Abstract
Aggregation functions have been used in the last decade in several edge detectors with notable success. Recently, a new family of aggregation functions defined as ordinal sums of conjunctive and disjunctive aggregation functions have been introduced with good results in classification problems. Due to this performance, in this paper, this family is considered in the aggregation step of the edge detection algorithm based on uninorms. This new edge detector is compared with other classical edge detectors concluding that this class of ordinal sums is a feasible family to be used for edge detection.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
The performance of the edge detector is similar if a decreasing order is applied.
- 2.
These regions contain mostly textures and an edge detector should not be penalized whatever result it obtains.
References
Barrenechea, E., Bustince, H., De Baets, B., Lopez-Molina, C.: Construction of interval-valued fuzzy relations with application to the generation of fuzzy edge images. IEEE Trans. Fuzzy Syst. 19(5), 819–830 (2011)
Bowyer, K., Kranenburg, C., Dougherty, S.: Edge detector evaluation using empirical ROC curves. In: Proceedings of the 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 1, pp. 354–359 (1999)
Bustince, H., Barrenechea, E., Pagola, M., Fernandez, J.: Interval-valued fuzzy sets constructed from matrices: application to edge detection. Fuzzy Sets Syst. 160(13), 1819–1840 (2009)
Fodor, J., Yager, R., Rybalov, A.: Structure of uninorms. Int. J. Uncertainty Fuzziness Knowl.-Based Syst. 5, 411–428 (1997)
Gonzalez, R.C., Woods, R.E.: Digital Image Processing, 3rd edn. Prentice-Hall Inc., Hoboken (2006)
González-Hidalgo, M., Massanet, S., Mir, A., Ruiz-Aguilera, D.: On the generalization of the fuzzy morphological operators for edge detection. In: Alonso, J.M., et al. (eds.) 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology (IFSA-EUSFLAT 2015). Atlantis Press (2015)
González-Hidalgo, M., Massanet, S., Mir, A., Ruiz-Aguilera, D.: On the generalization of the uninorm morphological gradient. In: Rojas, I., Joya, G., Catala, A. (eds.) IWANN 2015. LNCS, vol. 9095, pp. 436–449. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-19222-2_37
González-Hidalgo, M., Massanet, S., Mir, A., Ruiz-Aguilera, D.: A new edge detector based on uninorms. In: Laurent, A., Strauss, O., Bouchon-Meunier, B., Yager, R.R. (eds.) IPMU 2014. CCIS, vol. 443, pp. 184–193. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-08855-6_19
González-Hidalgo, M., Massanet, S., Mir, A., Ruiz-Aguilera, D.: On the choice of the pair conjunction-implication into the fuzzy morphological edge detector. IEEE Trans. Fuzzy Syst. 23(4), 872–884 (2015)
Grigorescu, C., Petkov, N., Westenberg, M.: Contour detection based on nonclassical receptive field inhibition. IEEE Trans. Image Process. 12(7), 729–739 (2003)
Hudec, M., Mináriková, E., Mesiar, R.: Aggregation functions in flexible classification by ordinal sums. In: Ciucci, D., et al. (eds.) IPMU 2022. CCIS, vol. 1601, pp. 372–383. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-08971-8_31
Hudec, M., Mináriková, E., Mesiar, R., Saranti, A., Holzinger, A.: Classification by ordinal sums of conjunctive and disjunctive functions for explainable AI and interpretable machine learning solutions. Knowl.-Based Syst. 220, 106916 (2021)
Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. TREN, Springer, Dordrecht (2000). https://doi.org/10.1007/978-94-015-9540-7
Mas, M., Massanet, S., Ruiz-Aguilera, D., Torrens, J.: A survey on the existing classes of uninorms. J. Intell. Fuzzy Syst. 29, 1021–1037 (2015)
Papari, G., Petkov, N.: Edge and line oriented contour detection: state of the art. Image Vis. Comput. 29(2–3), 79–103 (2011)
Pratt, W.K.: Digital Image Processing: PIKS Scientific Inside. Wiley, Hoboken (2007)
Acknowledgements
This work was partially supported by the R+D+i Project PID2020-113870GB-I00-“Desarrollo de herramientas de Soft Computing para la Ayuda al Diagnóstico Clínico y a la Gestión de Emergencias (HESOCODICE)”, funded by MCIN/AEI/10.13039/501100011033/, the KEGA No. 025EU-4/2021 by the Ministry of Education, Science, Research and Sport of the Slovak Republic, and SGS SP2023/078 by the Ministry of Education, Youth and Sports of the Czech Republic.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Munar, M., Hudec, M., Massanet, S., Mináriková, E., Ruiz-Aguilera, D. (2023). On an Edge Detector Based on Ordinal Sums of Conjunctive and Disjunctive Aggregation Functions. In: Massanet, S., Montes, S., Ruiz-Aguilera, D., González-Hidalgo, M. (eds) Fuzzy Logic and Technology, and Aggregation Operators. EUSFLAT AGOP 2023 2023. Lecture Notes in Computer Science, vol 14069. Springer, Cham. https://doi.org/10.1007/978-3-031-39965-7_23
Download citation
DOI: https://doi.org/10.1007/978-3-031-39965-7_23
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-39964-0
Online ISBN: 978-3-031-39965-7
eBook Packages: Computer ScienceComputer Science (R0)