Color Mathematical Morphology Based on Partial Ordering of Spectra

Mathematical morphology is based on the principle of ordering. There is no natural way to order colors (being triplets of scalars). A lot of different ordering relations have been proposed in the literature, most on an ad-hoc basis. In this paper, we propose an ordering relation for colors that is based on the natural (i.e. physically plausible) ordering of spectra. Therefore, we ensure that the ordering is independent of the chosen color parameterization. We discuss that part of colorimetric theory that enables us to reconstruct the spectrum given the three color parameters. Furthermore, we present the very basics of the algebraic framework of mathematical morphology. This allows us to embed the presented ordering of colors within the morphological framework such that we can fully exploit the possibilities to define morphological image operators working on color images.

[1]  J. Chanussot,et al.  Total ordering based on space filling curves for multivalued morphology , 1998 .

[2]  H. Heijmans,et al.  The algebraic basis of mathematical morphology , 1988 .

[3]  V. Barnett.  The Ordering of Multivariate Data , 1976 .

[4]  Constantin Vertan,et al.  Color morphology-like operators based on color geometric shape characteristics , 2003, Signals, Circuits and Systems, 2003. SCS 2003. International Symposium on.

[5]  José Crespo,et al.  The Flat Zone Approach and Color Images , 1994, ISMM.

[6]  Christian Ronse,et al.  Why mathematical morphology needs complete lattices , 1990, Signal Process..

[7]  C. Gu.  Multivalued morphology and segmentation-based coding , 1996 .

[8]  Krishnamoorthy Sivakumar,et al.  Morphological Operators for Image Sequences , 1995, Comput. Vis. Image Underst..

[9]  Allan Hanbury,et al.  Mathematical Morphology in the L * a * b * Colour Space , 2001 .

[10]  Thierry Carron,et al.  Color edge detector using jointly hue, saturation and intensity , 1994, Proceedings of 1st International Conference on Image Processing.

[11]  Hazem Munawer Al-Otum,et al.  Angle-Valued Mahalanobis-Based Image Morphological Operators , 2004 .

[12]  Marcos Cordeiro d'Ornellas,et al.  Generic algorithms for morphological image operators- a case study using watersheds , 1998 .

[13]  Wilfried Philips,et al.  Majority ordering for colour mathematical morphology , 2005, 2005 13th European Signal Processing Conference.

[14]  Fernando Torres Medina,et al.  Vectorial morphological reconstruction for brightness elimination in colour images , 2004, Real Time Imaging.

[15]  H. Heijmans.  Morphological image operators , 1994 .

[16]  Gaurav Sharma,et al.  Digital color imaging , 1997, IEEE Trans. Image Process..

[17]  M. Wheeler,et al.  Processing color and complex data using mathematical morphology , 2000, Proceedings of the IEEE 2000 National Aerospace and Electronics Conference. NAECON 2000. Engineering Tomorrow (Cat. No.00CH37093).

[18]  Edward J. Delp,et al.  Empirical study of morphological operators in color image enhancement , 1992, Electronic Imaging.

[19]  G B Arden,et al.  The Visual System , 2021, AMA Guides to the Evaluation of Permanent Impairment, 6th Edition, 2021.

[20]  C LAPICQUE,et al.  Categorical in Aperture Color-Name and Surface Regions of A Color Modes Color Space , 2007 .

[21]  Mei Yu,et al.  New morphological operators for color image processing , 2004, 2004 IEEE Region 10 Conference TENCON 2004..