Abstract

Morphological transformations are applied to industrial inspection problems. A real time optical architecture to implement morphological transformations such as erosion, opening, closing, and skeletonization is described and analyzed. The first real time optical laboratory results of erosion and opening are presented for locating string in tobacco.

© 1989 Optical Society of America

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References

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  1. G. Matheron, Random Sets and Integral Geometry (Wiley, New York, 1975).
  2. J. Serra, Image Analysis and Mathematical Morphology (Academic, New York, 1982).
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    [CrossRef]
  4. P. Maragos, “Tutorial on Advances in Morphological Image Processing and Analysis,” Opt. Eng. 26, 623–632 (1987).
    [CrossRef]
  5. D. Casasent, E. Botha, “Optical Symbolic Substitution for Morphological Transformations,” Appl. Opt. 27, 3806–3810 (1988).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  8. E. Botha, D. P. Casasent, E. Barnard, “Optical Symbolic Substitution Using Multichannel Correlators,” Appl. Opt. 27, 817–818 (1988).
    [CrossRef] [PubMed]
  9. A. B. Vander Lugt, “Signal Detection by Complex Spatial Filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
    [CrossRef]
  10. F. Mok, J. Diep, H. Liu, D. Psaltis, “Real-Time Computer Generated Hologram by Means of a Liquid Crystal TV Spatial Light Modulator,” Opt. Lett. 11, 748–750 (1986).
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    [CrossRef] [PubMed]
  12. D. Casasent, S. Xia, “Phase Correction of Light Modulators,” Opt. Lett. 11, 398–400 (1986).
    [CrossRef] [PubMed]
  13. D. Casasent, E. Botha, “Multi-functional Optical Logic, Numerical and Pattern Recognition Processor,” in Proceedings, AIAA Computers in Aerospace VI Conference (AIAA, Oct. 1987), pp. 213–218.
  14. D. Casasent, A. Furman, “Determining Optimal Matched Filter Parameters,” Appl. Opt. 15, 1690–1691 (1976).
    [CrossRef] [PubMed]
  15. D. Casasent, J. Richards, “Optical Hough and Fourier Processors for Product Inspection,” Opt. Eng. 27, 258–265 (1988).
    [CrossRef]
  16. C. Dyer, “Gauge Inspection Using Hough Transforms,” IEEE Trans. Pattern Anal. Machine Intell. PAMI-5, 621–623 (1983).
    [CrossRef]
  17. D. Casasent, J. Richards, “Industrial Use of a Real-Time Optical Inspection System,” Appl. Opt. 28, 4653–4659 (1988).
    [CrossRef]

1989

1988

1987

1986

1983

C. Dyer, “Gauge Inspection Using Hough Transforms,” IEEE Trans. Pattern Anal. Machine Intell. PAMI-5, 621–623 (1983).
[CrossRef]

S. R. Sternberg, “Biomedical Image Processing,” IEEE Comput. 16, 22–34 (1983).
[CrossRef]

1976

1964

A. B. Vander Lugt, “Signal Detection by Complex Spatial Filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[CrossRef]

Barnard, E.

Botha, E.

Casasent, D.

D. Casasent, J. Richards, “Optical Hough and Fourier Processors for Product Inspection,” Opt. Eng. 27, 258–265 (1988).
[CrossRef]

D. Casasent, J. Richards, “Industrial Use of a Real-Time Optical Inspection System,” Appl. Opt. 28, 4653–4659 (1988).
[CrossRef]

D. Casasent, E. Botha, “Optical Symbolic Substitution for Morphological Transformations,” Appl. Opt. 27, 3806–3810 (1988).
[CrossRef] [PubMed]

D. Casasent, S. Xia, “Phase Correction of Light Modulators,” Opt. Lett. 11, 398–400 (1986).
[CrossRef] [PubMed]

D. Casasent, A. Furman, “Determining Optimal Matched Filter Parameters,” Appl. Opt. 15, 1690–1691 (1976).
[CrossRef] [PubMed]

D. Casasent, E. Botha, “Multi-functional Optical Logic, Numerical and Pattern Recognition Processor,” in Proceedings, AIAA Computers in Aerospace VI Conference (AIAA, Oct. 1987), pp. 213–218.

Casasent, D. P.

Diep, J.

Dyer, C.

C. Dyer, “Gauge Inspection Using Hough Transforms,” IEEE Trans. Pattern Anal. Machine Intell. PAMI-5, 621–623 (1983).
[CrossRef]

Furman, A.

Goodman, S. D.

Gregory, D. A.

Huang, K. S.

Jenkins, B. K.

Jutamulia, S.

Lin, T. W.

Liu, H.

Maragos, P.

P. Maragos, “Tutorial on Advances in Morphological Image Processing and Analysis,” Opt. Eng. 26, 623–632 (1987).
[CrossRef]

Matheron, G.

G. Matheron, Random Sets and Integral Geometry (Wiley, New York, 1975).

Mok, F.

Psaltis, D.

Rhodes, W. T.

Richards, J.

D. Casasent, J. Richards, “Optical Hough and Fourier Processors for Product Inspection,” Opt. Eng. 27, 258–265 (1988).
[CrossRef]

D. Casasent, J. Richards, “Industrial Use of a Real-Time Optical Inspection System,” Appl. Opt. 28, 4653–4659 (1988).
[CrossRef]

Sawchuk, A. A.

Serra, J.

J. Serra, Image Analysis and Mathematical Morphology (Academic, New York, 1982).

Sternberg, S. R.

S. R. Sternberg, “Biomedical Image Processing,” IEEE Comput. 16, 22–34 (1983).
[CrossRef]

Vander Lugt, A. B.

A. B. Vander Lugt, “Signal Detection by Complex Spatial Filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[CrossRef]

Xia, S.

Yu, F. T. S.

Appl. Opt.

IEEE Comput.

S. R. Sternberg, “Biomedical Image Processing,” IEEE Comput. 16, 22–34 (1983).
[CrossRef]

IEEE Trans. Inf. Theory

A. B. Vander Lugt, “Signal Detection by Complex Spatial Filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[CrossRef]

IEEE Trans. Pattern Anal. Machine Intell.

C. Dyer, “Gauge Inspection Using Hough Transforms,” IEEE Trans. Pattern Anal. Machine Intell. PAMI-5, 621–623 (1983).
[CrossRef]

Opt. Eng.

D. Casasent, J. Richards, “Optical Hough and Fourier Processors for Product Inspection,” Opt. Eng. 27, 258–265 (1988).
[CrossRef]

P. Maragos, “Tutorial on Advances in Morphological Image Processing and Analysis,” Opt. Eng. 26, 623–632 (1987).
[CrossRef]

Opt. Lett.

Other

D. Casasent, E. Botha, “Multi-functional Optical Logic, Numerical and Pattern Recognition Processor,” in Proceedings, AIAA Computers in Aerospace VI Conference (AIAA, Oct. 1987), pp. 213–218.

G. Matheron, Random Sets and Integral Geometry (Wiley, New York, 1975).

J. Serra, Image Analysis and Mathematical Morphology (Academic, New York, 1982).

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Figures (10)

Fig. 1
Fig. 1

Images of (a) chopped tobacco with no string present, (b) partially covered string present in tobacco, and (c) uncovered string present.

Fig. 2
Fig. 2

Thresholded images of (a) chopped tobacco and string in tobacco background (b) and (c).

Fig. 3
Fig. 3

Simulation results of eroding (first step in opening) of (a) Fig. 2(a), (b) Fig. 2(b), and (c) Fig. 2(c).

Fig. 4
Fig. 4

Simulation results of the dilation of (a) Fig. 3(a), (b) Fig. 3(b), and (c) Fig. 3(c). This is equivalent to the opening of the images in Fig. 2.

Fig. 5
Fig. 5

Simulation results of the skeletons of (a) Fig. 2(a), (b) Fig. 2(b), and (c) Fig. 2(c).

Fig. 6
Fig. 6

Schematic of the experimental layout of the optical morphological architecture.

Fig. 7
Fig. 7

Optical morphological processor.

Fig. 8
Fig. 8

Optical outputs of the correlations of (a) Fig. 2(a), (b) Fig. 2(b), (c) Fig. 2(c) with the structuring element (before thresholding).

Fig. 9
Fig. 9

Optical morphological opening of (a) Fig. 2(a), (b) Fig. 2(b), (c) Fig. 2(c).

Tables (3)

Tables Icon

Table I Number of Pixels In Total Image and in Noise and the Corresponding SNRs In Decibels

Tables Icon

Table II Epson Color LCTV and Fourier Transform Data

Tables Icon

Table III Hough Transform Data of Original, Opened, and Skeletonized Images

Equations (10)

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

X B = { a B a X } ,
X B = { a B a X ϕ } ,
X B = ( X B ) B
X B = ( X B ) B .
S K ( X ) = 0 n N S n ( X ) ,
S n ( X ) = ( X n B ) ( X n B ) B ,
n B = B B B ( n times ) .
f s ( x , y ) = rect ( x a x , y a y ) { f ( x , y ) [ rect ( x d x , y d y ) * comb ( x s x , y s y ) ] } ,
t H I H = [ r 1 exp ( j 2 π α x ) + r 0 λ f L F s ( x / λ f L , y / λ f L ) ] 2 ,
[ F * * comb ( s x u , s y υ ) ] * sinc ( d x u , d y υ ) [ G * comb ( s x u , s y υ ) ] sinc ( d x u , d y υ ) ,

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