Abstract
Granulometries are morphological image analysis tools that are particularly useful for estimating object sizes in binary and grayscale images, or for characterizing textures based on their pattern spectra (i.e., granulometric curves). Though granulometric information is typically extracted globally for an image or a collection of images, local granulometries can also be useful for such applications as segmentation of texture images. However, computing local granulometries from a grayscale image by means of traditional sequences of openings and closings is either prohibitively slow, or produces results that are too coarse to be really useful. In the present paper, using the concept of opening trees proposed in [14], new local grayscale granulometry algorithms are introduced, that are both accurate and efficient. These algorithms can be used for any granulometry based on openings or closings with line segments or combinations of line segments. Among others, these local granulometries can be used to compute size transforms directly from grayscale images, a grayscale extension of the concept of an opening function. Other applications include adaptive openings and closings, as well as granulometric texture segmentation.
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Y. Chen and E. Dougherty. Texture classification by gray-scale morphological granulome tries. In SPIE Vol. 1818, Visual Communications and Image Processing, Boston MA, Nov. 1992.
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. Fleischer, P. Price, and R. Walker. Nuclear Tracks in Solids. University of California at Berkeley Press, 1975.
C. Gratin, J. Vitrià, F. Moreso, and D. Serón. Texture classification using neural networks and local granulometries. In J. Serra and P. Soille, editors, EURASIP Workshop ISMM’94, Mathematical Morphology and its Applications to Image Processing, pages 309–316, Fontainebleau, France, Sept. 1994. Kluwer Academic Publishers.
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.
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.
J. Mattioli and M. Schmitt. On information contained in the erosion curve. In NATO Shape in Picture Workshop, pages 177–195, Driebergen, The Netherlands, Sept. 1992.
J. Serra. Image Analysis and Mathematical Morphology. Academic Press, London, 1982.
X. Tang, L. Vincent, and K. Stewart. Automatic plankton image classification. International Artificial Intelligence Review Journal, 1996.
L. Vincent. Morphological transformations of binary images with arbitrary structuring elements. Signal Processing, 22(l):3–23, Jan. 1991.
L. Vincent. Fast grayscale granulometry algorithms. In J. Serra and P. Soille, editors, EURASIP Workshop ISMM’94, Mathematical Morphology and its Applications to Image Processing, pages 265–272, Fontainebleau, France, Sept. 1994. Kluwer Academic Publishers.
L. Vincent. Fast opening functions and morphological granulometries. In SPIE Vol. 2300, Image Algebra and Morphological Image Processing V, pages 253–267, San Diego, CA, July 1994.
R. C. Vogt. A spacially variant, locally adaptive, background normalization operator. In J. Serra and P. Soille, editors, EURASIP Workshop ISMM’94, Mathematical Morphology and its Applications to Image Processing, pages 45–52, Fontainebleau, France, Sept. 1994. Kluwer Academic Publishers.
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Vincent, L. (1996). Local Grayscale Granulometries Based on Opening Trees. In: Maragos, P., Schafer, R.W., Butt, M.A. (eds) Mathematical Morphology and its Applications to Image and Signal Processing. Computational Imaging and Vision, vol 5. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0469-2_31
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DOI: https://doi.org/10.1007/978-1-4613-0469-2_31
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