Abstract

An optoelectronic implementation for the morphological watershed transform is proposed. Fiber-optic programmable logic arrays are used in the implementation because of their high fan factors at high clock speeds. Image segmentation is one of the main applications of the watershed transform. Based on the optoelectronic implementation, an algorithm for the segmentation of axial magnetic resonance (MR) head images to extract information on brain matter is presented. Simulation results for the different steps of the segmentation process are presented.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Serra, Image Analysis and Mathematical Morphology (Academic, San Diego, Calif., 1982).
  2. E. R. Dougherty, An Introduction to Morphological Image Processing (SPIE Optical Engineering Press, Bellingham, Wash., 1992).
  3. R. Haralick, L. Shapiro, “Survey: image segmentation techniques,” Comput. Vision Graphics Image Process. 29(1), 100–132 (1985).
    [CrossRef]
  4. S. Beucher, “Segmentation tools in mathematical morphology,” in Image Algebra and Morphological Image Processing, P. D. Gader, ed., Proc. SPIE1350, 70–84 (1990).
  5. S. Beucher, “The watershed transformation applied to image segmentation,” in Proceedings of Scanning Microscopy (Scanning Microscopy International, Chicago, Ill., 1992), pp. 299–314.
  6. S. Beucher, F. Meyer, “The morphological approach to segmentation: the watershed transformation,” in Mathematical Morphology in Image Processing, E. R. Dougherty, ed. (Marcel Dekker, New York, 1993), pp. 433–481.
  7. S. Beucher, C. Lantuejoul, “Use of watersheds in contour detection,” paper presented at International Workshop on Image Processing: Real Time Edge and Motion Detection/Estimation, CCETT/IRISA, Rennes, France, September 1979.
  8. L. Vincent, P. Soille, “Watersheds in digital spaces: an efficient algorithm based on immersion simulations,” IEEE Trans. Pattern Anal. Mach. Intel. 13(6), 583–598 (1991).
    [CrossRef]
  9. F. Meyer, “Un algorithme optimal de partage des eaux,” in Proceedings 8e Congres AFCET, Reconnaissance des Formes et Intelligence Artificielle (Association Francaise des Sciences et Technologies de l’Information et des Systemes, 1992), Vol. 2, pp. 847–859.
  10. B. P. Dobrin, T. Viero, M. Gabbouj, “Fast watershed algorithms: analysis and extensions,” in Nonlinear Image Processing V, E. R. Dougherty, J. T. Astola, H. G. Longbotham, eds., Proc. SPIE2180, 209–220 (1994).
    [CrossRef]
  11. R. Arrathoon, “Historical perspectives: optical crossbars and optical computing,” in Digital Optical Computing, R. Arrathoon, ed., Proc. SPIE752, 2–11 (1987).
    [CrossRef]
  12. R. Arrathoon, “Fiber-optic programmable logic arrays,” in Optical Computing: Digital and Symbolic, R. Arrathoon, ed. (Marcel Dekker, New York, 1989), pp. 247–278.
  13. F. Y. Shih, O. R. Mitchell, “Threshold decomposition of gray-scale morphology into binary morphology,” IEEE Trans. Pattern Anal. Mach. Intel. 11(1), 31–42 (1989).
    [CrossRef]
  14. L. Vincent, “Morphological grayscale reconstruction in image analysis: applications and efficient algorithms,” IEEE Trans. Image Process. 2(2), 176–201 (1993).
    [CrossRef]
  15. N. Michael, R. Arrathoon, “Optoelectronic pipeline architecture for morphological image processing,” Appl. Opt. 36(8), 1718–1725 (1997).
  16. S. Beucher, M. Bilodeau, “Road segmentation and obstacle detection by a fast watershed transformation,” in Proceedings of the Intelligent Vehicles 1994 Symposium (Institute of Electricaland Electronics Engineers, New York, 1994), pp. 296–301.
  17. L. Vincent, “Morphological image processing and network analysis of cornea endothelial cell images,” in Image Algebra and Morphological Image Processing III, P. D. Gader, E. R. Dougherty, J. C. Serra, eds., Proc. SPIE1769, 212–226 (1992).
  18. N. Rougon, F. Preteux, “Quantitative automated analysis of cornea endothelial cell images,” in Image Algebra and Morphological Image Processing V, E. R. Dougherty, P. D. Gader, M. Schmitt, eds., Proc. SPIE2300, 133–144 (1994).
    [CrossRef]
  19. N. Michael, R. Arrathoon, “Optical PLA implementation for selected complex morphological algorithms,” in Hybrid Image and Signal Processing V, D. P. Casasent, A. G. Tescher, eds., Proc. SPIE2751, 186–198 (1996).
    [CrossRef]
  20. D. N. Levin, X. Hu, K. K. Tan, “Surface of the three-dimension MR images created with volume rendering,” Radiology 171, 277–280 (1989).
    [PubMed]
  21. K. H. Hoehne, M. Bomans, A. Pommert, M. Reimer, U. Tiede, G. Wiebecke, “Rendering tomographic volume data: adequacy of methods for different modalities and organs,” in 3D Imaging in Medicine: Algorithms, Systems, Applications, K. H. Hoehne, H. Fuchs, S. M. Pizer, eds. (Springer-Verlag, Berlin, 1990), pp. 197–215.
    [CrossRef]
  22. J. C. Bezdek, L. O. Hall, L. P. Clarke, “Review of MR image segmentation techniques using pattern recognition,” Med. Phys. 20(4), 1033–1048 (1993).
  23. L. P. Clarke, R. P. Velthuizen, M. A. Camacho, J. J. Heine, M. Vaidyanathan, L. O. Hall, R. W. Thatcher, M. S. Silbiger, “MRI segmentation: methodsand applications,” Magn. Resonance Imaging 13(3), 343–368 (1995).
    [CrossRef]
  24. M. C. Clark, L. O. Hall, D. B. Goldgof, L. P. Clarke, R. P. Velthuizen, M. S. Silbiger, “MRI segmentation using fuzzy clustering techniques,” IEEE Eng. Medicine Biol. 13(5), 730–742 (1994).
    [CrossRef]
  25. W. Connor, P. Diaz, “Morphological segmentation and 3-D rendering of the brain in magnetic resonance imaging,” in Image Algebra and Morphological Image Processing II, P. D. Gader, E. R. Dougherty, eds., Proc. SPIE1568, 327–334 (1991).
  26. M. E. Brummer, R. M. Mersereau, R. L. Eisner, R. J. Lewine, “Automatic detection of brain contours in MRI data sets,” IEEE Trans. Medical Imaging 12(2), 153–166 (1993).
    [CrossRef]
  27. R. Acharya, Y. Ma, “Segmentation algorithm for cranial magnetic resonance images,” in Medical Imaging VI: Image Processing, M. H. Loew, ed., Proc. SPIE1652, 50–61 (1992).
  28. M. Bomans, K. H. Hoehne, U. Tiede, M. Riemer, “3-D segmentation of MR images of the head for 3-D display,” IEEE Trans. Medical Imaging 9, 177–183 (1990).
    [CrossRef]
  29. KHOROS is an image processing system developed by Khoral, Inc., Albequerque, NM.
  30. J. Barrera, G. J. F. Banon, R. Lotufo, “Mathematical morphology toolbox for the Khoros system,” in Image Algebra and Morphological Image Processing V, E. R. Dougherty, P. D. Gader, M. Schmitt, eds., Proc. SPIE2300, 241–252 (1994).
    [CrossRef]

1997 (1)

1995 (1)

L. P. Clarke, R. P. Velthuizen, M. A. Camacho, J. J. Heine, M. Vaidyanathan, L. O. Hall, R. W. Thatcher, M. S. Silbiger, “MRI segmentation: methodsand applications,” Magn. Resonance Imaging 13(3), 343–368 (1995).
[CrossRef]

1994 (1)

M. C. Clark, L. O. Hall, D. B. Goldgof, L. P. Clarke, R. P. Velthuizen, M. S. Silbiger, “MRI segmentation using fuzzy clustering techniques,” IEEE Eng. Medicine Biol. 13(5), 730–742 (1994).
[CrossRef]

1993 (3)

M. E. Brummer, R. M. Mersereau, R. L. Eisner, R. J. Lewine, “Automatic detection of brain contours in MRI data sets,” IEEE Trans. Medical Imaging 12(2), 153–166 (1993).
[CrossRef]

L. Vincent, “Morphological grayscale reconstruction in image analysis: applications and efficient algorithms,” IEEE Trans. Image Process. 2(2), 176–201 (1993).
[CrossRef]

J. C. Bezdek, L. O. Hall, L. P. Clarke, “Review of MR image segmentation techniques using pattern recognition,” Med. Phys. 20(4), 1033–1048 (1993).

1991 (1)

L. Vincent, P. Soille, “Watersheds in digital spaces: an efficient algorithm based on immersion simulations,” IEEE Trans. Pattern Anal. Mach. Intel. 13(6), 583–598 (1991).
[CrossRef]

1990 (1)

M. Bomans, K. H. Hoehne, U. Tiede, M. Riemer, “3-D segmentation of MR images of the head for 3-D display,” IEEE Trans. Medical Imaging 9, 177–183 (1990).
[CrossRef]

1989 (2)

F. Y. Shih, O. R. Mitchell, “Threshold decomposition of gray-scale morphology into binary morphology,” IEEE Trans. Pattern Anal. Mach. Intel. 11(1), 31–42 (1989).
[CrossRef]

D. N. Levin, X. Hu, K. K. Tan, “Surface of the three-dimension MR images created with volume rendering,” Radiology 171, 277–280 (1989).
[PubMed]

1985 (1)

R. Haralick, L. Shapiro, “Survey: image segmentation techniques,” Comput. Vision Graphics Image Process. 29(1), 100–132 (1985).
[CrossRef]

Acharya, R.

R. Acharya, Y. Ma, “Segmentation algorithm for cranial magnetic resonance images,” in Medical Imaging VI: Image Processing, M. H. Loew, ed., Proc. SPIE1652, 50–61 (1992).

Arrathoon, R.

N. Michael, R. Arrathoon, “Optoelectronic pipeline architecture for morphological image processing,” Appl. Opt. 36(8), 1718–1725 (1997).

R. Arrathoon, “Fiber-optic programmable logic arrays,” in Optical Computing: Digital and Symbolic, R. Arrathoon, ed. (Marcel Dekker, New York, 1989), pp. 247–278.

N. Michael, R. Arrathoon, “Optical PLA implementation for selected complex morphological algorithms,” in Hybrid Image and Signal Processing V, D. P. Casasent, A. G. Tescher, eds., Proc. SPIE2751, 186–198 (1996).
[CrossRef]

R. Arrathoon, “Historical perspectives: optical crossbars and optical computing,” in Digital Optical Computing, R. Arrathoon, ed., Proc. SPIE752, 2–11 (1987).
[CrossRef]

Banon, G. J. F.

J. Barrera, G. J. F. Banon, R. Lotufo, “Mathematical morphology toolbox for the Khoros system,” in Image Algebra and Morphological Image Processing V, E. R. Dougherty, P. D. Gader, M. Schmitt, eds., Proc. SPIE2300, 241–252 (1994).
[CrossRef]

Barrera, J.

J. Barrera, G. J. F. Banon, R. Lotufo, “Mathematical morphology toolbox for the Khoros system,” in Image Algebra and Morphological Image Processing V, E. R. Dougherty, P. D. Gader, M. Schmitt, eds., Proc. SPIE2300, 241–252 (1994).
[CrossRef]

Beucher, S.

S. Beucher, M. Bilodeau, “Road segmentation and obstacle detection by a fast watershed transformation,” in Proceedings of the Intelligent Vehicles 1994 Symposium (Institute of Electricaland Electronics Engineers, New York, 1994), pp. 296–301.

S. Beucher, C. Lantuejoul, “Use of watersheds in contour detection,” paper presented at International Workshop on Image Processing: Real Time Edge and Motion Detection/Estimation, CCETT/IRISA, Rennes, France, September 1979.

S. Beucher, “The watershed transformation applied to image segmentation,” in Proceedings of Scanning Microscopy (Scanning Microscopy International, Chicago, Ill., 1992), pp. 299–314.

S. Beucher, F. Meyer, “The morphological approach to segmentation: the watershed transformation,” in Mathematical Morphology in Image Processing, E. R. Dougherty, ed. (Marcel Dekker, New York, 1993), pp. 433–481.

S. Beucher, “Segmentation tools in mathematical morphology,” in Image Algebra and Morphological Image Processing, P. D. Gader, ed., Proc. SPIE1350, 70–84 (1990).

Bezdek, J. C.

J. C. Bezdek, L. O. Hall, L. P. Clarke, “Review of MR image segmentation techniques using pattern recognition,” Med. Phys. 20(4), 1033–1048 (1993).

Bilodeau, M.

S. Beucher, M. Bilodeau, “Road segmentation and obstacle detection by a fast watershed transformation,” in Proceedings of the Intelligent Vehicles 1994 Symposium (Institute of Electricaland Electronics Engineers, New York, 1994), pp. 296–301.

Bomans, M.

M. Bomans, K. H. Hoehne, U. Tiede, M. Riemer, “3-D segmentation of MR images of the head for 3-D display,” IEEE Trans. Medical Imaging 9, 177–183 (1990).
[CrossRef]

K. H. Hoehne, M. Bomans, A. Pommert, M. Reimer, U. Tiede, G. Wiebecke, “Rendering tomographic volume data: adequacy of methods for different modalities and organs,” in 3D Imaging in Medicine: Algorithms, Systems, Applications, K. H. Hoehne, H. Fuchs, S. M. Pizer, eds. (Springer-Verlag, Berlin, 1990), pp. 197–215.
[CrossRef]

Brummer, M. E.

M. E. Brummer, R. M. Mersereau, R. L. Eisner, R. J. Lewine, “Automatic detection of brain contours in MRI data sets,” IEEE Trans. Medical Imaging 12(2), 153–166 (1993).
[CrossRef]

Camacho, M. A.

L. P. Clarke, R. P. Velthuizen, M. A. Camacho, J. J. Heine, M. Vaidyanathan, L. O. Hall, R. W. Thatcher, M. S. Silbiger, “MRI segmentation: methodsand applications,” Magn. Resonance Imaging 13(3), 343–368 (1995).
[CrossRef]

Clark, M. C.

M. C. Clark, L. O. Hall, D. B. Goldgof, L. P. Clarke, R. P. Velthuizen, M. S. Silbiger, “MRI segmentation using fuzzy clustering techniques,” IEEE Eng. Medicine Biol. 13(5), 730–742 (1994).
[CrossRef]

Clarke, L. P.

L. P. Clarke, R. P. Velthuizen, M. A. Camacho, J. J. Heine, M. Vaidyanathan, L. O. Hall, R. W. Thatcher, M. S. Silbiger, “MRI segmentation: methodsand applications,” Magn. Resonance Imaging 13(3), 343–368 (1995).
[CrossRef]

M. C. Clark, L. O. Hall, D. B. Goldgof, L. P. Clarke, R. P. Velthuizen, M. S. Silbiger, “MRI segmentation using fuzzy clustering techniques,” IEEE Eng. Medicine Biol. 13(5), 730–742 (1994).
[CrossRef]

J. C. Bezdek, L. O. Hall, L. P. Clarke, “Review of MR image segmentation techniques using pattern recognition,” Med. Phys. 20(4), 1033–1048 (1993).

Connor, W.

W. Connor, P. Diaz, “Morphological segmentation and 3-D rendering of the brain in magnetic resonance imaging,” in Image Algebra and Morphological Image Processing II, P. D. Gader, E. R. Dougherty, eds., Proc. SPIE1568, 327–334 (1991).

Diaz, P.

W. Connor, P. Diaz, “Morphological segmentation and 3-D rendering of the brain in magnetic resonance imaging,” in Image Algebra and Morphological Image Processing II, P. D. Gader, E. R. Dougherty, eds., Proc. SPIE1568, 327–334 (1991).

Dobrin, B. P.

B. P. Dobrin, T. Viero, M. Gabbouj, “Fast watershed algorithms: analysis and extensions,” in Nonlinear Image Processing V, E. R. Dougherty, J. T. Astola, H. G. Longbotham, eds., Proc. SPIE2180, 209–220 (1994).
[CrossRef]

Dougherty, E. R.

E. R. Dougherty, An Introduction to Morphological Image Processing (SPIE Optical Engineering Press, Bellingham, Wash., 1992).

Eisner, R. L.

M. E. Brummer, R. M. Mersereau, R. L. Eisner, R. J. Lewine, “Automatic detection of brain contours in MRI data sets,” IEEE Trans. Medical Imaging 12(2), 153–166 (1993).
[CrossRef]

Gabbouj, M.

B. P. Dobrin, T. Viero, M. Gabbouj, “Fast watershed algorithms: analysis and extensions,” in Nonlinear Image Processing V, E. R. Dougherty, J. T. Astola, H. G. Longbotham, eds., Proc. SPIE2180, 209–220 (1994).
[CrossRef]

Goldgof, D. B.

M. C. Clark, L. O. Hall, D. B. Goldgof, L. P. Clarke, R. P. Velthuizen, M. S. Silbiger, “MRI segmentation using fuzzy clustering techniques,” IEEE Eng. Medicine Biol. 13(5), 730–742 (1994).
[CrossRef]

Hall, L. O.

L. P. Clarke, R. P. Velthuizen, M. A. Camacho, J. J. Heine, M. Vaidyanathan, L. O. Hall, R. W. Thatcher, M. S. Silbiger, “MRI segmentation: methodsand applications,” Magn. Resonance Imaging 13(3), 343–368 (1995).
[CrossRef]

M. C. Clark, L. O. Hall, D. B. Goldgof, L. P. Clarke, R. P. Velthuizen, M. S. Silbiger, “MRI segmentation using fuzzy clustering techniques,” IEEE Eng. Medicine Biol. 13(5), 730–742 (1994).
[CrossRef]

J. C. Bezdek, L. O. Hall, L. P. Clarke, “Review of MR image segmentation techniques using pattern recognition,” Med. Phys. 20(4), 1033–1048 (1993).

Haralick, R.

R. Haralick, L. Shapiro, “Survey: image segmentation techniques,” Comput. Vision Graphics Image Process. 29(1), 100–132 (1985).
[CrossRef]

Heine, J. J.

L. P. Clarke, R. P. Velthuizen, M. A. Camacho, J. J. Heine, M. Vaidyanathan, L. O. Hall, R. W. Thatcher, M. S. Silbiger, “MRI segmentation: methodsand applications,” Magn. Resonance Imaging 13(3), 343–368 (1995).
[CrossRef]

Hoehne, K. H.

M. Bomans, K. H. Hoehne, U. Tiede, M. Riemer, “3-D segmentation of MR images of the head for 3-D display,” IEEE Trans. Medical Imaging 9, 177–183 (1990).
[CrossRef]

K. H. Hoehne, M. Bomans, A. Pommert, M. Reimer, U. Tiede, G. Wiebecke, “Rendering tomographic volume data: adequacy of methods for different modalities and organs,” in 3D Imaging in Medicine: Algorithms, Systems, Applications, K. H. Hoehne, H. Fuchs, S. M. Pizer, eds. (Springer-Verlag, Berlin, 1990), pp. 197–215.
[CrossRef]

Hu, X.

D. N. Levin, X. Hu, K. K. Tan, “Surface of the three-dimension MR images created with volume rendering,” Radiology 171, 277–280 (1989).
[PubMed]

Lantuejoul, C.

S. Beucher, C. Lantuejoul, “Use of watersheds in contour detection,” paper presented at International Workshop on Image Processing: Real Time Edge and Motion Detection/Estimation, CCETT/IRISA, Rennes, France, September 1979.

Levin, D. N.

D. N. Levin, X. Hu, K. K. Tan, “Surface of the three-dimension MR images created with volume rendering,” Radiology 171, 277–280 (1989).
[PubMed]

Lewine, R. J.

M. E. Brummer, R. M. Mersereau, R. L. Eisner, R. J. Lewine, “Automatic detection of brain contours in MRI data sets,” IEEE Trans. Medical Imaging 12(2), 153–166 (1993).
[CrossRef]

Lotufo, R.

J. Barrera, G. J. F. Banon, R. Lotufo, “Mathematical morphology toolbox for the Khoros system,” in Image Algebra and Morphological Image Processing V, E. R. Dougherty, P. D. Gader, M. Schmitt, eds., Proc. SPIE2300, 241–252 (1994).
[CrossRef]

Ma, Y.

R. Acharya, Y. Ma, “Segmentation algorithm for cranial magnetic resonance images,” in Medical Imaging VI: Image Processing, M. H. Loew, ed., Proc. SPIE1652, 50–61 (1992).

Mersereau, R. M.

M. E. Brummer, R. M. Mersereau, R. L. Eisner, R. J. Lewine, “Automatic detection of brain contours in MRI data sets,” IEEE Trans. Medical Imaging 12(2), 153–166 (1993).
[CrossRef]

Meyer, F.

F. Meyer, “Un algorithme optimal de partage des eaux,” in Proceedings 8e Congres AFCET, Reconnaissance des Formes et Intelligence Artificielle (Association Francaise des Sciences et Technologies de l’Information et des Systemes, 1992), Vol. 2, pp. 847–859.

S. Beucher, F. Meyer, “The morphological approach to segmentation: the watershed transformation,” in Mathematical Morphology in Image Processing, E. R. Dougherty, ed. (Marcel Dekker, New York, 1993), pp. 433–481.

Michael, N.

N. Michael, R. Arrathoon, “Optoelectronic pipeline architecture for morphological image processing,” Appl. Opt. 36(8), 1718–1725 (1997).

N. Michael, R. Arrathoon, “Optical PLA implementation for selected complex morphological algorithms,” in Hybrid Image and Signal Processing V, D. P. Casasent, A. G. Tescher, eds., Proc. SPIE2751, 186–198 (1996).
[CrossRef]

Mitchell, O. R.

F. Y. Shih, O. R. Mitchell, “Threshold decomposition of gray-scale morphology into binary morphology,” IEEE Trans. Pattern Anal. Mach. Intel. 11(1), 31–42 (1989).
[CrossRef]

Pommert, A.

K. H. Hoehne, M. Bomans, A. Pommert, M. Reimer, U. Tiede, G. Wiebecke, “Rendering tomographic volume data: adequacy of methods for different modalities and organs,” in 3D Imaging in Medicine: Algorithms, Systems, Applications, K. H. Hoehne, H. Fuchs, S. M. Pizer, eds. (Springer-Verlag, Berlin, 1990), pp. 197–215.
[CrossRef]

Preteux, F.

N. Rougon, F. Preteux, “Quantitative automated analysis of cornea endothelial cell images,” in Image Algebra and Morphological Image Processing V, E. R. Dougherty, P. D. Gader, M. Schmitt, eds., Proc. SPIE2300, 133–144 (1994).
[CrossRef]

Reimer, M.

K. H. Hoehne, M. Bomans, A. Pommert, M. Reimer, U. Tiede, G. Wiebecke, “Rendering tomographic volume data: adequacy of methods for different modalities and organs,” in 3D Imaging in Medicine: Algorithms, Systems, Applications, K. H. Hoehne, H. Fuchs, S. M. Pizer, eds. (Springer-Verlag, Berlin, 1990), pp. 197–215.
[CrossRef]

Riemer, M.

M. Bomans, K. H. Hoehne, U. Tiede, M. Riemer, “3-D segmentation of MR images of the head for 3-D display,” IEEE Trans. Medical Imaging 9, 177–183 (1990).
[CrossRef]

Rougon, N.

N. Rougon, F. Preteux, “Quantitative automated analysis of cornea endothelial cell images,” in Image Algebra and Morphological Image Processing V, E. R. Dougherty, P. D. Gader, M. Schmitt, eds., Proc. SPIE2300, 133–144 (1994).
[CrossRef]

Serra, J.

J. Serra, Image Analysis and Mathematical Morphology (Academic, San Diego, Calif., 1982).

Shapiro, L.

R. Haralick, L. Shapiro, “Survey: image segmentation techniques,” Comput. Vision Graphics Image Process. 29(1), 100–132 (1985).
[CrossRef]

Shih, F. Y.

F. Y. Shih, O. R. Mitchell, “Threshold decomposition of gray-scale morphology into binary morphology,” IEEE Trans. Pattern Anal. Mach. Intel. 11(1), 31–42 (1989).
[CrossRef]

Silbiger, M. S.

L. P. Clarke, R. P. Velthuizen, M. A. Camacho, J. J. Heine, M. Vaidyanathan, L. O. Hall, R. W. Thatcher, M. S. Silbiger, “MRI segmentation: methodsand applications,” Magn. Resonance Imaging 13(3), 343–368 (1995).
[CrossRef]

M. C. Clark, L. O. Hall, D. B. Goldgof, L. P. Clarke, R. P. Velthuizen, M. S. Silbiger, “MRI segmentation using fuzzy clustering techniques,” IEEE Eng. Medicine Biol. 13(5), 730–742 (1994).
[CrossRef]

Soille, P.

L. Vincent, P. Soille, “Watersheds in digital spaces: an efficient algorithm based on immersion simulations,” IEEE Trans. Pattern Anal. Mach. Intel. 13(6), 583–598 (1991).
[CrossRef]

Tan, K. K.

D. N. Levin, X. Hu, K. K. Tan, “Surface of the three-dimension MR images created with volume rendering,” Radiology 171, 277–280 (1989).
[PubMed]

Thatcher, R. W.

L. P. Clarke, R. P. Velthuizen, M. A. Camacho, J. J. Heine, M. Vaidyanathan, L. O. Hall, R. W. Thatcher, M. S. Silbiger, “MRI segmentation: methodsand applications,” Magn. Resonance Imaging 13(3), 343–368 (1995).
[CrossRef]

Tiede, U.

M. Bomans, K. H. Hoehne, U. Tiede, M. Riemer, “3-D segmentation of MR images of the head for 3-D display,” IEEE Trans. Medical Imaging 9, 177–183 (1990).
[CrossRef]

K. H. Hoehne, M. Bomans, A. Pommert, M. Reimer, U. Tiede, G. Wiebecke, “Rendering tomographic volume data: adequacy of methods for different modalities and organs,” in 3D Imaging in Medicine: Algorithms, Systems, Applications, K. H. Hoehne, H. Fuchs, S. M. Pizer, eds. (Springer-Verlag, Berlin, 1990), pp. 197–215.
[CrossRef]

Vaidyanathan, M.

L. P. Clarke, R. P. Velthuizen, M. A. Camacho, J. J. Heine, M. Vaidyanathan, L. O. Hall, R. W. Thatcher, M. S. Silbiger, “MRI segmentation: methodsand applications,” Magn. Resonance Imaging 13(3), 343–368 (1995).
[CrossRef]

Velthuizen, R. P.

L. P. Clarke, R. P. Velthuizen, M. A. Camacho, J. J. Heine, M. Vaidyanathan, L. O. Hall, R. W. Thatcher, M. S. Silbiger, “MRI segmentation: methodsand applications,” Magn. Resonance Imaging 13(3), 343–368 (1995).
[CrossRef]

M. C. Clark, L. O. Hall, D. B. Goldgof, L. P. Clarke, R. P. Velthuizen, M. S. Silbiger, “MRI segmentation using fuzzy clustering techniques,” IEEE Eng. Medicine Biol. 13(5), 730–742 (1994).
[CrossRef]

Viero, T.

B. P. Dobrin, T. Viero, M. Gabbouj, “Fast watershed algorithms: analysis and extensions,” in Nonlinear Image Processing V, E. R. Dougherty, J. T. Astola, H. G. Longbotham, eds., Proc. SPIE2180, 209–220 (1994).
[CrossRef]

Vincent, L.

L. Vincent, “Morphological grayscale reconstruction in image analysis: applications and efficient algorithms,” IEEE Trans. Image Process. 2(2), 176–201 (1993).
[CrossRef]

L. Vincent, P. Soille, “Watersheds in digital spaces: an efficient algorithm based on immersion simulations,” IEEE Trans. Pattern Anal. Mach. Intel. 13(6), 583–598 (1991).
[CrossRef]

L. Vincent, “Morphological image processing and network analysis of cornea endothelial cell images,” in Image Algebra and Morphological Image Processing III, P. D. Gader, E. R. Dougherty, J. C. Serra, eds., Proc. SPIE1769, 212–226 (1992).

Wiebecke, G.

K. H. Hoehne, M. Bomans, A. Pommert, M. Reimer, U. Tiede, G. Wiebecke, “Rendering tomographic volume data: adequacy of methods for different modalities and organs,” in 3D Imaging in Medicine: Algorithms, Systems, Applications, K. H. Hoehne, H. Fuchs, S. M. Pizer, eds. (Springer-Verlag, Berlin, 1990), pp. 197–215.
[CrossRef]

Appl. Opt. (1)

Comput. Vision Graphics Image Process (1)

R. Haralick, L. Shapiro, “Survey: image segmentation techniques,” Comput. Vision Graphics Image Process. 29(1), 100–132 (1985).
[CrossRef]

IEEE Eng. Medicine Biol. (1)

M. C. Clark, L. O. Hall, D. B. Goldgof, L. P. Clarke, R. P. Velthuizen, M. S. Silbiger, “MRI segmentation using fuzzy clustering techniques,” IEEE Eng. Medicine Biol. 13(5), 730–742 (1994).
[CrossRef]

IEEE Trans. Image Process (1)

L. Vincent, “Morphological grayscale reconstruction in image analysis: applications and efficient algorithms,” IEEE Trans. Image Process. 2(2), 176–201 (1993).
[CrossRef]

IEEE Trans. Medical Imaging (2)

M. E. Brummer, R. M. Mersereau, R. L. Eisner, R. J. Lewine, “Automatic detection of brain contours in MRI data sets,” IEEE Trans. Medical Imaging 12(2), 153–166 (1993).
[CrossRef]

M. Bomans, K. H. Hoehne, U. Tiede, M. Riemer, “3-D segmentation of MR images of the head for 3-D display,” IEEE Trans. Medical Imaging 9, 177–183 (1990).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intel. (2)

F. Y. Shih, O. R. Mitchell, “Threshold decomposition of gray-scale morphology into binary morphology,” IEEE Trans. Pattern Anal. Mach. Intel. 11(1), 31–42 (1989).
[CrossRef]

L. Vincent, P. Soille, “Watersheds in digital spaces: an efficient algorithm based on immersion simulations,” IEEE Trans. Pattern Anal. Mach. Intel. 13(6), 583–598 (1991).
[CrossRef]

Magn. Resonance Imaging (1)

L. P. Clarke, R. P. Velthuizen, M. A. Camacho, J. J. Heine, M. Vaidyanathan, L. O. Hall, R. W. Thatcher, M. S. Silbiger, “MRI segmentation: methodsand applications,” Magn. Resonance Imaging 13(3), 343–368 (1995).
[CrossRef]

Med. Phys. (1)

J. C. Bezdek, L. O. Hall, L. P. Clarke, “Review of MR image segmentation techniques using pattern recognition,” Med. Phys. 20(4), 1033–1048 (1993).

Radiology (1)

D. N. Levin, X. Hu, K. K. Tan, “Surface of the three-dimension MR images created with volume rendering,” Radiology 171, 277–280 (1989).
[PubMed]

Other (19)

K. H. Hoehne, M. Bomans, A. Pommert, M. Reimer, U. Tiede, G. Wiebecke, “Rendering tomographic volume data: adequacy of methods for different modalities and organs,” in 3D Imaging in Medicine: Algorithms, Systems, Applications, K. H. Hoehne, H. Fuchs, S. M. Pizer, eds. (Springer-Verlag, Berlin, 1990), pp. 197–215.
[CrossRef]

J. Serra, Image Analysis and Mathematical Morphology (Academic, San Diego, Calif., 1982).

E. R. Dougherty, An Introduction to Morphological Image Processing (SPIE Optical Engineering Press, Bellingham, Wash., 1992).

S. Beucher, M. Bilodeau, “Road segmentation and obstacle detection by a fast watershed transformation,” in Proceedings of the Intelligent Vehicles 1994 Symposium (Institute of Electricaland Electronics Engineers, New York, 1994), pp. 296–301.

L. Vincent, “Morphological image processing and network analysis of cornea endothelial cell images,” in Image Algebra and Morphological Image Processing III, P. D. Gader, E. R. Dougherty, J. C. Serra, eds., Proc. SPIE1769, 212–226 (1992).

N. Rougon, F. Preteux, “Quantitative automated analysis of cornea endothelial cell images,” in Image Algebra and Morphological Image Processing V, E. R. Dougherty, P. D. Gader, M. Schmitt, eds., Proc. SPIE2300, 133–144 (1994).
[CrossRef]

N. Michael, R. Arrathoon, “Optical PLA implementation for selected complex morphological algorithms,” in Hybrid Image and Signal Processing V, D. P. Casasent, A. G. Tescher, eds., Proc. SPIE2751, 186–198 (1996).
[CrossRef]

F. Meyer, “Un algorithme optimal de partage des eaux,” in Proceedings 8e Congres AFCET, Reconnaissance des Formes et Intelligence Artificielle (Association Francaise des Sciences et Technologies de l’Information et des Systemes, 1992), Vol. 2, pp. 847–859.

B. P. Dobrin, T. Viero, M. Gabbouj, “Fast watershed algorithms: analysis and extensions,” in Nonlinear Image Processing V, E. R. Dougherty, J. T. Astola, H. G. Longbotham, eds., Proc. SPIE2180, 209–220 (1994).
[CrossRef]

R. Arrathoon, “Historical perspectives: optical crossbars and optical computing,” in Digital Optical Computing, R. Arrathoon, ed., Proc. SPIE752, 2–11 (1987).
[CrossRef]

R. Arrathoon, “Fiber-optic programmable logic arrays,” in Optical Computing: Digital and Symbolic, R. Arrathoon, ed. (Marcel Dekker, New York, 1989), pp. 247–278.

S. Beucher, “Segmentation tools in mathematical morphology,” in Image Algebra and Morphological Image Processing, P. D. Gader, ed., Proc. SPIE1350, 70–84 (1990).

S. Beucher, “The watershed transformation applied to image segmentation,” in Proceedings of Scanning Microscopy (Scanning Microscopy International, Chicago, Ill., 1992), pp. 299–314.

S. Beucher, F. Meyer, “The morphological approach to segmentation: the watershed transformation,” in Mathematical Morphology in Image Processing, E. R. Dougherty, ed. (Marcel Dekker, New York, 1993), pp. 433–481.

S. Beucher, C. Lantuejoul, “Use of watersheds in contour detection,” paper presented at International Workshop on Image Processing: Real Time Edge and Motion Detection/Estimation, CCETT/IRISA, Rennes, France, September 1979.

W. Connor, P. Diaz, “Morphological segmentation and 3-D rendering of the brain in magnetic resonance imaging,” in Image Algebra and Morphological Image Processing II, P. D. Gader, E. R. Dougherty, eds., Proc. SPIE1568, 327–334 (1991).

KHOROS is an image processing system developed by Khoral, Inc., Albequerque, NM.

J. Barrera, G. J. F. Banon, R. Lotufo, “Mathematical morphology toolbox for the Khoros system,” in Image Algebra and Morphological Image Processing V, E. R. Dougherty, P. D. Gader, M. Schmitt, eds., Proc. SPIE2300, 241–252 (1994).
[CrossRef]

R. Acharya, Y. Ma, “Segmentation algorithm for cranial magnetic resonance images,” in Medical Imaging VI: Image Processing, M. H. Loew, ed., Proc. SPIE1652, 50–61 (1992).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (14)

Fig. 1
Fig. 1

Illustration of the geodesic influence zones.

Fig. 2
Fig. 2

Optical fiber connection pattern for the dilation operation.

Fig. 3
Fig. 3

Pixel arrangement for determination of SKIZ.

Fig. 4
Fig. 4

PLA implementation for determination of SKIZ pixels in a four-connected influence zones algorithm.

Fig. 5
Fig. 5

Flow chart of the IZONE–SKIZ algorithm.

Fig. 6
Fig. 6

Flow chart of the second phase of the watershed algorithm.

Fig. 7
Fig. 7

Determination of threshold levels by use of histograms: (a)–(c) three selected slices, (d)–(f) region of interest containing the brain in each slice and (g)–(i) corresponding histograms, and (j) overall histogram.

Fig. 8
Fig. 8

Marker selection for slice A from data set 1, where X refers to types of images described in text and M refers to the inside or outside marker image.

Fig. 9
Fig. 9

The watershed analysis of slice A from data set 1.

Fig. 10
Fig. 10

Segmentation of slice B from data set 1.

Fig. 11
Fig. 11

Segmentation of slice A from data set 2.

Fig. 12
Fig. 12

Segmentation of slice B from data set 2.

Fig. 13
Fig. 13

Segmentation of slice A from data set 3.

Fig. 14
Fig. 14

Segmentation of slice B from data set 3.

Tables (1)

Tables Icon

Table 1 Simulation Results for Segmentation of Slice A from Data Set 1

Equations (31)

Equations on this page are rendered with MathJax. Learn more.

DA, B=c|c=a+b for some a  A, b  B.
EA, B=c|c+b  A for every b  B.
OA, B=DEA, B, B.
CA, B=EDA, B, B.
DXY, B=DY, BX.
EXY, B=EY, BX.
n-conditional erosion, EXn=EXEX,
n-conditional dilation, DXn=DXDX.
RXY=limnDXnY.
DRXY=limnEXnY.
IZONEXYi=x  XdXx, Yifinite,ji, dXx, Yi<dXx, Yj.
SKIZXY=RXY-IZONEXY.
ZhI=p|iph.
mhI=ZhI-RZhI(Zh-1I, h=hmin:hmax,
mI=hminhmax mhI.
CBhI=IZONEZhImICBh-1I, h=hmin:hmax.
WSI=CBhmaxcI.
SKIZXY=xX, ji, dXx, Yi=dXx, Yj.
m=log2C+1,
Xp=1, Y20, Y70, Y2Y7; Xp=1, Y40, Y50, Y4Y5; Xp=1, Y20, Y40, Y2Y4; Xp=1, Y20, Y50, Y2Y5; Xp=1, Y50, Y70, Y5Y7;Xp=1, Y40, Y70, Y4Y7.
xij=Yi0Yj0+Yi1Yj1++Yim-1Yjm-1,
Xp=1, Y20, Y70, Y2Y7; Xp=1, Y40, Y50, Y4Y5; Xp=1, Y10, Y80, Y1Y8; Xp=1, Y30, Y60, Y3Y6.
X2=EX1, SE1.
X3=OX2, SE2,
Minside=RX2X3.
X5=CX4, SE3,
X6=EX5, SE4.
X7=OX6, SE5,
Moutside=RX6X7.
M=Minside+Moutside.
G=DX, SE-EX, SE.

Metrics