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Topological Concepts applied to Digital Image Processing
Keywords:
Segmentation, Topological Spaces, Connected Component, CATAbstract
This article describes an automatic method applicable to the segmentation of mediastinum Computerized Axial Tomography (CAT) images with tumors, by means of Alternating Sequential Filters (ASFs) of Mathematical Morphology, and connected components extraction based on continuous topology concepts. Digital images can be related to topological space structures, and then general topology principles can be straightforwardly implemented. This method allows not only to accurately determine the area and external boundary of the segmented structures but also to obtain their precise location. Throughout these last years, technological development has significantly improved diagnostic imaging, enabling renal tumor and incidental hepatic tumor detection -usually small in size- in younger people and with an eventually lower malignant potential. This has led to a remarkable advance in interventionist techniques such as cryosurgery and radiofrequency ablation, preventing, in some cases, major surgeries, decreasing morbid-mortality rate, hospital stay and total treatment costs. Notwithstanding this, both cryosurgery and radiofrequency ablation, through extremely low and high temperatures, respectively, kill tumor as well as healthy cells, rendering crucial the identification of tumors with an extraordinary spatial accuracy.
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References
[1] Dougherty, E. (1992): 'An Introduction to Morphological Image Processing,' (SPIE, Washington).
[2] Gonzalez, R. & Woods, R. (1992): ‘Digital Image Processing,’ (ed., Adison -Wesley, New York).
[3] Kelley, J. L., (1975): ‘General Topology,’ Springer Verlag, New York.
[4] Lantuéjoul, C. and Beucher, S. (1981): ' On the use of the geodesic metric in image analysis,' J. Microsc., 121, 39-49.
[5] Jain, (1989): ‘Fundamentals of Digital Image Processing,’ New Jersey: Prentice Hall, 1989.
[6] Lantuéjoul, C. and F. Maisonneuve (1984): ‘Geodesic methods in Quantitative Image Analysis,’ Pattern Recognition, 2, 177-187.
[7] Lima, E. L., (1977): ‘Espacios Métricos,’ Instituto de Matemática Pura y Aplicada. 2nd. Edition.
[8] Mukhopadhyay, S., Chanda, B. (2003): ‘Multiscale Morphological Segmentation of Gray-Scale Images,’ IEEE Transactions on Image Processing, 12, 533-549.
[9] Pastore, J.; Moler, E. and Ballarin, V. (2005): ‘Segmentation of brain magnetic resonance images through morphological operators and geodesic distance,’ Digital Signal Processing 15-2, pp. 153-160.
[10] SDC (2001): SDC Morphology Toolbox for MATLAB 5. User’s Guide. SDC Information Systems.
[11] Serra, J. (1982): 'Image Analysis and Mathematical Morphology,' Vol. I, (Academic Press, London).
[12] Serra, J. (1988): 'Image Analysis and Mathematical Morphology,' Vol. II, (Academic Press, London).
[13] Serra, J. and L. Vincent (1992): ‘An Overview of Morphological Filtering,’ Circuits, Systems and Signal Processing. 11 (1992) 47-108.
[14] Simmmons, G.F., (1963): ‘Introduction to Topology and Modern Analysis,’ International Student Edition. McGraw-Hill Kogakusha, Ltd.
[15] Vincent, L. (1993): ‘Morphological Grayscale Reconstruction in Image Analysis: Applications and efficient Algorithms,‘ IEEE Transactions On Image Processing, 2, 176-201.
[2] Gonzalez, R. & Woods, R. (1992): ‘Digital Image Processing,’ (ed., Adison -Wesley, New York).
[3] Kelley, J. L., (1975): ‘General Topology,’ Springer Verlag, New York.
[4] Lantuéjoul, C. and Beucher, S. (1981): ' On the use of the geodesic metric in image analysis,' J. Microsc., 121, 39-49.
[5] Jain, (1989): ‘Fundamentals of Digital Image Processing,’ New Jersey: Prentice Hall, 1989.
[6] Lantuéjoul, C. and F. Maisonneuve (1984): ‘Geodesic methods in Quantitative Image Analysis,’ Pattern Recognition, 2, 177-187.
[7] Lima, E. L., (1977): ‘Espacios Métricos,’ Instituto de Matemática Pura y Aplicada. 2nd. Edition.
[8] Mukhopadhyay, S., Chanda, B. (2003): ‘Multiscale Morphological Segmentation of Gray-Scale Images,’ IEEE Transactions on Image Processing, 12, 533-549.
[9] Pastore, J.; Moler, E. and Ballarin, V. (2005): ‘Segmentation of brain magnetic resonance images through morphological operators and geodesic distance,’ Digital Signal Processing 15-2, pp. 153-160.
[10] SDC (2001): SDC Morphology Toolbox for MATLAB 5. User’s Guide. SDC Information Systems.
[11] Serra, J. (1982): 'Image Analysis and Mathematical Morphology,' Vol. I, (Academic Press, London).
[12] Serra, J. (1988): 'Image Analysis and Mathematical Morphology,' Vol. II, (Academic Press, London).
[13] Serra, J. and L. Vincent (1992): ‘An Overview of Morphological Filtering,’ Circuits, Systems and Signal Processing. 11 (1992) 47-108.
[14] Simmmons, G.F., (1963): ‘Introduction to Topology and Modern Analysis,’ International Student Edition. McGraw-Hill Kogakusha, Ltd.
[15] Vincent, L. (1993): ‘Morphological Grayscale Reconstruction in Image Analysis: Applications and efficient Algorithms,‘ IEEE Transactions On Image Processing, 2, 176-201.
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Published
2006-10-02
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[1]
“Topological Concepts applied to Digital Image Processing”, JCS&T, vol. 6, no. 02, pp. p. 80–84, Oct. 2006, Accessed: Jul. 09, 2025. [Online]. Available: https://journal.info.unlp.edu.ar/JCST/article/view/818
