Abstract

A 2D complex Gabor-wavelet filter (CGWF) optical architecture based on the proposed Gaussian chirplet transform approach is presented together with its mathematical derivation. Far from the conventional setup schemes in which only the real part of the CGWF (even-symmetrical GWF) can be implemented optically, the proposed optical scheme shows that the real and also the imaginary part of the CGWF (odd-symmetrical GWF) can be achieved. The computer application simulations to the oriented edge feature extraction are given to validate the feasibility of the proposed scheme.

© 2009 Optical Society of America

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2007

2006

H. E. Hwang and P. Han, J. Opt. Soc. Am. A 23, 1870 (2006).
[CrossRef]

J. K. Kämäräinen, V. Kyrki, and H. Kälviäinen, IEEE Trans. Image Process. 15, 1088 (2006).
[CrossRef]

2005

M. Hamouz, J. Kittler, J. K. Kämäräinen, P. Paalanen, H. Kälviäinen, and J. Matas, IEEE Trans. Pattern Anal. Mach. Intell. 27, 1480 (2005).
[CrossRef]

2003

H. E. Hwang, Opt. Eng. 42, 3374 (2003).
[CrossRef]

1999

P. Kovesi, Videre: J. Computer Vision Res. 1, 1 (1999).

R. Navarro, A. Vargas, and J. Campos, J. Opt. A 1, 116 (1999).
[CrossRef]

1993

D. Mendlovic and N. Konforti, Appl. Opt. 32, 6542 (1993).
[CrossRef] [PubMed]

J. G. Daugman, IEEE Trans. Pattern Anal. Mach. Intell. 15, 1148 (1993).
[CrossRef]

1990

A. C. Bovik, M. Clark, and W. S. Geisler, IEEE Trans. Pattern Anal. Mach. Intell. 12, 55 (1990).
[CrossRef]

1987

1985

1980

J. G. Daugman, Vision Res. 20, 847 (1980).
[CrossRef] [PubMed]

1946

D. Gabor, J. Inst. Electr. Eng. 93, 429 (1946).

Bovik, A. C.

A. C. Bovik, M. Clark, and W. S. Geisler, IEEE Trans. Pattern Anal. Mach. Intell. 12, 55 (1990).
[CrossRef]

Campos, J.

R. Navarro, A. Vargas, and J. Campos, J. Opt. A 1, 116 (1999).
[CrossRef]

Clark, M.

A. C. Bovik, M. Clark, and W. S. Geisler, IEEE Trans. Pattern Anal. Mach. Intell. 12, 55 (1990).
[CrossRef]

Daugman, J. G.

J. G. Daugman, IEEE Trans. Pattern Anal. Mach. Intell. 15, 1148 (1993).
[CrossRef]

J. G. Daugman, J. Opt. Soc. Am. A 2, 1160 (1985).
[CrossRef] [PubMed]

J. G. Daugman, Vision Res. 20, 847 (1980).
[CrossRef] [PubMed]

Gabor, D.

D. Gabor, J. Inst. Electr. Eng. 93, 429 (1946).

Geisler, W. S.

A. C. Bovik, M. Clark, and W. S. Geisler, IEEE Trans. Pattern Anal. Mach. Intell. 12, 55 (1990).
[CrossRef]

Hamouz, M.

M. Hamouz, J. Kittler, J. K. Kämäräinen, P. Paalanen, H. Kälviäinen, and J. Matas, IEEE Trans. Pattern Anal. Mach. Intell. 27, 1480 (2005).
[CrossRef]

Han, P.

Heeger, D. J.

Hwang, H. E.

Kälviäinen, H.

J. K. Kämäräinen, V. Kyrki, and H. Kälviäinen, IEEE Trans. Image Process. 15, 1088 (2006).
[CrossRef]

M. Hamouz, J. Kittler, J. K. Kämäräinen, P. Paalanen, H. Kälviäinen, and J. Matas, IEEE Trans. Pattern Anal. Mach. Intell. 27, 1480 (2005).
[CrossRef]

Kämäräinen, J. K.

J. K. Kämäräinen, V. Kyrki, and H. Kälviäinen, IEEE Trans. Image Process. 15, 1088 (2006).
[CrossRef]

M. Hamouz, J. Kittler, J. K. Kämäräinen, P. Paalanen, H. Kälviäinen, and J. Matas, IEEE Trans. Pattern Anal. Mach. Intell. 27, 1480 (2005).
[CrossRef]

Kittler, J.

M. Hamouz, J. Kittler, J. K. Kämäräinen, P. Paalanen, H. Kälviäinen, and J. Matas, IEEE Trans. Pattern Anal. Mach. Intell. 27, 1480 (2005).
[CrossRef]

Konforti, N.

Kovesi, P.

P. Kovesi, Videre: J. Computer Vision Res. 1, 1 (1999).

Kyrki, V.

J. K. Kämäräinen, V. Kyrki, and H. Kälviäinen, IEEE Trans. Image Process. 15, 1088 (2006).
[CrossRef]

Matas, J.

M. Hamouz, J. Kittler, J. K. Kämäräinen, P. Paalanen, H. Kälviäinen, and J. Matas, IEEE Trans. Pattern Anal. Mach. Intell. 27, 1480 (2005).
[CrossRef]

Mendlovic, D.

Navarro, R.

R. Navarro, A. Vargas, and J. Campos, J. Opt. A 1, 116 (1999).
[CrossRef]

Paalanen, P.

M. Hamouz, J. Kittler, J. K. Kämäräinen, P. Paalanen, H. Kälviäinen, and J. Matas, IEEE Trans. Pattern Anal. Mach. Intell. 27, 1480 (2005).
[CrossRef]

Vargas, A.

R. Navarro, A. Vargas, and J. Campos, J. Opt. A 1, 116 (1999).
[CrossRef]

Appl. Opt.

IEEE Trans. Image Process.

J. K. Kämäräinen, V. Kyrki, and H. Kälviäinen, IEEE Trans. Image Process. 15, 1088 (2006).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell.

A. C. Bovik, M. Clark, and W. S. Geisler, IEEE Trans. Pattern Anal. Mach. Intell. 12, 55 (1990).
[CrossRef]

M. Hamouz, J. Kittler, J. K. Kämäräinen, P. Paalanen, H. Kälviäinen, and J. Matas, IEEE Trans. Pattern Anal. Mach. Intell. 27, 1480 (2005).
[CrossRef]

J. G. Daugman, IEEE Trans. Pattern Anal. Mach. Intell. 15, 1148 (1993).
[CrossRef]

J. Inst. Electr. Eng.

D. Gabor, J. Inst. Electr. Eng. 93, 429 (1946).

J. Opt. A

R. Navarro, A. Vargas, and J. Campos, J. Opt. A 1, 116 (1999).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

H. E. Hwang, Opt. Eng. 42, 3374 (2003).
[CrossRef]

Opt. Express

Videre: J. Computer Vision Res.

P. Kovesi, Videre: J. Computer Vision Res. 1, 1 (1999).

Vision Res.

J. G. Daugman, Vision Res. 20, 847 (1980).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of the optical CGWF based on the GCT approach.

Fig. 2
Fig. 2

Separate plots (a) for the input Gaussian pattern, (b) real part, and (c) imaginary part of the oriented phase function. (d) Real part and (e) imaginary part of the Gaussian envelope oriented phase function with the wave propagation direction μ x 2 + ν y 2 , respectively. (f) A couple of input Gaussian pattern is usually used to perform the ESGWT for the traditional scheme.

Fig. 3
Fig. 3

(a) A certain input object g ( x 2 , y 2 ) is prepared to be filtered in the ( x 2 , y 2 ) domain. (b)–(g) Edge features extraction resultants using the proposed ESCGWFs. (h)–(m) Edge features extraction resultants using the proposed OSCGWFs. The oriented features extractions are based on the proposed scheme, and six orientations are selected: θ = 0 ° , θ = 30 ° , θ = 60 ° , θ = 90 ° , θ = 120 ° , and θ = 150 ° .

Equations (5)

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FT { G ( x 1 , y 1 ) FrT z [ f 1 ( x 0 , y 0 ) ] } = exp ( j 2 π z λ ) j λ z g ( x 2 , y 2 ) FT { f 1 ( x 1 , y 1 ) exp [ j 2 π ( x 1 2 + y 1 2 ) λ z ] } ,
FT { G ( x 1 , y 1 ) FrT z [ f 1 ( x 0 , y 0 ) ] } [ g ( x 2 , y 2 ) ( exp [ 2 π 2 λ 2 f 2 ( η 2 x 2 2 + ξ 2 y 2 2 ) ] exp { j π z 2 λ f 2 [ ( x 2 2 μ f z ) 2 + ( y 2 2 ν f z ) 2 ] } ) ] .
FT { G ( x 1 , y 1 ) FrT z [ f 1 ( x 0 , y 0 ) ] } B ( g ( x 2 , y 2 ) { exp [ 2 π 2 λ 2 f 2 ( η 2 x 2 2 + ξ 2 y 2 2 ) ] exp [ j 2 π λ f ( μ x 2 + ν y 2 ) ] } ) ,
| FT { G ( x 1 , y 1 ) FrT z [ f 1 ( x 0 , y 0 ) + f 2 ( x 0 , y 0 ) ] } | | π η ξ 8 λ 2 f 2 ( g ( x 2 , y 2 ) { exp [ 2 π 2 λ 2 f 2 ( η 2 x 2 2 + ξ 2 y 2 2 ) ] cos [ 2 π λ f ( μ x 2 + ν y 2 ) ] } ) | ,
| FT { G ( x 1 , y 1 ) FrT z [ f 1 ( x 0 , y 0 ) + f 2 ( x 0 + Δ μ , y 0 + Δ ν ) ] } | | π | η ξ | 8 λ 2 f 2 ( g ( x 2 , y 2 ) { exp [ 2 π 2 λ 2 f 2 ( η 2 x 2 2 + ξ 2 y 2 2 ) ] sin [ 2 π λ f ( μ x 2 + ν y 2 ) ] } ) | .

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