Revised Mathematical Morphological Concepts

Daniel  Gyamfi; Eric Adu  Sakyi; Perpetual Saah  Andam; Robert Kofi  Acquah; Yao Elikem  Ayekple; Joseph  Ackora-Prah

doi:10.4236/apm.2015.54019

Joseph Ackora-Prah^*, Yao Elikem Ayekple, Robert Kofi Acquah, Perpetual Saah Andam, Eric Adu Sakyi, Daniel Gyamfi

Abstract: 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.

Keywords: Mathematical Morphology, Dilation, Erosion, Opening, Closing

Cite this paper: 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.

References

[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.
http://dx.doi.org/10.1007/BF01445180

[4] Hadwiger, H. (1957) Vorlesungen uber Inhalt, Oberflache und isoperimetrie. Springer Verlag, Berlin.
http://dx.doi.org/10.1007/978-3-642-94702-5

[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.
http://dx.doi.org/10.1109/TSMC.1978.4310040

[7] Goetcherian, V. (1980) From Binary To Greytone Image Processing Using Fuzzy Logic Concepts. Pattern Recognition, 12, 7-15.
http://dx.doi.org/10.1016/0031-3203(80)90049-7

[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.
http://dx.doi.org/10.1016/0734-189X(86)90004-6

[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.
http://dx.doi.org/10.1109/TPAMI.1987.4767941