Detecao de Bordas baseada em Morfologia Matemática Fuzzy Intervalar e as Funcoes de Agregacao K

Lisbeth Corbacho Carazas, Peter Sussner


A deteccao de bordas é uma ferramenta de processamento digital de imagenes. Ela determina pontos de uma imagem digital onde a intensidade da luz muda repentinamente. Esse processo aplica-se a uma imagem digital a qual supoe algum grau de incerteza na localizacao e na intensidade do pixel da imagem real. Neste trabalho, é proposto um modelo de detecao de bordas que consiste na captura dessa incerteza em termos de imagens intervalares, para depois aplicar a erosao e dilatacao intervalar fuzzy. Finalmente, por meio de uma combinacao convexa sobre os limites superiores e inferiores da erosao e a dilatacao intervalar, sao obtidas a erosao e a dilatacao morfológica respectivamente, com as quais se faz possível produzir uma imagem borda.

Palabras clave

Deteccao de bordas; morfologia matemática fuzzy intervalar; morfologia gradiente


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: 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.


Enlaces refback

  • No hay ningún enlace refback.

Short Title: Sel. mat.


 ISSN:  2411-1783  Versión Electrónica.                      


Derechos reservados © 2014 Departamento de Matemáticas.

Para la distribución y cosecha de los Metadatos de nuestros artículos, usar el Protocolo de Interoperabilidad OAI-PMH: 



Selecciones Matemáticas es una revista de la Universidad Nacional de Trujillo publica sus contenidos bajo licencia Creative Commons Attribution-NoComercial-ShareAlike 4.0.