Edge Detection based in Interval-Valued Fuzzy Mathematical Morphology and Aggregation Functions K

• Corbacho Carazas, Lisbeth ^[1] ; Sussner, Peter ^[1]
  1. [1] Universidade Estadual de Campinas

     Universidade Estadual de Campinas

     Brasil

     
• Localización: Selecciones Matemáticas, ISSN-e 2411-1783, Vol. 6, Nº. 2, 2019 (Ejemplar dedicado a: Agosto-Diciembre), págs. 238-247
• Idioma: inglés
• DOI: 10.17268/sel.mat.2019.02.10
• Títulos paralelos:
  • Detecao de Bordas baseada em Morfologia Matemática Fuzzy Intervalar e as Funcoes de Agregacao K
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    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.

  • English

    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.

• Referencias bibliográficas
  • 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;...
  • Bustince, H., Fernández, J., Kolesárová, A. and Mesiar, R. Generation of linear orders for intervals by means of aggregation functions, Fuzzy...
  • 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...
  • 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...
  • González-Hidalgo, M. and Massanet, S. A fuzzy mathematical morphology based on discrete t-norms: fundamentals and applications to image processing,...
  • Grana, M., and Chyzhyk, D. Image understanding applications of lattice autoassociative memories, IEEE Transactions on Neural Networks and...
  • 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...
  • Law, T., Itoh, H. and Seki„ H. Image filtering, edge detection, and edge tracing using fuzzy reasoning, IEEE transactions on pattern analysis...
  • Lopez-Molina, C., Marco-Detchart, C., Cerron, J., Bustince, H. and De Baets. Gradient extraction operators for discrete interval-valued data,...
  • 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...
  • Nachtegael, M., Sussner, P., Mélange, T. and Kerre, E. On the role of complete lattices in mathematical morphology: From tool to uncertainty...
  • 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...
  • Sussner, Nachtegael, P., élange, M., Deschrijver, G., Esmi, E. and Kerre, E. Interval-valued and intuitionistic fuzzy mathematical morphologies...
  • Sobel, I. E. Camera models and machine perception, 1970.