Abstract

We present a novel scheme of visible gray-image morphology with the visual-area-coding technique (VACT). The VACT is a technique of digitized analog–optical computing in which data are converted into visible coded patterns and processed with the visible form. Because the achievable operations in the VACT are identical to those of mathematical morphology, mathematical morphology is adapted to gray-image morphology with the VACT. Computer simulation and optical experiments of the several operations in mathematical morphology verify the correctness of the proposed technique. The processing capacity of the proposed method is estimated in terms of the space–bandwidth product.

© 1996 Optical Society of America

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1995 (2)

1993 (2)

1992 (1)

1991 (2)

B. D. Duncan, T.-C. Poon, R. J. Pieper, “Real-time nonlinear image processing using an active optical scanning technique,” Opt. Laser Technol. 23, 19–24 (1991).

H. Tanigawa, T. Ichibashi, A. Nagata, “Hologram record ing on multicomponent monomer materials,” Jpn. J. Opt. 20, 227–231 (1991).

1989 (5)

1988 (1)

J. M. Hereford, W. T. Rhodes, “Nonlinear optical image filtering by time sequential threshold decomposition,” Opt. Eng. 27, 274–279 (1988).

1987 (3)

P. Maragos, “Tutorial on advantages in morphological image processing and analysis,” Opt. Eng. 26, 623–632 (1987).

E. Ochoa, J. P. Allebach, D. W. Sweeney, “Optical median filtering using threshold decomposition,” Appl. Opt. 26, 253–260 (1987).

P. Maragos, R. W. Schafer, “Morphological filters—Part II: their relations to median, order-statistic, and stack filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 1170–1184 (1987).

1986 (1)

1985 (1)

F. Ono, “Binary rendition of continuous-tone pictures using binary patterns having similar Fourier spectra,” Trans. Inst. Electron. Commun. Eng. Jpn. Part D J68D, 686–693 (1985).

1983 (1)

Allebach, J. P.

E. Ochoa, J. P. Allebach, D. W. Sweeney, “Optical median filtering using threshold decomposition,” Appl. Opt. 26, 253–260 (1987).

Awwal, A. A. S.

A. K. Cherri, A. A. S. Awwal, M. A. Karim, “Morphological transformation using optical symbolic substitution,” Micro wave Opt. Technol. Lett. 2, 282–285 (1989).

Brenner, K.-H.

Cambon, P.

Cherri, A. K.

A. K. Cherri, A. A. S. Awwal, M. A. Karim, “Morphological transformation using optical symbolic substitution,” Micro wave Opt. Technol. Lett. 2, 282–285 (1989).

de la Tocknaye Bougrenet, J.-L.

Duncan, B. D.

B. D. Duncan, T.-C. Poon, R. J. Pieper, “Real-time nonlinear image processing using an active optical scanning technique,” Opt. Laser Technol. 23, 19–24 (1991).

Eichmann, G.

Ferreira, C.

Fukui, M.

Gaecia, J.

Garcia, J.

Hereford, J. M.

J. M. Hereford, W. T. Rhodes, “Nonlinear optical image filtering by time sequential threshold decomposition,” Opt. Eng. 27, 274–279 (1988).

Huang, A.

Huang, K.-S.

Ichibashi, T.

H. Tanigawa, T. Ichibashi, A. Nagata, “Hologram record ing on multicomponent monomer materials,” Jpn. J. Opt. 20, 227–231 (1991).

Ichioka, Y.

Jenkins, B. K.

Karim, M. A.

A. K. Cherri, A. A. S. Awwal, M. A. Karim, “Morphological transformation using optical symbolic substitution,” Micro wave Opt. Technol. Lett. 2, 282–285 (1989).

Kim, D. H.

Kitayama, K.

Konishi, T.

Kostrzewski, A.

Li, Y.

Liu, L.

Z. Zhu, L. Liu, “Optical cellular continuous logic array for gray-scale image processing,” Appl. Opt. 32, 3676–3683 (1993).

L. Liu, “Optical implementation of parallel fuzzy logic,” Opt. Commun. 73, 183–187 (1989).

Maragos, P.

P. Maragos, R. W. Schafer, “Morphological filters—Part II: their relations to median, order-statistic, and stack filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 1170–1184 (1987).

P. Maragos, “Tutorial on advantages in morphological image processing and analysis,” Opt. Eng. 26, 623–632 (1987).

Nagata, A.

H. Tanigawa, T. Ichibashi, A. Nagata, “Hologram record ing on multicomponent monomer materials,” Jpn. J. Opt. 20, 227–231 (1991).

Ochoa, E.

E. Ochoa, J. P. Allebach, D. W. Sweeney, “Optical median filtering using threshold decomposition,” Appl. Opt. 26, 253–260 (1987).

Ono, F.

F. Ono, “Binary rendition of continuous-tone pictures using binary patterns having similar Fourier spectra,” Trans. Inst. Electron. Commun. Eng. Jpn. Part D J68D, 686–693 (1985).

Pieper, R. J.

B. D. Duncan, T.-C. Poon, R. J. Pieper, “Real-time nonlinear image processing using an active optical scanning technique,” Opt. Laser Technol. 23, 19–24 (1991).

Poon, T.-C.

B. D. Duncan, T.-C. Poon, R. J. Pieper, “Real-time nonlinear image processing using an active optical scanning technique,” Opt. Laser Technol. 23, 19–24 (1991).

Rhodes, W. T.

J. M. Hereford, W. T. Rhodes, “Nonlinear optical image filtering by time sequential threshold decomposition,” Opt. Eng. 27, 274–279 (1988).

Sawchuk, A. A.

Schafer, R. W.

P. Maragos, R. W. Schafer, “Morphological filters—Part II: their relations to median, order-statistic, and stack filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 1170–1184 (1987).

Streibl, N.

Sweeney, D. W.

E. Ochoa, J. P. Allebach, D. W. Sweeney, “Optical median filtering using threshold decomposition,” Appl. Opt. 26, 253–260 (1987).

Szoplik, T.

Tanida, J.

Tanigawa, H.

H. Tanigawa, T. Ichibashi, A. Nagata, “Hologram record ing on multicomponent monomer materials,” Jpn. J. Opt. 20, 227–231 (1991).

Wang, X. H.

Zhu, Z.

Appl. Opt. (8)

IEEE Trans. Acoust. Speech Signal Process. (1)

P. Maragos, R. W. Schafer, “Morphological filters—Part II: their relations to median, order-statistic, and stack filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 1170–1184 (1987).

J. Opt. Soc. Am. (1)

Jpn. J. Opt. (1)

H. Tanigawa, T. Ichibashi, A. Nagata, “Hologram record ing on multicomponent monomer materials,” Jpn. J. Opt. 20, 227–231 (1991).

Micro wave Opt. Technol. Lett. (1)

A. K. Cherri, A. A. S. Awwal, M. A. Karim, “Morphological transformation using optical symbolic substitution,” Micro wave Opt. Technol. Lett. 2, 282–285 (1989).

Opt. Commun. (1)

L. Liu, “Optical implementation of parallel fuzzy logic,” Opt. Commun. 73, 183–187 (1989).

Opt. Eng. (2)

P. Maragos, “Tutorial on advantages in morphological image processing and analysis,” Opt. Eng. 26, 623–632 (1987).

J. M. Hereford, W. T. Rhodes, “Nonlinear optical image filtering by time sequential threshold decomposition,” Opt. Eng. 27, 274–279 (1988).

Opt. Laser Technol. (1)

B. D. Duncan, T.-C. Poon, R. J. Pieper, “Real-time nonlinear image processing using an active optical scanning technique,” Opt. Laser Technol. 23, 19–24 (1991).

Opt. Lett. (2)

Trans. Inst. Electron. Commun. Eng. Jpn. Part D (1)

F. Ono, “Binary rendition of continuous-tone pictures using binary patterns having similar Fourier spectra,” Trans. Inst. Electron. Commun. Eng. Jpn. Part D J68D, 686–693 (1985).

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Figures (12)

Fig. 1
Fig. 1

Visual area codes for 17 levels.

Fig. 2
Fig. 2

Processing procedure for optical parallel implementation of maximum, minimum, and negation operations with the VACT. The shaded area in the configuration kernel indicates the center of the neighborhood area.

Fig. 3
Fig. 3

Fundamental operations of mathematical morphology: erosion and dilation of a binary image X by a binary structuring element B.

Fig. 4
Fig. 4

Comparison of the dilation procedure in mathematical morphology and the maximum operation in the VACT: (a) dilation in mathematical morphology, (b) maximum operation in the VACT.

Fig. 5
Fig. 5

Sequence of gray-image processing with the VACT.

Fig. 6
Fig. 6

Simulations of fundamental operations for gray-image processing with the VACT: (a) input image, (b) dilation, (c) erosion. The binary discrete structuring element is a rhombus.

Fig. 7
Fig. 7

Simulations of noise reduction with the VACT: (a) input image for noise reduction, (b) simulated result of noise reduction. The binary discrete structuring element is a rhombus.

Fig. 8
Fig. 8

Simulations of edge detection with the VACT: (a) input image for edge detection, (b) simulated result of edge detection. The binary discrete structuring element is a rhombus.

Fig. 9
Fig. 9

Experimental system for correlation.

Fig. 10
Fig. 10

Optical setup for recording the holographic filter. BS's, beam splitters.

Fig. 11
Fig. 11

Experimental results of two fundamental operations for gray-image processing with the VACT: (a) input image, (b) dilation, (c) erosion. The binary discrete structuring element is a rhombus.

Fig. 12
Fig. 12

Achievable pixel number N as a function of the diameter of the lens, D, for λ = 441.6 nm and f-number = 1.30. Cases L = 2, L = 5, L = 17, and L = 257 are plotted.

Equations (3)

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A max = D 2 f λ v max ,
SBWP = A max v max = 2 f λ ( v max D 4 f λ ) 2 + D 2 8 f λ .
N = ( SBWP max ) 2 L 1 = D 4 64 ( L 1 ) f 2 λ 2 ,

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