Revised Mathematical Morphological Concepts


We revise some mathematical morphological operators such as Dilation, Erosion, Opening and Closing. We show proofs of our theorems for the above operators when the structural elements are partitioned. Our results show that structural elements can be partitioned before carrying out morphological operations.

Share and Cite:

Ackora-Prah, J. , Ayekple, Y. , Acquah, R. , Andam, P. , Sakyi, E. and Gyamfi, D. (2015) Revised Mathematical Morphological Concepts. Advances in Pure Mathematics, 5, 155-161. doi: 10.4236/apm.2015.54019.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Matheron, G. (1975) Random Sets and Integral Geometry. Wiley, New York.
[2] Serra, J.C. (1982) Image Analysis and Mathematical Morphology. Academic Press, New York.
[3] Minkowski, H. (1903) Vorlumen und Oberflache. Mathematische Annalen, 57, 447-495.
[4] Hadwiger, H. (1957) Vorlesungen uber Inhalt, Oberflache und isoperimetrie. Springer Verlag, Berlin.
[5] Meyer, F. (1977) Contrast Feature Extraction. In: Special Issues of Practical Metallography, Ederer Verlag GmbH, Stuttgart, Proc. 2nd European Symp. on Quant. Anal. of Microstruct. in Materials Science, Biology and Medicine, France.
[6] Nakagawa, Y. and Rosenfeld, A. (1978) A Note on the Use of Local Min and Max Operations in Digital Picture Processing. IEEE Transactions on Systems, Man, and Cybernetics, 8, 632-635.
[7] Goetcherian, V. (1980) From Binary To Greytone Image Processing Using Fuzzy Logic Concepts. Pattern Recognition, 12, 7-15.
[8] Sternberg, S.R. (1980) Language and Architecture for Parallel Image Processing. In: Gelsema, E. and Kanal, L., Eds., Pattern Recognition in Practice, North Holland Publishing, Holland.
[9] Sternberg, S.R. (1986) Grayscale Morphology. Computer Vision, Graphics and Image Processing, 35, 333-355.
[10] Haralick, R.M., Sternberg, S.R. and Zhuang, X. (1987) Image Analysis Using Mathematical Morphology. IEEE Transactions on Pattern Analysis and Machine Intelligence, 9, 532-550.

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.