Application of PDE and Mathematical Morphology in the Extraction Validation of the Roads


The digital images generated by remote sensors often contain noises that are inherent in the process of imaging and transmission. The application of digital processing techniques greatly enhances the ability to extract information on surface targets from remote sensing data. When digital images are used with high spatial resolution, one of the problems emerging the high variability of targets presents in such images. From the computational point of view, the use of partial differential equations is favored by the large number of numerical methods showed in the literature. Many of the models are considered non-complex both from the mathematical and computational standpoints, due to the characteristics of explicit equations. This work uses techniques of the partial differential equations (PDE) and mathematical morphology to extract cartographic features in digital images of the remote sensing. The selected study area corresponds to an image containing part of the Mário Covas Ring Road, located in the metropolitan region of Sao Paulo (SP), Brazil. The results are promising and show the high potential of using mathematical morphology in the field of cartography.

Share and Cite:

F. Leonardi, V. Santiago, C. Chaves and E. Silva, "Application of PDE and Mathematical Morphology in the Extraction Validation of the Roads," Journal of Signal and Information Processing, Vol. 4 No. 3, 2013, pp. 308-313. doi: 10.4236/jsip.2013.43039.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] A. P. Dal Poz, R. B. Zanin and G. M. Vale, “Extracao Automática de Feicoes Rodoviárias em Imagens Digitais,” Revista Controle & Automacao, Campinas, Vol. 18, No. 1, 2007, pp. 44-54.
[2] Y. Chen, B. C. Vemuri and L. Wang, “Image Denoising and Segmentation via Nonlinear Diffusion,” Computers Mathematics with Applications, Vol. 39, No. 5-6, 2000, pp. 131-149. doi:10.1016/S0898-1221(00)00050-X
[3] C. A. Z. Barcelos and Y. Chen, “Heat Flow and Related Minimization Problem in Image Restoration,” Computers Mathematics with Applications, Vol. 39, No. 5-6, 2000, pp. 81-97. doi:10.1016/S0898-1221(00)00048-1
[4] P. Soille, “Morphological Image Analysis: Principles and applications,” Springer-Verlag, Berlin, 2003.
[5] J. Goutsias and H. J. A. M. Heijmans, “Mathematical Morphology,” IOS Press, Amsterdan, 2000.
[6] J. Facon, “Morfologia Matemática: Teorias e Exemplos,” Editora Universitária Champagnat da Pontifícia Universidade Católica do Paraná, Curitiba, 1996.
[7] J. I. Miranda and J. Camargo, “Deteccao de Bordas com o Modelo de Difusao Anisotrópica,” Anais XIII Simpósio Brasileiro de Sensoriamento Remoto, Florianópolis, 2007, pp. 5957-5964.
[8] C. A. Z. Barcelos, “Restauracao e Análise de Imagens via Equacoes Diferenciais Parciais,” Tendências em Matemática Aplicada e Computacional, Vol. 3, No. 2, 2002, pp. 1-13.

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.