Abstract
In this work, an analysis of the influence of the fuzzy measure for Choquet integral and its generalizations is presented. The work has been done in the context of feature fusion for edge detection with gray-scale images. The particular case of adaptative fuzzy measure is considered, testing a variety of approaches. We have tested our proposal using the power measure adapting the exponent depending on the local information of each particular image. For comparison purposes and to test the performance of our proposal, we compare our approach to the results obtained with the Canny edge detector.
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References
Alsina, C., Frank, M.J., Schweizer, B.: Associative Functions: Triangular Norms and Copulas. World Scientific Publishing Company, Singapore (2006)
Arbelaez, P., Maire, M., Fowlkes, C., Malik, J.: Contour detection and hierarchical image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 33(5), 898–916 (2011)
Bedregal, B.C., Dimuro, G.P., Bustince, H., Barrenechea, E.: New results on overlap and grouping functions. Inf. Sci. 249, 148–170 (2013)
Beliakov, G., Bustince Sola, H., Calvo, T.: A Practical Guide to Averaging Functions, Studies in Fuzziness and Soft Computing, vol. 329. Springer, Cham (2016)
Bezdek, J., Chandrasekhar, R., Attikouzel, Y.: A geometric approach to edge detection. IEEE Trans. Fuzzy Syst. 6(1), 52–75 (1998)
Bustince, H., Fernandez, J., Mesiar, R., Montero, J., Orduna, R.: Overlap functions. Nonlinear Anal. Theory Methods Appl. 72(3–4), 1488–1499 (2010)
Canny, J.F.: A computational approach to edge detection. IEEE Trans. Pattern Anal. Mach. Intell. 8(6), 679–698 (1986)
Choquet, G.: Theory of capacities. Ann. l’Institut Fourier 5, 131–295 (1953–1954)
Estrada, F.J., Jepson, A.D.: Benchmarking image segmentation algorithms. International J. Comput. Vis. 85(2), 167–181 (2009)
Hubel, D.H., Wiesel, T.N.: Integrative action in the cat’s lateral geniculate body. J. Physiol. 155(2), 385–398 (1961)
Hubel, D.H., Wiesel, T.N.: Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex. J. Physiol. 160(1), 106–154 (1962)
Lopez-Molina, C., De Baets, B., Bustince, H.: Quantitative error measures for edge detection. Pattern Recogn. 46(4), 1125–1139 (2013)
Lucca, G., et al.: Preaggregation functions: construction and an application. IEEE Trans. Fuzzy Syst. 24(2), 260–272 (2016)
Lucca, G., Sanz, J.A., Dimuro, G.P., Bedregal, B., Bustince, H., Mesiar, R.: CF-integrals: A new family of pre-aggregation functions with application to fuzzy rule-based classification systems. Inf. Sci. 435, 94–110 (2018)
Marr, D.: Vision. MIT Press, Cambridge (1982)
Marr, D.: Early processing of visual information. Philos. Trans. Roy. Soc. London. B Biol. Sci. 275(942), 483–519 (1976)
Marr, D., Hildreth, E.: Theory of edge detection. Proc. Roy. Soc. London. Ser. B. Biol. Sci. 207(1167), 187–217 (1980)
Martin, D.R., Fowlkes, C.C., Malik, J.: Learning to detect natural image boundaries using local brightness, color, and texture cues. IEEE Trans. Pattern Anal. Mach. Intell. 26(5), 530–549 (2004)
Murofushi, T., Sugeno, M., Machida, M.: Non-monotonic fuzzy measures and the Choquet integral. Fuzzy Sets Syst. 64(1), 73–86 (1994)
Prewitt, J.: Object enhancement and extraction (1970)
Sobel, I., Feldman, G.: A 3x3 isotropic gradient operator for image processing. Hart, P.E., Duda, R.O. Pattern Classif. Scene Anal., 271–272 (1973)
Acknowledgements
This work was partially supported with grant PID2021-123673OB-C31 funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”, Consellería d’Innovació, Universitats, Ciencia i Societat Digital from Comunitat Valenciana (APOSTD/2021/227) through the European Social Fund (Investing In Your Future) and grant from the Research Services of Universitat Politècnica de València (PAID-PD-22).
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Marco-Detchart, C., Lucca, G., Dimuro, G., Rincon, J.A., Julian, V. (2023). Adaptative Fuzzy Measure for Edge Detection. In: Quaresma, P., Camacho, D., Yin, H., Gonçalves, T., Julian, V., Tallón-Ballesteros, A.J. (eds) Intelligent Data Engineering and Automated Learning – IDEAL 2023. IDEAL 2023. Lecture Notes in Computer Science, vol 14404. Springer, Cham. https://doi.org/10.1007/978-3-031-48232-8_45
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DOI: https://doi.org/10.1007/978-3-031-48232-8_45
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