Abstract
The erosion of an image not only removes all structures that cannot contain the structuring element but it also shrinks all the other ones. The search for an operator recovering most structures lost by the erosion leads to the definition of the morphological opening operator. The principle consists in dilating the image previously eroded using the same structuring element. In general, not all structures are recovered. For example, objects completely destroyed by the erosion are not recovered at all. This behaviour is at the very basis of the filtering properties of the opening operator: image structures are selectively filtered out, the selection depending on the shape and size of the SE. The dual operator of the morphological opening is the morphological closing. Both operators are at the basis of the morphological approach to image filtering developed in Chap. 8.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliographical notes and references
Beucher, S. (1990), Segmentation d’images et morphologie mathématique, PhD thesis, Ecole des Mines de Paris.
Breen, E. and Jones, R. (1996a), An attribute-based approach to mathematical morphology, in P. Maragos, R. Schafer and M. Butt, eds, ‘Mathematical morphology and its applications to image and signal processing’, Kluwer Academic Publishers, Boston, pp. 41–48.
Breen, E. andJones, R. (1996b), ‘Attribute openings, thinnings, and granulometries’, Computer Vision and Image Understanding 64(3), 377–389.
Breen, E. and Monro, D. (1994), An evaluation of priority queues for mathematical morphology, in J. Serra and P. Soille, eds, ‘Mathematical morphology and its applications to image processing’, Kluwer Academic Publishers, pp. 249–256.
Chen, Y. and Dougherty, E. (1994), ‘Gray-scale morphological granulometric texture classification’, Optical Engineering 33(8), 2713–2722.
Cheng, F. and Venetsanopoulos, A. (1992), ‘An adaptive morphological filter for image processing’, IEEE Transactions on Image Processing 1 (4), 533–539.
Dougherty, E., Newell, J. and Pelz, J. (1992), ‘Morphological texture-based maximum likelihood pixel classification based on local granulometric moments’, Pattern Recognition 25 (10), 1181–1198.
Goldmark, P. and Hollywood, J. (1951), A new technique for improving the sharpness of television pictures, in ‘Prot. IRE’, pp. 1314–1322.
Jones, R. and Soille, P. (1996a), Periodic lines and their applications to granulome-tries, in P. Maragos, W. Schafer and M. Butt, eds, ‘Mathematical Morphology and its Applications to Image and Signal Processing’, Kluwer Academic Publishers, pp. 264–272.
Jones, R. and Soille, P. (1996b), ‘Periodic lines: Definition, cascades, and application to granulometries’, Pattern Recognition Letters 17 (10), 1057–1063.
Laÿ, B. (1987), ‘Recursive algorithms in mathematical morphology’, Acta Stereologica 6 (3), 691–696.
Maragos, P. (1989), ‘Pattern spectrum and multiscale shape representation’, IEEE Transactions on Pattern Analysis and Machine Intelligence 11(7), 701 716.
Matheron, G. (1967), Eléments pour une théorie des milieux poreux,Masson, Paris. Matheron, G. (1975), Random sets and integral geometry,Wiley.
Meyer, F. (1979), ‘Iterative image transformations for an automatic screening of cervical smears’, Journal of Histochemistry and Cytochemistry 27, 128–135.
Meyer, F. (1986), ‘Automatic screening of cytological specimens’, Computer Vision, Graphics, and Image Processing 35, 356–369.
Nacken, P. (1996), ‘Chamfer metrics, the medial axis and mathematical morphology’, Journal of Mathematical Imaging and Vision 6 (2/3), 235–248.
Oppenheim, A., Schafer, R. and Stockham, T. (1968), Nonlinear filtering of multiplied and convolved signals, in ‘Prot. IEEE’, Vol. 56, pp. 1264–1291.
Peyrard, R., Soille, P., Klein, J.-C. and Tuzikov, A. (1995), A dedicated hardware system for the extraction of grid patterns on stamped metal sheets, in I. Pitas, ed., ‘Prot. of 1995 IEEE Workshop on Nonlinear Signal and Image Processing’, Neos Marmaras, pp. 867–870. URL: http://poseidon.csd.auth.gr/Workshop/papers/p_34_3. html.
Ronse, C. (1986), Erosion of narrow image features by combination of local low rank and max filters, in ‘Prot. 2nd Int. Conf. on Image Processing and its Applications’, London, pp. 77–81.
Ronse, C. andHeijmans, H. (1990), ‘The algebraic basis of mathematical morphology ii. openings and closings’, Computer Vision, Graphics,and Image Processing: Image Understanding 54(1), 74–97.
Ronse, C. and Heijmans, H. (1998), ‘A lattice-theoretical framework for annular filters in morphological image processing’, Applicable Algebra in Engineering, Communication, and Computing 9(1), 45–89.
Soille, P. (1997), A note on morphological contrast enhancement, Technical report., Ecole des Mines d’Alès-EERIE.
Soille, P. (1998), Grey scale convex hulls: definition, implementation, and application, in H. Heijmans and J. Roerdink, eds, ‘Mathematical Morphology and its Applications to Image and Signal Processing’, Vol. 12 of Computational Imaging and Vision, Kluwer Academic Publishers, Dordrecht, pp. 83–90.
Soille, P. and Talbot, H. (1998), Image structure orientation using mathematical morphology, in A. Jain, S. Venkatesh and B. Lovell, eds, ‘14th International Conference on Pattern Recognition’, Vol. 2, IAPR, IEEE Computer Society, Brisbane, pp. 1467–1469.
Stockham, T. (1972), Image processing in the context of a visual model, in ‘Prot. IEEE’, Vol. 60, pp. 828–842.
Talbot, H. and Soille, P. (1998), ‘Advances in directional image analysis using mathematical morphology’, Acta Stereologica p. In Press.
Tuzikov, A., Soille, P., Jeulin, D., Bruneel, H. and Vermeulen, M. (1992), Extraction of grid lines on stamped metal pieces using mathematical morphology, in ‘Proc. 11th IAPR International Conference on Pattern Recognition, Conference A: Computer Vision and Applications’, Vol. 1, The Hague, pp. 425–428.
Van Droogenbroeck, M. (1994), On the implementation of morphological operations, in J. Serra and P. Soille, eds, ‘Mathematical morphology and its applications to image processing’, Kluwer Academic Publishers, pp. 241–248.
Vanrell, M. and Vitrià , J. (1993), Mathematical morphology, granulometries, and texture perception, in E. Dougherty, P. Gader and J. Serra, eds, ‘Image algebra and morphological image processing IV’, Vol. SPIE-2030, pp. 152–161.
Vincent, L. (1992), Morphological area openings and closings for greyscale images, in ‘Proc. Shape in Picture ‘82, NATO Workshop’, Springer-Verlag, Driebergen, The Netherlands.
Vincent, L. (1993), Grayscale area openings and closings, their efficient implementation and applications, in J. Serra and P. Salembier, eds, ‘Proc. EURASIP workshop on Mathematical morphology and its applications to signal processing’, Barcelona, pp. 22–27.
Vincent, L. (1994), Fast grayscale granulometry algorithms, in J. Serra and P. Soille, eds, ‘Mathematical morphology and its applications to image processing’, Kluwer Academic Publishers, pp. 265–272.
Vincent, L. (1996), Local grayscale granulometries based on opening trees, in P. Maragos, R. Schafer and M. Butt, eds, ‘Mathematical morphology and its applications to image and signal processing’, Kluwer Academic Publishers, Boston, pp. 273–280.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Soille, P. (1999). Opening and Closing. In: Morphological Image Analysis. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03939-7_4
Download citation
DOI: https://doi.org/10.1007/978-3-662-03939-7_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-03941-0
Online ISBN: 978-3-662-03939-7
eBook Packages: Springer Book Archive