Abstract

Edge detection schemes based on Prewitt, Sobel, and Roberts operators are realized using optical symbolic substitution. The corresponding optical systems are compared in terms of hardware and performance.

© 1989 Optical Society of America

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References

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  1. K.-H. Brenner, A. Huang, N. Streibl, “Digital Optical Computing with Symbolic Substitution,” Appl. Opt. 25, 3054–3060 (1986).
    [CrossRef] [PubMed]
  2. E. L. Johnson, M. A. Karim, Digital Design: A Pragmatic Approach (PWS Publishers, Boston, 1987).
  3. M. M. Mirsalehi, T. K. Gaylord, “Truth-Table Look-Up Optical Parallel Processing Using an Optical Content-Address-able Memory,” Appl. Opt. 25,2277–2283 (1986).
    [CrossRef] [PubMed]
  4. A. K. Cherri, M. A. Karim, “Median Filtering Using Optical Symbolic Substitution,” under review, Appl. Opt. (1989).
    [PubMed]
  5. G. Eichmann, J. Zhu, Y. Li, “Optical Parallel Image Skeletonization Using Content-Addressable Memory-Based Symbolic Substitution,” Appl. Opt. 27,2905–2911 (1988).
    [CrossRef] [PubMed]
  6. A. K. Cherri, M. A. Karim, “Modified-Signed Digit Arithmetic Using an Efficient Symbolic Substitution,” Appl. Opt. 27, 3824–3827 (1988).
    [CrossRef] [PubMed]
  7. A. K. Cherri, M. A. Karim, “Simplified Arithmetic for Optical Symbolic Substitution,” Microwave Opt. Technol. Lett. 1, 310–311 (1988).
    [CrossRef]
  8. A. Rosenfield, A. C. Kak, Digital Picture Processing, Vol. 2 (Academic, New York, 1982).
  9. E. R. Dougherty, C. R. Giardina, Matrix Structured Image Processing (Prentice-Hall, Englewood Cliffs, NJ, 1987).

1989 (1)

A. K. Cherri, M. A. Karim, “Median Filtering Using Optical Symbolic Substitution,” under review, Appl. Opt. (1989).
[PubMed]

1988 (3)

1986 (2)

Brenner, K.-H.

Cherri, A. K.

A. K. Cherri, M. A. Karim, “Median Filtering Using Optical Symbolic Substitution,” under review, Appl. Opt. (1989).
[PubMed]

A. K. Cherri, M. A. Karim, “Simplified Arithmetic for Optical Symbolic Substitution,” Microwave Opt. Technol. Lett. 1, 310–311 (1988).
[CrossRef]

A. K. Cherri, M. A. Karim, “Modified-Signed Digit Arithmetic Using an Efficient Symbolic Substitution,” Appl. Opt. 27, 3824–3827 (1988).
[CrossRef] [PubMed]

Dougherty, E. R.

E. R. Dougherty, C. R. Giardina, Matrix Structured Image Processing (Prentice-Hall, Englewood Cliffs, NJ, 1987).

Eichmann, G.

Gaylord, T. K.

Giardina, C. R.

E. R. Dougherty, C. R. Giardina, Matrix Structured Image Processing (Prentice-Hall, Englewood Cliffs, NJ, 1987).

Huang, A.

Johnson, E. L.

E. L. Johnson, M. A. Karim, Digital Design: A Pragmatic Approach (PWS Publishers, Boston, 1987).

Kak, A. C.

A. Rosenfield, A. C. Kak, Digital Picture Processing, Vol. 2 (Academic, New York, 1982).

Karim, M. A.

A. K. Cherri, M. A. Karim, “Median Filtering Using Optical Symbolic Substitution,” under review, Appl. Opt. (1989).
[PubMed]

A. K. Cherri, M. A. Karim, “Simplified Arithmetic for Optical Symbolic Substitution,” Microwave Opt. Technol. Lett. 1, 310–311 (1988).
[CrossRef]

A. K. Cherri, M. A. Karim, “Modified-Signed Digit Arithmetic Using an Efficient Symbolic Substitution,” Appl. Opt. 27, 3824–3827 (1988).
[CrossRef] [PubMed]

E. L. Johnson, M. A. Karim, Digital Design: A Pragmatic Approach (PWS Publishers, Boston, 1987).

Li, Y.

Mirsalehi, M. M.

Rosenfield, A.

A. Rosenfield, A. C. Kak, Digital Picture Processing, Vol. 2 (Academic, New York, 1982).

Streibl, N.

Zhu, J.

Appl. Opt. (5)

Microwave Opt. Technol. Lett. (1)

A. K. Cherri, M. A. Karim, “Simplified Arithmetic for Optical Symbolic Substitution,” Microwave Opt. Technol. Lett. 1, 310–311 (1988).
[CrossRef]

Other (3)

A. Rosenfield, A. C. Kak, Digital Picture Processing, Vol. 2 (Academic, New York, 1982).

E. R. Dougherty, C. R. Giardina, Matrix Structured Image Processing (Prentice-Hall, Englewood Cliffs, NJ, 1987).

E. L. Johnson, M. A. Karim, Digital Design: A Pragmatic Approach (PWS Publishers, Boston, 1987).

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Figures (7)

Fig. 1
Fig. 1

Reduced minterms for Prewitt based edge detection for a threshold value of 3 and Sobel based edge detection for a threshold value of 4.

Fig. 2
Fig. 2

Reduced minterms for Roberts mask based edge detector by (a) grouping 1s and (b) 0s.

Fig. 3
Fig. 3

Optical edge detection system: (a) spatial encoding of 1, 0, and d; (b) recording and processing unit; (c) example of a recording reduced minterm.

Fig. 4
Fig. 4

A 64 × 64 binary image input.

Fig. 5
Fig. 5

Processed image using Prewitt operators with a threshold value of (a) 1, (b) 2, and (c) 3.

Fig. 6
Fig. 6

Processed images using Sobel operators with a threshold value of (a) 1, (b) 2, (c) 3, and (d) 4.

Fig. 7
Fig. 7

Processed image using Roberts operators.

Tables (4)

Tables Icon

Table I Partial List of Symbolic Substitution Rules for Edge Detection Using Prewitt Operators for Threshold Values of 1, 2, and 3

Tables Icon

Table II Number of Reduced Minterms for Prewitt and Sobel Operators

Tables Icon

Table III Partial List of Symbolic Substitution Rules for Edge Detection Using Sobel Operators for Threshold Values of 1, 2, 3, and 4

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Table IV Symbolic Substitution Rules for Edge Detection Using Roberts Operators

Equations (10)

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

P 1 = | 1 1 1 0 0 0 1 1 1 | * X ;
P 2 = | 1 0 1 1 0 1 1 0 1 | * X ;
P 3 = | 1 1 0 1 0 1 0 1 1 | * X ;
P 4 = | 0 1 1 1 0 1 1 1 0 | * X ;
i , j = 1 3 p 1 i j x i j ,
S 1 = | 1 2 1 0 0 0 1 2 1 | * X ;
S 2 = | 1 0 1 2 0 2 1 0 1 | * X ;
S 3 = | 2 1 0 1 0 1 0 1 2 | * X ;
S 4 = | 0 1 2 1 0 1 2 1 0 | * X ;
R 1 = | 1 0 0 1 | R 2 = | 0 1 1 0 |

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