Multiscale Extension of the Gravitational Approach to Edge Detection

  • Carlos Lopez-Molina
  • Bernard De Baets
  • Humberto Bustince
  • Edurne Barrenechea
  • Mikel Galar
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7023)


The multiscale techniques for edge detection aim to combine the advantages of small and large scale methods, usually by blending their results. In this work we introduce a method for the multiscale extension of the Gravitational Edge Detector based on a t-norm T. We smoothen the image with a Gaussian filter at different scales then perform inter-scale edge tracking. Results are included illustrating the improvements resulting from the application of the multiscale approach in both a quantitative and a qualitative way.


True Positive Edge Detection Machine Intelligence Edge Image Edge Pixel 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Babaud, J., Witkin, A.P., Baudin, M., Duda, R.O.: Uniqueness of the gaussian kernel for scale-space filtering. IEEE Trans. on Pattern Analysis and Machine Intelligence 8(1), 26–33 (1986)CrossRefzbMATHGoogle Scholar
  2. 2.
    Baddeley, A.J.: Errors in binary images and an L p version of the Hausdorff metric. Nieuw Archief voor Wiskunde 10, 157–183 (1992)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Canny, J.: A computational approach to edge detection. IEEE Trans. on Pattern Analysis and Machine Intelligence 8(6), 679–698 (1986)CrossRefGoogle Scholar
  4. 4.
    Carlotto, M.J.: Histogram analysis using a scale-space approach. IEEE Trans. on Pattern Analysis and Machine Intelligence 9(1), 121–129 (1987)CrossRefGoogle Scholar
  5. 5.
    Coleman, S., Scotney, B., Suganthan, S.: Multi-scale edge detection on range and intensity images. Pattern Recognition 44(4), 821–838 (2011)CrossRefzbMATHGoogle Scholar
  6. 6.
    Demigny, D.: On optimal linear filtering for edge detection. IEEE Trans. on Image Processing 11(7), 728–737 (2002)CrossRefGoogle Scholar
  7. 7.
    Florack, L., Kuijper, A.: The topological structure of scale-space images. Journal of Mathematical Imaging and Vision 12, 65–79 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Heath, M., Sarkar, S., Sanocki, T., Bowyer, K.: A robust visual method for assessing the relative performance of edge-detection algorithms. IEEE Trans. on Pattern Analysis and Machine Intelligence 19(12), 1338–1359 (1997)CrossRefGoogle Scholar
  9. 9.
    Jackway, P., Deriche, M.: Scale-space properties of the multiscale morphological dilation-erosion. IEEE Trans. on Pattern Analysis and Machine Intelligence 18(1), 38–51 (1996)CrossRefGoogle Scholar
  10. 10.
    Konishi, S., Yuille, A., Coughlan, J.: A statistical approach to multi-scale edge detection. Image and Vision Computing 21(1), 37–48 (2003)CrossRefGoogle Scholar
  11. 11.
    Leung, Y., Zhang, J.S., Xu, Z.B.: Clustering by scale-space filtering. IEEE Trans. on Pattern Analysis and Machine Intelligence 22(12), 1396–1410 (2000)CrossRefGoogle Scholar
  12. 12.
    Lindeberg, T.: Edge detection and ridge detection with automatic scale selection. International Journal of Computer Vision 30(2), 117–156 (1998)CrossRefGoogle Scholar
  13. 13.
    Lopez-Molina, C., Bustince, H., Fernandez, J., Couto, P., De Baets, B.: A gravitational approach to edge detection based on triangular norms. Pattern Recognition 43(11), 3730–3741 (2010)CrossRefzbMATHGoogle Scholar
  14. 14.
    Mallat, S., Hwang, W.: Singularity detection and processing with wavelets. IEEE Trans. on Information Theory 38(2), 617–643 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Marr, D., Hildreth, E.: Theory of edge detection. Proceedings of the Royal Society of London 207(1167), 187–217 (1980)CrossRefGoogle Scholar
  16. 16.
    Martin, D., Fowlkes, C., Tal, D., Malik, J.: A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In: Proceedings of the 8th International Conference on Computer Vision, vol. 2, pp. 416–423 (2001)Google Scholar
  17. 17.
    McIlhagga, W.: The canny edge detector revisited. International Journal of Computer Vision 91, 251–261 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Peli, T., Malah, D.: A study of edge detection algorithms. Computer Graphics and Image Processing 20(1), 1–21 (1982)CrossRefzbMATHGoogle Scholar
  19. 19.
    Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. on Pattern Analysis and Machine Intelligence 12(7), 629–639 (1990)CrossRefGoogle Scholar
  20. 20.
    Prewitt, J.M.S.: Object enhancement and extraction. In: Picture Processing and Psychopictorics, pp. 75–149. Academic Press (1970)Google Scholar
  21. 21.
    Qian, R., Huang, T.: Optimal edge detection in two-dimensional images. IEEE Trans. on Image Processing 5(7), 1215–1220 (1996)CrossRefGoogle Scholar
  22. 22.
    Rosin, P.L.: Unimodal thresholding. Pattern Recognition 34(11), 2083–2096 (2001)CrossRefzbMATHGoogle Scholar
  23. 23.
    Russo, F.: FIRE operators for image processing. Fuzzy Sets and Systems 103(2), 265–275 (1999)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Shih, M.Y., Tseng, D.C.: A wavelet-based multiresolution edge detection and tracking. Image and Vision Computing 23(4), 441–451 (2005)CrossRefGoogle Scholar
  25. 25.
    Sobel, I., Feldman, G.: A 3x3 isotropic gradient operator for image processing (1968); presented at a talk at the Stanford Artificial Intelligence ProjectGoogle Scholar
  26. 26.
    Sun, G., Liu, Q., Liu, Q., Ji, C., Li, X.: A novel approach for edge detection based on the theory of universal gravity. Pattern Recognition 40(10), 2766–2775 (2007)CrossRefzbMATHGoogle Scholar
  27. 27.
    Torre, V., Poggio, T.: On edge detection. IEEE Trans. on Pattern Analysis and Machine Intelligence 8, 147–163 (1984)Google Scholar
  28. 28.
    Weickert, J.: Anisotropic Diffusion in Image Processing. ECMI Series, Teubner-Verlag (1998)Google Scholar
  29. 29.
    Witkin, A.P.: Scale-Space Filtering. In: 8th Int. Joint Conf. Artificial Intelligence, Karlsruhe, vol. 2, pp. 1019–1022 (1983)Google Scholar
  30. 30.
    Yuille, A.L., Poggio, T.A.: Scaling theorems for zero crossings. IEEE Trans. on Pattern Analisys and Machine Intelligence 8, 15–25 (1986)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Carlos Lopez-Molina
    • 1
    • 2
  • Bernard De Baets
    • 2
  • Humberto Bustince
    • 1
  • Edurne Barrenechea
    • 1
  • Mikel Galar
    • 1
  1. 1.Dpto. Automatica y ComputacionUniversidad Publica de NavarraPamplonaSpain
  2. 2.Dept. of Applied Mathematics, Biometrics and Process ControlGhent UniversityGentBelgium

Personalised recommendations