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The weighted gradient: A color image gradient applied to morphological segmentation

Abstract

This paper proposes a method for color gradient computation applied to morphological segmentation of color images. The weighted gradient (with weights estimated automatically), proposed in this paper, applied in conjunction with the watershed from markers technique, provides excelent segmentation results, according to a subjective visual criterion. The weighted gradient is computed by linear combination of the gradients from each band of an image under the IHS color space model. The weights to each gradient are estimated by a systematic method that computes the similarity between the image to compute the gradient and an ”ideal image”, whose histogram has an uniform distribution. Several experiments were done in order to compare the segmentation results provided by the weighted gradient to the results provided by other color space metrics, also according to a subjective criterion, and such comparison is present in this paper.

References

  1. S. Beucher and F. Meyer.Mathematical Morphology in Image Processing, chapter 12. The Morphological Approach to Segmentation: The Watershed Transformation, pages 433–481. Marcel Dekker, 1992.

  2. J. Chanussot and P. Lambert. Total Ordering Based on Space Filling Curves for Multivalued Morphology. In Henk J.A.M. Heijmans and Jos B.T.M. Roerdink, editors,Mathematical Morphology and its Applications to Image and Signal Processing, volume 12 ofComputational Imaging and Vision, pages 51–58. Kluwer Academic Publishers, Dordrecht, May 1998.

    Google Scholar 

  3. F. C. Flores, A. M. Polidório and R. A. Lotufo. Color Image Gradients for Morphological Segmentation: The Weighted Gradient Improved by Automatic Imposition of Weights. InIEEE Proceedings of SIBGRAPI’2004, pages 146–153, Curitiba, Brazil, October 2004.

  4. F. C. Flores, R. Hirata Jr., J. Barrera, R. A. Lotufo, and F.Meyer. Morphological Operators for Segmentation of Color Sequences. InIEEE Proceedings of SIBGRAPI’2000, pages 300–307, Gramado, Brazil, October 2000.

  5. G. F. Estabrook, D. J. Rogers. A general method of taxonomic description for a computed similarity measure.Bioscience, 16:789–793, 1966.

    Article  Google Scholar 

  6. R. C. Gonzalez and R. E. Woods.Digital Image Processing. Addison-Wesley Publishing Company, 1992.

  7. H. J. A. M. Heijmans.Morphological Image Operators. Academic Press, Boston, 1994.

    MATH  Google Scholar 

  8. R. Hirata Jr., F. C. Flores, J. Barrera, R. A. Lotufo, and F. Meyer. Color Image Gradients for Morphological Segmentation. InIEEE Proceedings of SIBGRAPI’2000, pages 316–322, Gramado, Brazil, October 2000.

  9. J. C. Gower. A general coeficient of similarity and some of its properties.Biometrics, 27:857–871, 1971.

    Article  Google Scholar 

  10. F. Meyer and S. Beucher. Morphological Segmentation.Journal of Visual Communication and Image Representation, 1(1):21–46, September 1990.

    Article  Google Scholar 

  11. Pratt.Digital Image Processing, chapter 18. Image Segmentation, pages 597–627. Wiley, 1991.

  12. R. A. Lotufo and A. X. Falcão. The Ordered Queue and the Optimality of theWatershed Approaches. In J. Goutsias, L. Vincent, and D. S. Bloomberg, editors,MathematicalMorphology and its Applications to Image and Signal Processing, volume 18, pages 341–350. Kluwer Academic Publishers, 2000. Fifth ISMM.

  13. R. J. Bray, J. T. Curtis. An ordination of the upland forests communities of southern Wiscounsin.Ecological Monography, 27:325–349, 1957.

    Article  Google Scholar 

  14. J. Serra.Image Analysis and Mathematical Morphology. Academic Press, 1982.

  15. H. Talbot, C. Evans, and R. Jones. Complete Ordering and Multivariate Mathematical Morphology: Algorithms and Applications. In Henk J.A.M. Heijmans and Jos B.T.M. Roerdink, editors,Mathematical Morphology and its Applications to Image and Signal Processing, volume 12 ofComputational Imaging and Vision, pages 27–34. Kluwer Academic Publishers, Dordrecht, May 1998.

    Google Scholar 

  16. L. Vincent and P. Soille. Watersheds in Digital Spaces: An Efficient Algorithm Based on Immersion Simulations.IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(6):583–598, June 1991.

    Article  Google Scholar 

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Flores, F.C., Polidório, A.M. & Lotufo, R.d.A. The weighted gradient: A color image gradient applied to morphological segmentation. J Braz Comp Soc 11, 53–63 (2005). https://doi.org/10.1007/BF03192382

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