., Dickinson, S.J., Zucker, S.W.: Shock graphs and shape matching. Int. J. Comput. Vis. 35(1), 13–32 (1999)

    Article  Google Scholar 

  61. Siddiqi, K., Bouix, S., Tannenbaum, A., Zucker, S.W.: The Hamilton–Jacobi skeleton. In: IEEE International Conference on Computer Vision, Kerkyra, Greece, vol. 2. pp. 828–834 (1999)

  62. Hesselink, W.H., Roerdink, J.B.: Euclidean skeletons of digital image and volume data in linear time by the integer medial axis transform. IEEE Trans. Pattern Anal. Mach. Intell. 30(12), 2204–2217 (2008)

    Article  Google Scholar 

  63. Telea, A., van Wijk, J.J.: An augmented fast marching method for computing skeletons and centerlines. In: Proceedings of the Symposium on Data Visualisation, Barcelona, Spain, pp. 251–260, (2002)

  64. Maragos, P., Schafer, R.: Morphological skeleton representation and coding of binary images. IEEE Trans. Acoust. Speech Signal Process. 34(5), 1228–1244 (1986)

    Article  Google Scholar 

  65. Zhang, T., Suen, C.Y.: A fast parallel algorithm for thinning digital patterns. Commun. ACM 27(3), 236–239 (1984)

    Article  Google Scholar 

  66. Chen, Y.-S., Hsu, W.-H.: A modified fast parallel algorithm for thinning digital patterns. Pattern Recogn. Lett. 7(2), 99–106 (1988)

    Article  Google Scholar 

  67. Boudaoud, L.B., Sider, A., Tari, A.: A new thinning algorithm for binary images. In: International Conference on Control, Engineering and Information Technology, Tlemcen, Algeria, pp. 1–6 (2015)

  68. Vincent, L.: Morphological grayscale reconstruction in image analysis: applications and efficient algorithms. IEEE Trans. Image Process. 2(2), 176–201 (1993)

    Article  Google Scholar 

  69. Arcelli, C., Di Baja, G.S.: Finding local maxima in a pseudo-Euclidian distance transform. Comput. Vis., Graph., Image Process. 43(3), 361–367 (1988)

    Article  Google Scholar 

  70. Borgefors, G.: Centres of maximal discs in the 5-7-11 distance transform. Scand. Conf. Image Anal. 1, 105 (1993)

    Google Scholar 

  71. Chatzis, V., Pitas, I.: A generalized fuzzy mathematical morphology and its application in robust 2-D and 3-D object representation. IEEE Trans. Image Process. 9(10), 1798–1810 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  72. Sharma, O., Mioc, D., Anton, F.: Voronoi diagram based automated skeleton extraction from colour scanned maps. In: IEEE International Symposium on Voronoi Diagrams in Science and Engineering, Banff, Canada, pp. 186–195 (2006)

  73. Corson, F.: Quelques aspects physiques du développement végétal. Ph.D. thesis, Université Pierre et Marie Curie-Paris, VI (2008)

  74. Willcocks, C.G., Li, F.W.: Feature-varying skeletonization. Vis. Comput. 28(6–8), 775–785 (2012)

    Article  Google Scholar 

  75. Sironi, A., Türetken, E., Lepetit, V., Fua, P.: Multiscale centerline detection. IEEE Trans. Pattern Anal. Mach. Intell. 38(7), 1327–1341 (2016)

    Article  Google Scholar 

  76. Shen, W., Bai, X., Hu, Z., Zhang, Z.: Multiple instance subspace learning via partial random projection tree for local reflection symmetry in natural images. Pattern Recogn. 52, 306–316 (2016)

    Article  Google Scholar 

  77. Shen, W., Zhao, K., Jiang, Y., Wang, Y., Bai, X., Yuille, A.: Deepskeleton: learning multi-task scale-associated deep side outputs for object skeleton extraction in natural images. IEEE Trans. Image Process. 26(11), 5298–5311 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  78. Wang, G., Van Stappen, G., De Baets, B.: Automated artemia length measurement using u-shaped fully convolutional networks and second-order anisotropic gaussian kernels. Comput. Electron. Agric. 168, 105102 (2020)

    Article  Google Scholar 

  79. Lindeberg, T.: Feature detection with automatic scale selection. Int. J. Comput. Vis. 30(2), 79–116 (1998)

    Article  Google Scholar 

  80. Do Carmo, M.P.: Differential Geometry of Curves and Surfaces: Revised and Updated, 2nd edn. Courier Dover, USA (2016)

    MATH  Google Scholar 

  81. Steger, C.: An unbiased detector of curvilinear structures. IEEE Trans. Pattern Anal. Mach. Intell. 20(2), 113–125 (1998)

    Article  Google Scholar 

  82. Jacob, M., Unser, M.: Design of steerable filters for feature detection using canny-like criteria. IEEE Trans. Pattern Anal. Mach. Intell. 26(8), 1007–1019 (2004)

    Article  Google Scholar 

  83. Alharbi, S.S., Willcocks, C.G., Jackson, P.T., Alhasson, H.F., Obara, B.: Sequential graph-based extraction of curvilinear structures. SIViP 13(5), 941–949 (2019)

    Article  Google Scholar 

  84. Niemeijer, M., Staal, J., van Ginneken, B., Loog, M., Abramoff, M.D., et al.: Comparative study of retinal vessel segmentation methods on a new publicly available database. In: SPIE Medical Imaging, vol. 5370, San Diego, CA, pp. 648–656 (2004)

  85. Kovesi, P.: Image features from phase congruency. Videre: J. Comput. Vis. Res. 1(3), 1–26 (1999)

    Google Scholar 

  86. Holm, S., Russell, G., Nourrit, V., McLoughlin, N.: DR HAGIS—a fundus image database for the automatic extraction of retinal surface vessels from diabetic patients. J. Med. Imaging 4(1), 014503 (2017)

    Article  Google Scholar 

  87. Budai, A., Bock, R., Maier, A., Hornegger, J., Michelson, G.: Robust vessel segmentation in fundus images. Int. J. Biomed. Imaging 2013(11), 1–11 (2013)

    Article  Google Scholar 

  88. Shi, Y., Cui, L., Qi, Z., Meng, F., Chen, Z.: Automatic road crack detection using random structured forests. IEEE Trans. Intell. Transp. Syst. 17(12), 3434–3445 (2016)

    Article  Google Scholar 

  89. Goldberg, D.E., Holland, J.H.: Genetic algorithms and machine learning. Mach. Learn. 3(2), 95–99 (1988)

    Article  Google Scholar 

  90. Conn, A.R., Gould, N.I., Toint, P.: A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds. SIAM J. Numer. Anal. 28(2), 545–572 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  91. Klette, R., Zamperoni, P.: Measures of correspondence between binary patterns. Image Vis. Comput. 5(4), 287–295 (1987)

    Article  Google Scholar 

  92. Baddeley, A.: Errors in binary images and an Lp version of the Hausdorff metric. Nieuw Arch. Wiskd. 10(4), 157–183 (1992)

    MATH  Google Scholar 

  93. Huttenlocher, D.P., Klanderman, G.A., Rucklidge, W.J.: Comparing images using the Hausdorff distance. IEEE Trans. Pattern Anal. Mach. Intell. 15(9), 850–863 (1993)

    Article  Google Scholar 

  94. Lu, Y., Tan, C.L., Huang, W., Fan, L.: An approach to word image matching based on weighted Hausdorff distance. In: International Conference on Document Analysis and Recognition, Seattle, USA, pp. 921–925 (2001)

  95. Zhao, C., Shi, W., Deng, Y.: A new Hausdorff distance for image matching. Pattern Recogn. Lett. 26(5), 581–586 (2005)

    Article  Google Scholar 

  96. Olson, C.F., Huttenlocher, D.P.: Automatic target recognition by matching oriented edge pixels. IEEE Trans. Image Process. 6(1), 103–113 (1997)

    Article  Google Scholar 

  97. Mount, D.M., Netanyahu, N.S., Le Moigne, J.: Efficient algorithms for robust feature matching. Pattern Recogn. 32(1), 17–38 (1999)

    Article  Google Scholar 

  98. Kwon, O.-K., Sim, D.-G., Park, R.-H.: Robust Hausdorff distance matching algorithms using pyramidal structures. Pattern Recogn. 34(10), 2005–2013 (2001)

    Article  MATH  Google Scholar 

  99. Dubuisson, M.-P., Jain, A.K.: A modified Hausdorff distance for object matching. In: International Conference on Pattern Recognition, Computer Vision and Image Processing, Jerusalem, pp. 566–568 (1994)

  100. Takacs, B.: Comparing face images using the modified Hausdorff distance. Pattern Recogn. 31(12), 1873–1881 (1998)

    Article  Google Scholar 

  101. Lin, K.-H., Guo, B., Lam, K.-M., Siu, W.-C.: Human face recognition using a spatially weighted modified Hausdorff distance. In: IEEE International Symposium on Intelligent Multimedia, Video and Speech Processing, pp. 477–480 (2001)

  102. Yu, C.-B., Qin, H.-F., Cui, Y.-Z., Hu, X.-Q.: Finger-vein image recognition combining modified Hausdorff distance with minutiae feature matching. Interdiscip. Sci.: Comput. Life Sci. 1(4), 280–289 (2009)

    Article  Google Scholar 

  103. Sarangi, P.P., Panda, M., Mishra, B.P., Dehuri, S.: An automated ear localization technique based on modified Hausdorff distance. In: International Conference on Computer Vision and Image Processing, Hong Kong, pp. 229–240 (2017)

  104. Shrout, P.E., Fleiss, J.L.: Intraclass correlations: uses in assessing rater reliability. Psychol. Bull. 86(2), 420 (1979)

    Article  Google Scholar 

  105. McCall, R.B., Kagan, J.: Fundamental Statistics for Psychology. Tech. Rep., Harcourt Brace Jovanovich, New York (1975)

  106. Benjamini, Y., Hochberg, Y.: Controlling the false discovery rate: a practical and powerful approach to multiple testing. J. R. Stat. Soc., Ser. B (Methodol.) 1(1), 289–300 (1995)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

Haifa Alhasson and Shuaa Alharbi are supported by the Saudi Arabian Ministry of Education Doctoral Scholarship and Qassim University in Saudi Arabia.

Author information

Authors and Affiliations

  1. Department of Computer Science, Durham University, Durham, UK

    Haifa F. Alhasson, Chris G. Willcocks, Shuaa S. Alharbi & Boguslaw Obara

  2. Department of Anthropology, Durham University, Durham, UK

    Adetayo Kasim

  3. Department of Information Technology, Collage of Computer, Qassim University, Buraidah, Saudi Arabia

    Haifa F. Alhasson & Shuaa S. Alharbi

Authors
  1. Haifa F. Alhasson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chris G. Willcocks
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shuaa S. Alharbi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Adetayo Kasim
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Boguslaw Obara
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Boguslaw Obara.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Alhasson, H.F., Willcocks, C.G., Alharbi, S.S. et al. The relationship between curvilinear structure enhancement and ridge detection methods. Vis Comput 37, 2263–2283 (2021). https://doi.org/10.1007/s00371-020-01985-4

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-020-01985-4

Keywords

Search

Navigation