Edge Detection based in Interval-Valued Fuzzy Mathematical Morphology and Aggregation Functions K
DOI:
https://doi.org/10.17268/sel.mat.2019.02.10Keywords:
Edge detection, interval-valued fuzzy morphology, gradient morphologicalAbstract
Edge detection is a digital image processing tool. It determines points in a digital image where light intensity suddenly changes. This process applies to a digital image which assumes some degree of uncertainty in the location and intensity of the pixel in the real image. In this work, we propose an edge detection model which consists in capturing this uncertainty in terms of interval images. Then we apply interval-valued fuzzy morphology to calculate the interval-valued erosion and dilation. Finally, we compute the convex combinations of the upper and lower bounds of the interval-valued erosion and dilation image, to obtain a morphological erosion and dilation respectively, and thus an edge image.References
Baczynski, M., Beliakov, G., Humberto, H. and Pradera, A. Advances in Fuzzy Implication Functions. Springer, 2013.
Birkhoff, G. Lattice Theory. Providence: American Mathematical Society, 3rd, ed., 1993.
Bowyer, K. Kranenburg, C. and Dougherty,S. Edge detector evaluation using empirical ROC curves, Computer Vision and Image Understanding, 2001; 84(1):77–103.
Bustince, H., Fernández, J., Kolesárová, A. and Mesiar, R. Generation of linear orders for intervals by means of aggregation functions, Fuzzy Sets and Systems, 2013; 220:69-77.
Canny, J. F. A computational approach to edge-detection, IEEE Transactions on Pattern Analysis and Machine Intelligence, 1986; 8:679-700.
Davey, B. A. and Priestley, H. A. Introduction to lattices and Order. Cambridge University Press, 2002.
Deng, T. and Heijmans, H. J.Grey-scale morphology based on fuzzy logic, Journal of Mathematical Imaging and Vision, 2002; 16(2);155-171.
Deschrijver, G. and Cornelis, C. Representability in interval-valued fuzzy set theory, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2007; 15(3):345-361.
Grätzer, G. A. Lattice Theory: First Concepts and Distributive Lattices. San Francisco, CA: W. H. Freeman, 1971.
Heijmans, H. J. Morphological image operators, Advances in Electronics and Electron Physics Suppl., Boston: Academic Press,| c1994.
González-Hidalgo, M., Massanet, S., Mir, A. and Ruiz-Aguilera, D. On the choice of the pair conjunction–implication into the fuzzy morphological edge detector, IEEE Transactions on Fuzzy Systems, 2015; 23(4):872-884.
González-Hidalgo, M. and Massanet, S. A fuzzy mathematical morphology based on discrete t-norms: fundamentals and applications to image processing, Soft Computing, 2014; 18(11):2297-2311
Grana, M., and Chyzhyk, D. Image understanding applications of lattice autoassociative memories, IEEE Transactions on Neural Networks and Learning Systems, 2015; 27(9):1920-1932.
Klir, G., and Yuan, B. Fuzzy sets and fuzzy logic, vol. 4. Prentice hall New Jersey, 1995.
Kovesi, P. D. Matlab and Octave functions for computer vision and image processing, Centre for Exploration Targeting, School of Earth and Environment, The University of Western Australia, available from: http://www.csse.uwa.edu. au/pk/research/matlabfns, 2000; 147:230.
Law, T., Itoh, H. and Seki„ H. Image filtering, edge detection, and edge tracing using fuzzy reasoning, IEEE transactions on pattern analysis and machine intelligence, 1996; 18(5):481-491.
Lopez-Molina, C., Marco-Detchart, C., Cerron, J., Bustince, H. and De Baets. Gradient extraction operators for discrete interval-valued data, in 16th IFSAWorld Congress; 9th Conference of the European Society for Fuzzy Logic and Technology, Atlantis Press, 2015; 89:836-843.
Medina-Carnicer, R., Munoz-Salinas, R., Yeguas-Bolivar, E. and Diaz-Mas, L. A novel method to look for the hysteresis thresholds for the Canny edge detector, Pattern Recognition, 2011; 44(6):1201-1211.
Nachtegael, M., Sussner, P., Mélange, T. and Kerre, E. On the role of complete lattices in mathematical morphology: From tool to uncertainty model, Information Sciences, 2011; 181(10):1971-1988.
Nachtegael, M. and Kerre, E. Connections between binary, gray-scale and fuzzy mathematical morphologies, Fuzzy sets and systems, 2001; 124(1):73–85.
Prewitt, J. Object enhancement and extraction, Picture Proc. Psychopictorics, 1970; 75-149.
Sussner, P. and Valle, M. Classification of fuzzy mathematical morphologies based on concepts of inclusion measure and duality, Journal of Mathematical Imaging and Vision, 2008; 32(2):139-159.
Sussner, Nachtegael, P., élange, M., Deschrijver, G., Esmi, E. and Kerre, E. Interval-valued and intuitionistic fuzzy mathematical morphologies as special cases of L-fuzzy mathematical morphology, Journal of Mathematical Imaging and Vision, 2012; 43(1):50-71.
Sobel, I. E. Camera models and machine perception, 1970.
Published
How to Cite
Issue
Section
License
The authors who publish in this journal accept the following conditions:
1. The authors retain the copyright and assign to the journal the right of the first publication, with the work registered with the Creative Commons Attribution License,Atribución 4.0 Internacional (CC BY 4.0) which allows third parties to use what is published whenever they mention the authorship of the work And to the first publication in this magazine.
2. Authors may make other independent and additional contractual arrangements for non-exclusive distribution of the version of the article published in this journal (eg, include it in an institutional repository or publish it in a book) provided they clearly state that The paper was first published in this journal.
3. Authors are encouraged to publish their work on the Internet (for example, on institutional or personal pages) before and during the review and publication process, as it can lead to productive exchanges and to a greater and more rapid dissemination Of the published work.
