ISMM 2009: Mathematical Morphology and Its Application to Signal and Image Processing pp 13-23 | Cite as
The “False Colour” Problem
Abstract
The emergence of new data in multidimensional function lattices is studied. A typical example is the apparition of false colours when (R,G,B) images are processed. Two lattice models are specially analysed. Firstly, one considers a mixture of total and marginal orderings where the variations of some components are governed by other ones. This constraint yields the “pilot lattices”. The second model is a cylindrical polar representation in n dimensions. In this model, data that are distributed on the unit sphere of n − 1 dimensions need to be ordered. The proposed orders, and lattices are specific to each image. They are obtained from Voronoi tesselation of the unit sphere The case of four dimensions is treated in detail and illustrated.
Keywords
Unit Sphere Total Ordering Complete Lattice False Colour Voronoi TesselationPreview
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References
- 1.Angulo, J., Serra, J.: Modeling and segmentation of colour images in polar representations. Image and Vision Computing 25, 475–495 (2007)CrossRefGoogle Scholar
- 2.Angulo, J.: Quaternions colour representation and derived total orderings for morphological operators. Note interne CMM (May 2008)Google Scholar
- 3.Aptoula, E., Lefèvre, S.: A comparative study on multivariate morphology. Pattern Recognition 40(11), 2914–2929 (2007)CrossRefMATHGoogle Scholar
- 4.Aptoula, E.: Analyse d’images couleur par morphologie mathématique, application à la description, l’annotation et la recherche d’images Thèse d’informatique. Univ. Louis Pasteur, Strasbourg (July 10, 2008)Google Scholar
- 5.Chanussot, J., Lambert, P.: Total ordering based on space filling curves for multi-valued morphology. In: ISMM 1998, Norwell, MA, USA, pp. 51–58. Kluwer Academic Publishers, Dordrecht (1998)Google Scholar
- 6.Chanussot, J., Benediktsson, J.A., Fauvel, M.: Classification of Remote Sensing Images from Urban Areas Using a Fuzzy Possibilistic Model. IEEE Trans. Geosci. Remote Sens. 3(1), 40–44 (2006)CrossRefGoogle Scholar
- 7.Ell, T.A., Sangwine, S.J.: Hypercomplex Fourier transform of color images. IEEE Trans. Image Processing 16(1), 22–35 (2007)MathSciNetCrossRefMATHGoogle Scholar
- 8.Evans, A., Gimenez, D.: Extending Connected Operators To Colour Images. In: Proc. Int. Conf. Image Proc. 2008, pp. 2184–2187 (2008)Google Scholar
- 9.Hanbury, A., Serra, J.: Morphological operators on the unit circle. IEEE Trans. Image Processing 10(12), 1842–1850 (2001)MathSciNetCrossRefMATHGoogle Scholar
- 10.Hanbury, A., Serra, J.: Colour Image Analysis in 3D-polar coordinates. In: Michaelis, B., Krell, G. (eds.) DAGM 2003. LNCS, vol. 2781, pp. 124–131. Springer, Heidelberg (2003)CrossRefGoogle Scholar
- 11.Meyer, F.: Color image segmentation. In: Proc. 4th International Conference on Image Processing and its Applications 1992, pp. 303–306 (1992)Google Scholar
- 12.Serra, J.: Les treillis pilotes. Rapport Technique CMM-Ecole des Mines de Paris (January 2009)Google Scholar
- 13.Soille, P.: Constrainted connectivity for hierarchical image partitioning and simplification. IEEE Trans. PAMI 30(7), 1132–1145 (2008)CrossRefGoogle Scholar
- 14.Talbot, H., Evans, C., Jones, R.: Complete ordering and multivariate mathematical morphology: Algorithms and applications. In: ISMM 1998, Norwell, MA, USA, pp. 27–34. Kluwer Academic Publishers, Dordrecht (1998)Google Scholar