Morphological colour operators in totally ordered lattices based on distances: Application to image filtering, enhancement and analysis

The extension of mathematical morphology operators to multi-valued functions, and in particular to colour images, is neither direct nor general. In this paper, a generalisation of distance-based and lexicographical-based approaches is proposed, allowing the extension of morphological operators to colour images for any colour representation (e.g., RGB, LSH and L^*a^*b^*) and for any metric distance to a reference colour. The performance of the introduced operators is illustrated by means of different applications: colour feature extraction using openings (closings) by reconstruction, colour gradients for segmenting, colour denoising by the centre operator and colour enhancement by the contrast mapping. Examples from natural colour images and biomedical microscopic colour images are given.

[1]  Ioannis Andreadis,et al.  A new vector median filter for colour image processing , 2001, Pattern Recognit. Lett..

[2]  A. Venetsanopoulos,et al.  A multichannel order-statistic technique for cDNA microarray image processing , 2004, IEEE Transactions on NanoBioscience.

[3]  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).

[4]  Ioannis Pitas,et al.  Multivariate ordering in color image filtering , 1991, IEEE Trans. Circuits Syst. Video Technol..

[5]  J. Slavik,et al.  Fluorescence Microscopy and Fluorescent Probes , 1996, Springer US.

[6]  Allan Hanbury,et al.  Mathematical Morphology in the HLS Colour Space , 2001, BMVC.

[7]  John I. Goutsias,et al.  Mathematical Morphology and its Applications to Image and Signal Processing , 2000, Computational Imaging and Vision.

[8]  Arthur Robert Weeks,et al.  Color morphological operators using conditional and reduced ordering , 1999, Optics & Photonics.

[9]  Edward J. Delp,et al.  Morphological operations for color image processing , 1999, J. Electronic Imaging.

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

[11]  Jean Serra,et al.  Image Analysis and Mathematical Morphology , 1983 .

[12]  Vincent Agnus,et al.  Morphology on Label Images: Flat-Type Operators and Connections , 2005, Journal of Mathematical Imaging and Vision.

[13]  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.

[14]  Luc Vincent,et al.  Morphological grayscale reconstruction in image analysis: applications and efficient algorithms , 1993, IEEE Trans. Image Process..

[15]  Antonio J. Plaza,et al.  Spatial/spectral endmember extraction by multidimensional morphological operations , 2002, IEEE Trans. Geosci. Remote. Sens..

[16]  Panos E. Trahanias,et al.  Directional processing of color images: theory and experimental results , 1996, IEEE Trans. Image Process..

[17]  Henk J. A. M. Heijmans,et al.  Inf-Semilattice Approach to Self-Dual Morphology , 2004, Journal of Mathematical Imaging and Vision.

[18]  Jesús Angulo,et al.  Morphological coding of color images by vector connected filters , 2003, Seventh International Symposium on Signal Processing and Its Applications, 2003. Proceedings..

[19]  Rastislav Lukac,et al.  A Taxonomy of Color Image Filtering and Enhancement Solutions , 2006 .

[20]  J. Serra,et al.  Contrasts and activity lattice , 1989 .

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

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

[23]  J. Andrew Bangham,et al.  Evaluating a colour morphological scale-space , 2003 .

[24]  Fernando Torres-Medina,et al.  Comparative study of vectorial morphological operations in different color spaces , 2001, SPIE Optics East.

[25]  Aleksandra Mojsilovic,et al.  Quantization of color spaces and processing of color images by fibonacci lattices , 2000, Electronic Imaging.

[26]  Gunther Wyszecki,et al.  Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd Edition , 2000 .

[27]  K. Martin,et al.  Vector filtering for color imaging , 2005, IEEE Signal Processing Magazine.

[28]  Jesús Angulo,et al.  Modelling and segmentation of colour images in polar representations , 2007, Image Vis. Comput..

[29]  Edward R. Dougherty,et al.  Mathematical Morphology in Image Processing , 1992 .

[30]  Arthur R. Weeks,et al.  Morphological operations on color images , 2001, J. Electronic Imaging.

[31]  Jean Paul Frédéric Serra,et al.  Morphological interpolation and color images , 1999, Proceedings 10th International Conference on Image Analysis and Processing.

[32]  Henry P. Kramer,et al.  Iterations of a non-linear transformation for enhancement of digital images , 1975, Pattern Recognit..

[33]  Jesús Angulo.  Morphologie mathématique et indexation d'images couleur : application à la microscopie en biomédecine. (Mathematical morphology and image colour indexing : application in bio-medical microscopy) , 2003 .

[34]  Richard Alan Peters,et al.  Mathematical morphology for angle-valued images , 1997, Electronic Imaging.

[35]  Hugues Talbot,et al.  Complete ordering and multivariate mathematical morphology , 1998 .

[36]  G. Wyszecki,et al.  Color Science Concepts and Methods , 1982 .

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

[38]  Ioannis Andreadis,et al.  A new approach to morphological color image processing , 2002, Pattern Recognit..

[39]  Stephen S. Wilson.  Theory of Matrix Morphology , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

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

[41]  Allan Hanbury,et al.  Morphological operators on the unit circle , 2001, IEEE Trans. Image Process..

[42]  Christoph Busch,et al.  Morphological Operations for Color‐Coded Images , 1995, Comput. Graph. Forum.

[43]  李幼升,et al.  Ph , 1989 .

[44]  Scott T. Acton,et al.  On connected filters in color image processing , 2004, J. Electronic Imaging.

[45]  Fernand Meyer,et al.  The levelings , 1998 .

[46]  Ean,et al.  MATHEMATICAL MORPHOLOGY IN THE CIELAB SPACE A , 2022 .

[47]  J. Astola,et al.  Vector median filters , 1990, Proc. IEEE.

[48]  Azriel Rosenfeld,et al.  From pixels to features: J C Simon (ed). Published by Nort-Holland, Netherlands. 1989. 416 pp. $94.75 , 1990 .

[49]  J. Andrew Bangham,et al.  Evaluating colour morphological scale-spaces , 2003, BMVC.

[50]  Rastislav Lukac,et al.  cDNA microarray image processing using fuzzy vector filtering framework , 2005, Fuzzy Sets Syst..

[51]  Jonathan Li,et al.  MULTIVARIATE MATHEMATICAL MORPHOLOGY BASED ON PRINCIPAL COMPONENT ANALYSIS : INITIAL RESULTS IN BUILDING EXTRACTION , 2004 .

[52]  Hazem Munawer Al-Otum,et al.  Morphological operators for color image processing based on Mahalanobis distance measure , 2003 .

[53]  L. Rudin,et al.  Feature-oriented image enhancement using shock filters , 1990 .

[54]  Jesús Angulo,et al.  Unified Morphological Color Processing Framework in a Lum/Sat/Hue Representation , 2005, ISMM.

[55]  Jesús Angulo,et al.  Automatic analysis of DNA microarray images using mathematical morphology , 2003, Bioinform..

[56]  Jean Paul Frédéric Serra,et al.  Morphological Segmentations of Colour Images , 2005, ISMM.

[57]  Mark D. Fairchild,et al.  Visual psychophysics and color appearance , 2002 .