Abstract
Granulometries constitute an extremely useful set of morphological operators, applicable to a variety of image analysis tasks. Traditional granulometry algorithms involve sequences of openings or closings of increasing size, and are therefore very slow on non-dedicated hardware. Efficient techniques have been proposed to compute granulometries in binary images, based on the concept of opening functions. In the present paper, a class of algorithms for computing granulometries in grayscale images is introduced. The most advanced among them are based on the new concept of opening tree. These algorithms are several orders of magnitude faster than traditional techniques, thereby opening up a range of new applications for grayscale granulometries.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Y. Chen and E. Dougherty. Texture classification by gray-scale morphological granulometries. In SPIE Vol. 1818, Visual Communications and Image Processing, Boston MA, Nov. 1992.
M. Coster and J.-L. Charmant. Précis d’Analyse d’Images. CNRS Ed., Paris, 1985.
C. S. Davis, S. M. Gallager, and A. R. Solow. Microaggregations of oceanic plankton observed by towed video microscopy. Science, 257:230–232, Jan. 1992.
E. Dougherty, J. Pelz, F. Sand, and A. Lent. Morphological image segmentation by local granulometric size distributions. Journal of Electronic Imaging, 1(1), Jan. 1992.
R. M. Haralick, S. Chen, and T. Kanungo. Recursive opening transform. In IEEE Int. Computer Vision and Pattern Recog. Conference, pages 560–565, Champaign IL, June 1992.
B. Laÿ. Recursive algorithms in mathematical morphology. In Acta Stereologica Vol. 6/III, pages 691–696, Caen, France, Sept. 1987. 7th International Congress For Stereology.
F. Maisonneuve. Extrema régionaux. Algorithme parallèle. Technical Report 781, Ecole des Mines, CGMM, Paris, 1982.
P. Maragos. Pattern spectrum and multiscale shape representation. IEEE Trans. Pattern Anal. Machine Intell., 11(7):701–716, July 1989.
G. Matheron. Eléments pour une Théorie des Milieux Poreux. Masson, Paris, 1967.
G. Matheron. Random Sets and Integral Geometry. John Wiley and Sons, New York, 1975.
L. Vincent. Morphological area openings and closings for grayscale images. In NATO Shape in Picture Workshop, pages 197–208, Driebergen, The Netherlands, Sept. 1992.
L. Vincent. Fast opening functions and morphological granulometries. In SPIE Image Algebra and Morphological Image Processing V, San Diego, CA, July 1994.
L. Vincent. Grayscale granulometries: Fast algorithms and new image analysis applications. manuscript, to be published, June 1994.
L.-P. Yuan. A fast algorithm for size analysis of irregular pore areas. In SPIE/SPSE Vol. 1451, Nonlinear Image Processing II, pages 125–136, San Jose, CA, Feb. 1991.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Vincent, L. (1994). Fast Grayscale Granulometry Algorithms. In: Serra, J., Soille, P. (eds) Mathematical Morphology and Its Applications to Image Processing. Computational Imaging and Vision, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1040-2_34
Download citation
DOI: https://doi.org/10.1007/978-94-011-1040-2_34
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4453-0
Online ISBN: 978-94-011-1040-2
eBook Packages: Springer Book Archive