Similarity Measures for Radial Data

  • Carlos Lopez-MolinaEmail author
  • Cedric Marco-Detchart
  • Javier Fernandez
  • Juan Cerron
  • Mikel Galar
  • Humberto Bustince
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 610)


Template-based methods for image processing hold a list of advantages over other families of methods, e.g. simplicity and ability to mimic human behaviour. However, they also demand a careful design of the pattern representatives as well as that of the operators in charge of measuring/detecting their presence in the data. This work presents a method for fingerprint analysis, specifically for singular point detection, based on template matching. The matching process sparks the need for similarity measures able to cope with radial data. As a result, we introduce the concepts of Restricted Radial Equivalence Function (RREF) and Radial Similarity Measure (RSM), further used to evaluate the perceptual closeness of scalar and vectorial pieces of radial data, respectively. Our method, which goes by the name of Template-based Singular Point Detection method (TSPD), has qualitative advantages over other alternatives, and proves to be competitive with state-of-the art methods in quantitative terms.


Fingerprint analysis Singular point detection Radial data Restricted equivalence function Similarity measure 



The authors gratefully acknowledge the financial support of the Spanish Ministry of Science (project TIN2013-40765-P), as well as the financial support of the Research Foundation Flanders (FWO project 3G.0838.12.N).


  1. 1.
    Bazen, A.M., Gerez, S.H.: Systematic methods for the computation of the directional fields and singular points of fingerprints. IEEE Trans. Pattern Anal. Mach. Intell. 24(7), 905–919 (2002)CrossRefGoogle Scholar
  2. 2.
    Beliakov, G., Pradera, A., Calvo, T.: Aggregation Functions: A Guide for Practitioners, Studies in Fuzziness and Soft Computing, vol. 221. Springer, Heidelberg (2007)Google Scholar
  3. 3.
    Bustince, H., Barrenechea, E., Pagola, M.: Restricted equivalence functions. Fuzzy Sets Syst. 157(17), 2333–2346 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Cerron, J., Marco-Detchart, C., Lopez-Molina, C., Bustince, H., Galar, M.: Singular point location for NIST-4 database (2015).
  5. 5.
    Chaudhuri, S., Chatterjee, S., Katz, N., Nelson, M., Goldbaum, M.: Detection of blood vessels in retinal images using two-dimensional matched filters. IEEE Trans. Med. Imaging 8(3), 263–269 (1989)CrossRefGoogle Scholar
  6. 6.
    De Baets, B., De Meyer, H., Naessens, H.: A class of rational cardinality-based similarity measures. J. Comput. Appl. Math. 132(1), 51–69 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Fisher, N.I.: Statistical Analysis of Circular Data. Cambridge University Press, Cambridge (1993)CrossRefzbMATHGoogle Scholar
  8. 8.
    Galar, M., Derrac, J., Peralta, D., Triguero, I., Paternain, D., Lopez-Molina, C., García, S., Benítez, J.M., Pagola, M., Barrenechea, E., Bustince, H., Herrera, F.: A survey of fingerprint classification part I: taxonomies on feature extraction methods and learning models. Knowl. Based Syst. 81, 76–97 (2015)CrossRefGoogle Scholar
  9. 9.
    Galar, M., Derrac, J., Peralta, D., Triguero, I., Paternain, D., Lopez-Molina, C., García, S., Benítez, J.M., Pagola, M., Barrenechea, E., Bustince, H., Herrera, F.: A survey of fingerprint classification part II: experimental analysis and ensemble proposal. Knowl. Based Syst. 81, 98–116 (2015)CrossRefGoogle Scholar
  10. 10.
    Gregori, V., Morillas, S., Sapena, A.: Examples of fuzzy metrics and applications. Fuzzy Sets Syst. 170(1), 95–111 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Hueckel, M.H.: An operator which locates edges in digitized pictures. J. ACM 18(1), 113–125 (1971)CrossRefzbMATHGoogle Scholar
  12. 12.
    Karu, K., Jain, A.K.: Fingerprint classification. Pattern Recogn. 29(3), 389–404 (1996)CrossRefGoogle Scholar
  13. 13.
    Kass, M., Witkin, A.: Analyzing oriented patterns. Comput. Vis. Graph. Image Process. 37(3), 362–385 (1987)CrossRefGoogle Scholar
  14. 14.
    Kawagoe, M., Tojo, A.: Fingerprint pattern classification. Pattern Recogn. 17(3), 295–303 (1984)CrossRefGoogle Scholar
  15. 15.
    Kramosil, I., Michálek, J.: Fuzzy metrics and statistical metric spaces. Kybernetika 11(5), 336–344 (1975)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Li, Y., Qi, X., Wang, Y.: Eye detection by using fuzzy template matching and feature-parameter-based judgement. Pattern Recogn. Lett. 22(10), 1111–1124 (2001)CrossRefzbMATHGoogle Scholar
  17. 17.
    Liu, M.: Fingerprint classification based on Adaboost learning from singularity features. Pattern Recogn. 43, 1062–1070 (2010)CrossRefzbMATHGoogle Scholar
  18. 18.
    Maltoni, D., Maio, D., Jain, A.K., Prabhakar, S.: Handbook of Fingerprint Recognition. Springer, Heidelberg (2009)CrossRefzbMATHGoogle Scholar
  19. 19.
    Mardia, K.V., Jupp, P.E.: Directional Statistics. Wiley, New York (2000)zbMATHGoogle Scholar
  20. 20.
    Marr, D.: Vision. MIT Press, Massachusetts (1982)Google Scholar
  21. 21.
    Nyongesa, H.O., Al-Khayatt, S., Mohamed, S.M., Mahmoud, M.: Fast robust fingerprint feature extraction and classification. J. Intell. Rob. Syst. 40(1), 103–112 (2004)CrossRefGoogle Scholar
  22. 22.
    Poli, R., Valli, G.: An algorithm for real-time vessel enhancement and detection. Comput. Meth. Programs Biomed. 52(1), 1–22 (1997)CrossRefGoogle Scholar
  23. 23.
    Prewitt, J.M.S.: Object enhancement and extraction. In: Lipkin, B., Rosenfeld, A. (eds.) Picture Processing and Psychopictorics, pp. 75–149. Academic Press, New York (1970)Google Scholar
  24. 24.
    Turroni, F., Maltoni, D., Cappelli, R., Maio, D.: Improving fingerprint orientation extraction. IEEE Trans. Inf. Forensics Secur. 6(3), 1002–1013 (2011)CrossRefGoogle Scholar
  25. 25.
    Tversky, A.: Features of similarity. Psychol. Rev. 84(4), 327–352 (1977)CrossRefGoogle Scholar
  26. 26.
    Watson, C.I., Wilson, C.L.: NIST Special Database 4, Fingerprint Database. Technical report, U.S. National Institute of Standards and Technology (1992)Google Scholar
  27. 27.
    Xuecheng, L.: Entropy, distance measure and similarity measure of fuzzy sets and their relations. Fuzzy Sets Syst. 52(3), 305–318 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Zadeh, L.A.: Similarity relations and fuzzy orderings. Inf. Sci. 3(2), 177–200 (1971)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Zhang, F., Hancock, E.R.: New Riemannian techniques for directional and tensorial image data. Pattern Recogn. 43(4), 1590–1606 (2010)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Carlos Lopez-Molina
    • 1
    • 2
    Email author
  • Cedric Marco-Detchart
    • 1
  • Javier Fernandez
    • 1
  • Juan Cerron
    • 1
  • Mikel Galar
    • 1
  • Humberto Bustince
    • 1
    • 3
  1. 1.Dpto. Automatica y ComputacionUniversidad Publica de NavarraPamplonaSpain
  2. 2.Department of Mathematical Modeling, Statistics and BioinformaticsGhent UniversityGhentBelgium
  3. 3.Institute of Smart CitiesUniversidad Publica de NavarraPamplonaSpain

Personalised recommendations