Abstract
In this paper we give an overview of both classical and more modern morphological techniques. We will demonstrate their utility through a range of practical examples. After discussing the fundamental morphological ideas, we show how the classic morphological opening and closing filters lead to measures of size via granulometries, and we will discuss briefly their implementation. We also present an overview of morphological segmentation techniques, and the use of connected openings and thinnings will be demonstrated. This then leads us into the more recent set-theoretic notions of graph based approaches to image analysis.
Similar content being viewed by others
References
Adams R. and Bischof L. 1994. Seeded region growing. IEEE Transactions on Pattern Analysis and Machine Intelligence 16: 641–647.
Borgefors G. 1986. Distance transformations in digital images. Computer Vision, Graphics, and Image Processing 34: 344–371.
Breen E. and Jones R. 1996a. An attribute-based approach to mathematical morphology, In: Maragos P., Schafer R., and Butt M. (Eds.), Mathematical Morphology and its Applications to Image and Signal Processing. Kluwer Academic Press, Atlanta, pp. 41–48.
Breen E.J. and Jones R. 1996b. Attribute openings, thinnings and granulometries. ComputerVision and Image Understanding 64(3): 377–389.
Breen E., Jones R., and Talbot H. To appear. The morphological approach to industrial image analysis applications. Acta Stereologica.
Coade R. 1993. Determination of effective temperature for residual life, assessment of microstructural methods. Technical Report ESAA/1.7/MET/WP 005.
Crespo J., Serra J., and Schafer R. 1995. Theoretical aspects of morphological filters by reconstruction. Signal Processing 47(2): 201–225.
Gonzalez R. and Wintz P. 1987. Digital Image Processing, 2nd edn. Reading, Addison Wesley, Massachusetts.
Heijmans H., Nacken P., Toet A., and Vincent L. 1992. Graph morphology. Journal of Visual Communication and Image Representation 3(1): 24–38.
Jones R. 1997. Component trees for image filtering and segmentation. In: Coyle E. (Ed.), Proceedings of the 1997 IEEE Workshop on Nonlinear Signal and Image Processing. Mackinac Island.
Jones R., Berman M., Jiang Y., Buckley M., and Drew M. 1995. Image analysis of microstructural steels exposed to elevated temperatures. Technical Report E 95/20, CSIRO, Division of Mathematics and Statistics.
Kaufmann A. 1972. Points and Arrows: the Theory of Graphs. Transworld Student Library, Transworld Publishers Ltd., London.
Klein J.C. 1976. Conception et rélisation d'une unité logique pour l'analyse quantitative d'images. PhD Thesis, Nancy University, France.
Lantuéjoul C. and Beucher S. 1981. On the use of the geodesic metric in image analysis. Journal of Microscopy 121: 39–49.
Matheron G. 1967. Eléments pour une théorie des milieux poreux. Masson, Paris.
Matheron G. 1975. Random Sets and Integral Geometry. Wiley, New York.
Matheron G. 1988. Filters and lattices. In: Serra J. (Ed.), Image Analysis and Mathematical Morphology, Vol. II: Theoretical Advances. Academic Press, London, pp. 115–140.
Meyer F. and Beucher S. 1990. Morphological segmentation. Journal of Visual Communication and Image Representation 1(1): 21–46.
Ronse C. and Heijmans H. 1991. The algebraic basis of mathematical morphology-part 2: Openings and closings. Computer Vision, Graphics, and Image Processing: Image Understanding 54(1): 74–97.
Salembier P. and Oliveras A. 1996. Practical extensions of connected operators. In: Maragos P., Schafer R.W., and Butt M.A. (Eds.), Mathematical Morphology and its Application to Image and Signal Processing. Kluwer Academic Publishers, Atlanta, pp. 97–110.
Salembier P., Oliveras A., and Garrido L. 1998. Anti-extensive connected operators for image and sequence processing. IEEE Transactions on Image Processing 7(4): 555–570.
Salembier P. and Serra J. 1995. Flat zones filtering, connected operators and filters by reconstruction. IEEE Transactions on Image Processing 3(8): 1153–1160.
Serra J. 1982. Image Analysis and Mathematical Morphology. Academic Press, London.
Serra J. (Ed.) 1988. Image Analysis and Mathematical Morphology, Vol. 2: Theoretical Advances. Academic Press, London.
Serra J. and Salembier P. 1993. Connected operators and pyramids. In: Image Algebra and Mathematical Morphology, Vol. 2030. SPIE, San Diego, pp. 65–76.
Serra J. and Vincent L. 1992. An overview of morphological filtering. Circuits, Systems and Signal Processing 11(1): 47–108.
Soille P., Breen E., and Jones R. 1996. Recursive implementation of erosions and dilation along discrete lines at arbitrary angles. IEEE Transactions on Pattern Analysis and Machine Intelligence 18(5): 562–567.
Soille P., Serra J., and Rivest J.-F. 1992. Dimensional measurements and operators in mathematical morphology. In: Nonlinear Image Processing III. pp. 127–138.
Sternberg S. 1986. Grayscale morphology. Computer Graphics and Image Processing 35: 333–355.
Sun C. and Wu X. 1997. A method for automatic segmentation of fiducial markers. In: Pan H., Brooks M., McMichael D., and Newsam G. (Eds.), Image Analysis and Information Fusion. CSSIP, Adelaide, pp. 43–52.
Talbot H., Jeulin D., and Hanton D. 1996. Image analysis of insulation mineral fibres. Microscopy, Microanalysis and Microstructures 7: 361–368.
Vandroogenboeck M. and Talbot H. 1996. Fast computation of morphological operations with arbitrary structuring elements. Pattern Recognition Letters 17: 1451–1460.
Vincent L. 1989. Graphs and mathematical morphology. Signal Processing 16: 365–388.
Vincent L. 1990. Algorithmes morphologiques à base de files d'attente et de lacets. Extension aux graphes. PhD Thesis, Ecole des Mines de Paris.
Vincent L. 1991. Efficient computation of various types of skeletons. In: Medical Imaging V. SPIE, San Jose.
Vincent L. 1992. Morphological algorithms. In: Dougherty. E. (Ed.), Mathematical Morphology in Image Processing. Marcel-Dekker, New York, pp. 255–288.
Vincent L. 1993a. Grayscale area openings and closings, their efficient implementation and applications. In: Serra J. and Salembier P. (Eds.), Mathematical Morphology and its Applications to Signal Processing. UPC Publications, Barcelona, pp. 22–27.
Vincent L. 1993b. Morphological grayscale reconstruction in image analysis: Applications and efficient algorithms. IEEE Transactions on Image Processing 22(2): 176–201.
Vincent L. and Soille P. 1991. Watersheds in digital spaces: an efficient algorithm based on immersion simulations. IEEE Transactions on Pattern Analysis and Machine Intelligence 13(6): 583–598.
Wendt P.D., Coyle E.J., and Gallagher N.C. 1986. Stack filters. IEEE Transactions on Acoustics, Speech and Signal Processing 34(4): 898–911.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Breen, E.J., Jones, R. & Talbot, H. Mathematical morphology: A useful set of tools for image analysis. Statistics and Computing 10, 105–120 (2000). https://doi.org/10.1023/A:1008990208911
Issue Date:
DOI: https://doi.org/10.1023/A:1008990208911