In this paper we describe the mathematical morphology in the form of high level image processing and mid level image processing. We study two approaches, for “color morphology” are vector approach and component-wise approach. In set theory approach, Mathematical morphology is developed by J.Serra and G. Matheron. Edge Detection is well known approach which aims at searching and detecting the points in a digital image at which the image brightness changes stridently. Edges are significant local changes of strength in an image. 3D biomedical images edge detection is an essential for object recognition of the human organs. Object recognition is a vital processing step in biomedical image segmentation. Important appearance can be extracted from the edges an image (e.g., corners, line, curves, etc.). In this paper, basic mathematical morphological operators are introduced at first then a mathematical edge detection algorithm is proposed to detect edges of the lungs CT image with salt-and-pepper noise and the Gaussian noise.

1. David Dagan Feng, “Information Technology Applications in Biomedical Functional Imaging”, IEEE TRANSACTIONS ON INFORMATION TECHNOLOGY IN BIOMEDICINE, Vol. 3, NO.3, pp. 221-230. March 2000.
2. Huertas, A. and Medioni, G., “Detection of intensity changes with sub pixel accuracy using Laplacian-Gaussian masks,” IEEE Trans.On Pattern Analysis and Machine Intelligence, PAMI, vol. 8, pp. 651–664, 1986.
3. Zhao Fang, Ma Yulei, Zhang Junpeng, “Medical Image Processing on Mathematical Morphology”, 2nd International Conference on Computer Application and System Modelling, 2012.
4. G. Matheron, Random Sets and Integral Geometry. New York: Wiley, 1974. J. Serra, Image Analysis and Mathematical Morphology, Vol. 1. London: Academic, 1982.
5. J. Serra, Editor. Image Analysis and Mathematical Morphology, Vol. 2: Theoretical Advances. London: Academic, 1988.
6. P. Maragos and R. W. Schafer, “Morphological filters—Part I: Their set theoretic analysis and relations to linear shift-invariant filters,” IEEETrans. Acoust., Speech, Signal Process., vol. 35, no. 8, pp. 1153-1169, 1987.
7. Edge detection, Trucco, Chapt 4 AND Jain et al., Chapter 5
8. https://www.cs.auckland.ac.nz/courses/compsci773s1c/lectures/ImageProcessing-html/topic4.htm /
9. Jonathan W. Valvano, John A. Pearce, Rebecca Richards-Kortum, Ronald E. Barr, J. K. Aggarwal, Mark Allen Schulze, Dissertation: “Biomedical Image Processing with Morphology-Based Nonlinear Filters”, The University of Texas at Austin December 1994.
10. Aboul ella Hassanien, Ajith Abraham, “Rough Morphology Hybrid Approach for Mammography Image Classification and Prediction”, International Journal of Computational Intelligence and Applications, ijcia2008.
11. Aboul Ella Hassanien, Ajith Abraham, James F. Petersand Gerald Schaefer, “An Overview of Rough-Hybrid Approaches in Image Processing”.

3D Biomedical Images Edge Detection Morphological Operators Structural Element