Abstract

A more powerful tool for binary image processing, i.e., logic-operated mathematical morphology (LOMM), is proposed. With LOMM the image and the structuring element (SE) are treated as binary logical variables, and the multiply between the image and the SE in correlation is replaced with 16 logical operations. A total of 12 LOMM operations are obtained. The optical implementation of LOMM is described. The application of LOMM and its experimental results are also presented.

© 1999 Optical Society of America

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References

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    [CrossRef]
  4. K. S. Huang, B. K. Jenkins, A. A. Sawchuk, “Binary image algebra and optical cellular logic processor design,” Comput. Vision Graph. Image Process. 45, 295–345 (1989).
    [CrossRef]
  5. K. S. Huang, A. A. Sawchuk, B. K. Jenkins, P. Chavel, J.-M. Wang, “Digital optical cellular image processor (DOCIP): experimental implementation,” Appl. Opt. 32, 166–173 (1993).
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  9. L. Liu, “Morphological hit-or-miss transform for binary and gray-tone image processing and its optical implementation,” Opt. Eng. 33, 3447–3454 (1994).
    [CrossRef]
  10. D. Casasent, R. Schaefer, R. Sturgill, “Optical hit–miss morphological transform,” Appl. Opt. 31, 6255–6263 (1992).
    [CrossRef] [PubMed]
  11. L. Liu, “Optoelectronic implementation of mathematical morphology,” Opt. Lett. 14, 482–484 (1989).
    [CrossRef] [PubMed]

1994

L. Liu, “Morphological hit-or-miss transform for binary and gray-tone image processing and its optical implementation,” Opt. Eng. 33, 3447–3454 (1994).
[CrossRef]

L. Liu, Z. Zhang, X. Zhang, “One-operation image algebra and optoelectronic cellular two-layer logic array,” J. Opt. Soc. Am. A 11, 1789–1797 (1994).
[CrossRef]

1993

1992

1990

P. Maragos, R. W. Schafer, “Morphological systems for multidimensional signal processing,” Proc. IEEE 78, 690–710 (1990).
[CrossRef]

1989

K. S. Huang, B. K. Jenkins, A. A. Sawchuk, “Binary image algebra and optical cellular logic processor design,” Comput. Vision Graph. Image Process. 45, 295–345 (1989).
[CrossRef]

L. Liu, “Optoelectronic implementation of mathematical morphology,” Opt. Lett. 14, 482–484 (1989).
[CrossRef] [PubMed]

1986

Casasent, D.

Chavel, P.

Fukui, M.

Huang, K. S.

K. S. Huang, A. A. Sawchuk, B. K. Jenkins, P. Chavel, J.-M. Wang, “Digital optical cellular image processor (DOCIP): experimental implementation,” Appl. Opt. 32, 166–173 (1993).
[CrossRef] [PubMed]

K. S. Huang, B. K. Jenkins, A. A. Sawchuk, “Binary image algebra and optical cellular logic processor design,” Comput. Vision Graph. Image Process. 45, 295–345 (1989).
[CrossRef]

Jenkins, B. K.

K. S. Huang, A. A. Sawchuk, B. K. Jenkins, P. Chavel, J.-M. Wang, “Digital optical cellular image processor (DOCIP): experimental implementation,” Appl. Opt. 32, 166–173 (1993).
[CrossRef] [PubMed]

K. S. Huang, B. K. Jenkins, A. A. Sawchuk, “Binary image algebra and optical cellular logic processor design,” Comput. Vision Graph. Image Process. 45, 295–345 (1989).
[CrossRef]

Kitayama, K.

Liu, L.

Maragos, P.

P. Maragos, R. W. Schafer, “Morphological systems for multidimensional signal processing,” Proc. IEEE 78, 690–710 (1990).
[CrossRef]

Matheron, G.

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

Sawchuk, A. A.

K. S. Huang, A. A. Sawchuk, B. K. Jenkins, P. Chavel, J.-M. Wang, “Digital optical cellular image processor (DOCIP): experimental implementation,” Appl. Opt. 32, 166–173 (1993).
[CrossRef] [PubMed]

K. S. Huang, B. K. Jenkins, A. A. Sawchuk, “Binary image algebra and optical cellular logic processor design,” Comput. Vision Graph. Image Process. 45, 295–345 (1989).
[CrossRef]

Schaefer, R.

Schafer, R. W.

P. Maragos, R. W. Schafer, “Morphological systems for multidimensional signal processing,” Proc. IEEE 78, 690–710 (1990).
[CrossRef]

Serra, J.

J. Serra, Image Analysis and Mathematical Morphology (Academic, New York, 1988).

Sturgill, R.

Wang, J.-M.

Yatagai, T.

Zhang, X.

Zhang, Z.

Appl. Opt.

Comput. Vision Graph. Image Process.

K. S. Huang, B. K. Jenkins, A. A. Sawchuk, “Binary image algebra and optical cellular logic processor design,” Comput. Vision Graph. Image Process. 45, 295–345 (1989).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

L. Liu, “Morphological hit-or-miss transform for binary and gray-tone image processing and its optical implementation,” Opt. Eng. 33, 3447–3454 (1994).
[CrossRef]

Opt. Lett.

Proc. IEEE

P. Maragos, R. W. Schafer, “Morphological systems for multidimensional signal processing,” Proc. IEEE 78, 690–710 (1990).
[CrossRef]

Other

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

J. Serra, Image Analysis and Mathematical Morphology (Academic, New York, 1988).

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Figures (11)

Fig. 1
Fig. 1

Arrangement of three-plane two-lens incoherent optical correlator for LOMM.

Fig. 2
Fig. 2

Coding principles of the square cells.

Fig. 3
Fig. 3

Cell structures of decoding masks for 16 logic operations.

Fig. 4
Fig. 4

Geometrical configuration of the optical setup.

Fig. 5
Fig. 5

(a) Input binary image and (b) SE in the experiment to realize dilation operation.

Fig. 6
Fig. 6

(a) Encoded image and (b) encoded SE in the experiment to realize dilation operation.

Fig. 7
Fig. 7

(a) Optical correlation pattern and (b) experimental result of dilation.

Fig. 8
Fig. 8

(a) Input binary image of the face, (b) SE of the mouth used for mouth recognition in the pattern-recognition experiment, (c) SE of the left eye (right-hand side) used for eye recognition.

Fig. 9
Fig. 9

(a) Encoded image of the face, (b) encoded SE of the mouth in the pattern-recognition experiment, (c) encoded SE of the eye.

Fig. 10
Fig. 10

(a) Correlation pattern between the face and the left eye (right-hand side), (b) experimental result of the HMT in the left-eye-recognition experiment.

Fig. 11
Fig. 11

(a) Correlation pattern between the face and the mouth, (b) experimental result of the HMT in the mouth-recognition experiment.

Tables (2)

Tables Icon

Table 1 Sixteen Logical Operations of Two Binary Variables

Tables Icon

Table 2 Basic Set of LOMM Operations

Equations (10)

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Z=XΘS=z:S+zX,
Z=XS={z:Sˇ+zXΦ},
XS=X * S|T=1=i, jk,l xk, l×si-k, j-11.
XΘS=XS|T=k1=i, jk,l xk, l×sk-i, l-jk1,
Ψf0, 1, * , x, s=i, jk,l f0xk, lsi-k, j-l1=i, jk,l 01=Φ,
Ψf4, k1, , x, s=i, jk,lxk, l¯sk-i, l-jk1=i, j|xk, l¯=1, sk-i, l-j=1=i, j|k, lX¯, k-i, l-jS1=i, j|i+k, j+lX¯, k, lS1=X¯ΘS1.
Ψf9, k1+k2, , x, s=i, jk,l xk, lsk-i, l-j+xk, lsk-i, l-j¯k1+k2=i, j|xk, lsk-i, l-j+xk, lsk-i, l-j¯=1=i, j|k, lX, k-i, l-jS1i, j|i+k, j+lX¯, k, lS2=XΘS1X¯ΘS2.
d/Din=f1/L,
I2mDout, nDout=I1md, ndmn×fxm-m, n-n, sm, n,
Dout/Din=f2/L.

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