Abstract

We discuss and implement a wavelet-modified maximum average correlation height (MACH) filter for 0°360° in-plane rotations in a hybrid digital–optical correlator. Use of a wavelet transform improves the performance of the MACH filter by reducing the number of filters that are required to identify a target rotated at any angle between 0°  and  360° in-plane rotations and enhances the autocorrelation peak intensity significantly. The output of a hybrid digital–optical correlator contains two autocorrelation peaks and a strong dc. Using a chirp function with the wavelet-modified MACH filter, the correlation signals are focused in three different planes. Thus placing a peak-capturing CCD camera at a particular plane, only one autocorrelation peak is recorded, discarding the strong dc and other autocorrelation peaks. A signal-to-noise ratio has been calculated as a metric of goodness of the proposed wavelet-modified MACH filter.

© 2006 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2005

A. Sinha and K. Singh, "The design of a composite wavelet matched filter for face recognition using breeder genetic algorithm," Opt. Lasers Eng. 43, 1277-1291 (2005).
[CrossRef]

2003

A. V. Nevel and A. Mahalanobis, "Comparative study of maximum average correlation height filter variants using ladar imagery," Opt. Eng. 42, 541-550 (2003).
[CrossRef]

J. A. Davis, K. O. Valadez, and D. M. Cottrell, "Encoding amplitude and phase information onto a binary phase-only spatial light modulator," Appl. Opt. 42, 2003-2008 (2003).
[CrossRef] [PubMed]

2002

P. Birch, R. Young, F. Claret-Tournier, D. Budgett, and C. Chatwin, "Computer-generated complex filter for an all-optical and a digital-optical hybrid correlator," Opt. Eng. 41, 105-111 (2002).
[CrossRef]

P. M. Birch, G. Li, F. Claret-Tournier, R. Young, D. Budgett, and C. Chatwin, "Optical design of a miniature Fourier transform lens system for a hybrid digital-optical correlator," Opt. Eng. 41, 1650-1654 (2002).
[CrossRef]

P. M. Birch, F. Claret-Tournier, D. Budgett, R. Young, and C. Chatwin, "Optical and electronic design of a hybrid-optical correlator system," Opt. Eng. 41, 32-40 (2002).
[CrossRef]

2001

M. Pohit and K. Singh, "Performance of a wavelet matched filter with optimized dilation designed using simulated annealing algorithm," Opt. Commun. 187, 337-346 (2001).
[CrossRef]

2000

1999

1998

R. Tripathi and K. Singh, "Pattern discrimination using a bank of wavelet filters in a joint transform correlator," Opt. Eng. 37, 1-7 (1998).
[CrossRef]

1997

A. Mahalanobis and B. V. K. Vijaya Kumar, "Optimality of the maximum average correlation height filter for detection of targets in noise," Opt. Eng. 36, 2642-2648 (1997).
[CrossRef]

1994

1993

1992

Alkanhal, M.

M. Alkanhal, B. V. K. Vijaya Kumar, and A. Mahalanobis, "Improving the false alarm capabilities of the maximum average correlation height correlation filter," Opt. Eng. 39, 1133-1141 (2000).
[CrossRef]

Aran, A.

V. K. Beri, A. Aran, S. Goyal, A. Bhagatji, and A. K. Gupta, "Rotation/scale invariant hybrid digital/optical correlator system for automatic target recognition," J. Opt. (India) (to be published).

Beri, V. K.

V. K. Beri, A. Aran, S. Goyal, A. Bhagatji, and A. K. Gupta, "Rotation/scale invariant hybrid digital/optical correlator system for automatic target recognition," J. Opt. (India) (to be published).

Bhagatji, A.

V. K. Beri, A. Aran, S. Goyal, A. Bhagatji, and A. K. Gupta, "Rotation/scale invariant hybrid digital/optical correlator system for automatic target recognition," J. Opt. (India) (to be published).

Birch, P.

P. Birch, R. Young, F. Claret-Tournier, D. Budgett, and C. Chatwin, "Computer-generated complex filter for an all-optical and a digital-optical hybrid correlator," Opt. Eng. 41, 105-111 (2002).
[CrossRef]

Birch, P. M.

P. M. Birch, G. Li, F. Claret-Tournier, R. Young, D. Budgett, and C. Chatwin, "Optical design of a miniature Fourier transform lens system for a hybrid digital-optical correlator," Opt. Eng. 41, 1650-1654 (2002).
[CrossRef]

P. M. Birch, F. Claret-Tournier, D. Budgett, R. Young, and C. Chatwin, "Optical and electronic design of a hybrid-optical correlator system," Opt. Eng. 41, 32-40 (2002).
[CrossRef]

Bopardikar, A. S.

R. M. Rao and A. S. Bopardikar, Wavelet Transforms: Introduction to Theory and Applications (Addison-Wesley, 1998).

Budgett, D.

P. M. Birch, F. Claret-Tournier, D. Budgett, R. Young, and C. Chatwin, "Optical and electronic design of a hybrid-optical correlator system," Opt. Eng. 41, 32-40 (2002).
[CrossRef]

P. M. Birch, G. Li, F. Claret-Tournier, R. Young, D. Budgett, and C. Chatwin, "Optical design of a miniature Fourier transform lens system for a hybrid digital-optical correlator," Opt. Eng. 41, 1650-1654 (2002).
[CrossRef]

P. Birch, R. Young, F. Claret-Tournier, D. Budgett, and C. Chatwin, "Computer-generated complex filter for an all-optical and a digital-optical hybrid correlator," Opt. Eng. 41, 105-111 (2002).
[CrossRef]

Campos, J.

Chang, J.

Chatwin, C.

P. M. Birch, G. Li, F. Claret-Tournier, R. Young, D. Budgett, and C. Chatwin, "Optical design of a miniature Fourier transform lens system for a hybrid digital-optical correlator," Opt. Eng. 41, 1650-1654 (2002).
[CrossRef]

P. Birch, R. Young, F. Claret-Tournier, D. Budgett, and C. Chatwin, "Computer-generated complex filter for an all-optical and a digital-optical hybrid correlator," Opt. Eng. 41, 105-111 (2002).
[CrossRef]

P. M. Birch, F. Claret-Tournier, D. Budgett, R. Young, and C. Chatwin, "Optical and electronic design of a hybrid-optical correlator system," Opt. Eng. 41, 32-40 (2002).
[CrossRef]

R. Young, C. Chatwin, and B. Scott, "High-speed hybrid optical/digital correlator system," Opt. Eng. 32, 2608-2615 (1993).
[CrossRef]

Cheng, Y.-S.

T.-C. Liang and Y.-S. Cheng, "Rotational-invariant pattern recognition using circular harmonic and optical wavelet transform," Opt. Rev. 1, 198-201 (1994).

Claret-Tournier, F.

P. Birch, R. Young, F. Claret-Tournier, D. Budgett, and C. Chatwin, "Computer-generated complex filter for an all-optical and a digital-optical hybrid correlator," Opt. Eng. 41, 105-111 (2002).
[CrossRef]

P. M. Birch, G. Li, F. Claret-Tournier, R. Young, D. Budgett, and C. Chatwin, "Optical design of a miniature Fourier transform lens system for a hybrid digital-optical correlator," Opt. Eng. 41, 1650-1654 (2002).
[CrossRef]

P. M. Birch, F. Claret-Tournier, D. Budgett, R. Young, and C. Chatwin, "Optical and electronic design of a hybrid-optical correlator system," Opt. Eng. 41, 32-40 (2002).
[CrossRef]

Cottrell, D. M.

Davis, J. A.

Epperson, J. F.

Goyal, S.

V. K. Beri, A. Aran, S. Goyal, A. Bhagatji, and A. K. Gupta, "Rotation/scale invariant hybrid digital/optical correlator system for automatic target recognition," J. Opt. (India) (to be published).

Gupta, A. K.

V. K. Beri, A. Aran, S. Goyal, A. Bhagatji, and A. K. Gupta, "Rotation/scale invariant hybrid digital/optical correlator system for automatic target recognition," J. Opt. (India) (to be published).

Javidi, B.

Kumar, B. V. K. Vijaya

M. Alkanhal, B. V. K. Vijaya Kumar, and A. Mahalanobis, "Improving the false alarm capabilities of the maximum average correlation height correlation filter," Opt. Eng. 39, 1133-1141 (2000).
[CrossRef]

A. Mahalanobis and B. V. K. Vijaya Kumar, "Optimality of the maximum average correlation height filter for detection of targets in noise," Opt. Eng. 36, 2642-2648 (1997).
[CrossRef]

A. Mahalanobis, B. V. K. Vijaya Kumar, S. Song, S. R. F. Sims, and J. F. Epperson, "Unconstrained correlation filters," Appl. Opt. 33, 3751-3759 (1994).
[CrossRef] [PubMed]

Lewis, M. F.

Li, G.

P. M. Birch, G. Li, F. Claret-Tournier, R. Young, D. Budgett, and C. Chatwin, "Optical design of a miniature Fourier transform lens system for a hybrid digital-optical correlator," Opt. Eng. 41, 1650-1654 (2002).
[CrossRef]

Liang, T.-C.

T.-C. Liang and Y.-S. Cheng, "Rotational-invariant pattern recognition using circular harmonic and optical wavelet transform," Opt. Rev. 1, 198-201 (1994).

Lowans, B. S.

Lu, T.

Mahalanobis, A.

A. V. Nevel and A. Mahalanobis, "Comparative study of maximum average correlation height filter variants using ladar imagery," Opt. Eng. 42, 541-550 (2003).
[CrossRef]

M. Alkanhal, B. V. K. Vijaya Kumar, and A. Mahalanobis, "Improving the false alarm capabilities of the maximum average correlation height correlation filter," Opt. Eng. 39, 1133-1141 (2000).
[CrossRef]

A. Mahalanobis and B. V. K. Vijaya Kumar, "Optimality of the maximum average correlation height filter for detection of targets in noise," Opt. Eng. 36, 2642-2648 (1997).
[CrossRef]

A. Mahalanobis, B. V. K. Vijaya Kumar, S. Song, S. R. F. Sims, and J. F. Epperson, "Unconstrained correlation filters," Appl. Opt. 33, 3751-3759 (1994).
[CrossRef] [PubMed]

McNamara, D. E.

Moreno, I.

Nevel, A. V.

A. V. Nevel and A. Mahalanobis, "Comparative study of maximum average correlation height filter variants using ladar imagery," Opt. Eng. 42, 541-550 (2003).
[CrossRef]

Pohit, M.

M. Pohit and K. Singh, "Performance of a wavelet matched filter with optimized dilation designed using simulated annealing algorithm," Opt. Commun. 187, 337-346 (2001).
[CrossRef]

Rao, R. M.

R. M. Rao and A. S. Bopardikar, Wavelet Transforms: Introduction to Theory and Applications (Addison-Wesley, 1998).

Roberge, D.

Scott, B.

R. Young, C. Chatwin, and B. Scott, "High-speed hybrid optical/digital correlator system," Opt. Eng. 32, 2608-2615 (1993).
[CrossRef]

Sheng, Y.

Sims, S. R. F.

Singh, K.

A. Sinha and K. Singh, "The design of a composite wavelet matched filter for face recognition using breeder genetic algorithm," Opt. Lasers Eng. 43, 1277-1291 (2005).
[CrossRef]

M. Pohit and K. Singh, "Performance of a wavelet matched filter with optimized dilation designed using simulated annealing algorithm," Opt. Commun. 187, 337-346 (2001).
[CrossRef]

R. Tripathi and K. Singh, "Pattern discrimination using a bank of wavelet filters in a joint transform correlator," Opt. Eng. 37, 1-7 (1998).
[CrossRef]

Sinha, A.

A. Sinha and K. Singh, "The design of a composite wavelet matched filter for face recognition using breeder genetic algorithm," Opt. Lasers Eng. 43, 1277-1291 (2005).
[CrossRef]

Sonehara, T.

Song, S.

Szu, H.

Tang, Q.

Tripathi, R.

R. Tripathi and K. Singh, "Pattern discrimination using a bank of wavelet filters in a joint transform correlator," Opt. Eng. 37, 1-7 (1998).
[CrossRef]

Valadez, K. O.

Young, R.

P. M. Birch, F. Claret-Tournier, D. Budgett, R. Young, and C. Chatwin, "Optical and electronic design of a hybrid-optical correlator system," Opt. Eng. 41, 32-40 (2002).
[CrossRef]

P. M. Birch, G. Li, F. Claret-Tournier, R. Young, D. Budgett, and C. Chatwin, "Optical design of a miniature Fourier transform lens system for a hybrid digital-optical correlator," Opt. Eng. 41, 1650-1654 (2002).
[CrossRef]

P. Birch, R. Young, F. Claret-Tournier, D. Budgett, and C. Chatwin, "Computer-generated complex filter for an all-optical and a digital-optical hybrid correlator," Opt. Eng. 41, 105-111 (2002).
[CrossRef]

R. Young, C. Chatwin, and B. Scott, "High-speed hybrid optical/digital correlator system," Opt. Eng. 32, 2608-2615 (1993).
[CrossRef]

Yzuel, M. J.

Appl. Opt.

J. Opt.

V. K. Beri, A. Aran, S. Goyal, A. Bhagatji, and A. K. Gupta, "Rotation/scale invariant hybrid digital/optical correlator system for automatic target recognition," J. Opt. (India) (to be published).

Opt. Commun.

M. Pohit and K. Singh, "Performance of a wavelet matched filter with optimized dilation designed using simulated annealing algorithm," Opt. Commun. 187, 337-346 (2001).
[CrossRef]

Opt. Eng.

R. Young, C. Chatwin, and B. Scott, "High-speed hybrid optical/digital correlator system," Opt. Eng. 32, 2608-2615 (1993).
[CrossRef]

P. Birch, R. Young, F. Claret-Tournier, D. Budgett, and C. Chatwin, "Computer-generated complex filter for an all-optical and a digital-optical hybrid correlator," Opt. Eng. 41, 105-111 (2002).
[CrossRef]

P. M. Birch, G. Li, F. Claret-Tournier, R. Young, D. Budgett, and C. Chatwin, "Optical design of a miniature Fourier transform lens system for a hybrid digital-optical correlator," Opt. Eng. 41, 1650-1654 (2002).
[CrossRef]

P. M. Birch, F. Claret-Tournier, D. Budgett, R. Young, and C. Chatwin, "Optical and electronic design of a hybrid-optical correlator system," Opt. Eng. 41, 32-40 (2002).
[CrossRef]

A. Mahalanobis and B. V. K. Vijaya Kumar, "Optimality of the maximum average correlation height filter for detection of targets in noise," Opt. Eng. 36, 2642-2648 (1997).
[CrossRef]

M. Alkanhal, B. V. K. Vijaya Kumar, and A. Mahalanobis, "Improving the false alarm capabilities of the maximum average correlation height correlation filter," Opt. Eng. 39, 1133-1141 (2000).
[CrossRef]

A. V. Nevel and A. Mahalanobis, "Comparative study of maximum average correlation height filter variants using ladar imagery," Opt. Eng. 42, 541-550 (2003).
[CrossRef]

R. Tripathi and K. Singh, "Pattern discrimination using a bank of wavelet filters in a joint transform correlator," Opt. Eng. 37, 1-7 (1998).
[CrossRef]

Opt. Lasers Eng.

A. Sinha and K. Singh, "The design of a composite wavelet matched filter for face recognition using breeder genetic algorithm," Opt. Lasers Eng. 43, 1277-1291 (2005).
[CrossRef]

Opt. Lett.

Opt. Rev.

T.-C. Liang and Y.-S. Cheng, "Rotational-invariant pattern recognition using circular harmonic and optical wavelet transform," Opt. Rev. 1, 198-201 (1994).

Other

B. Javidi and J.L.Horner, eds., Real-time Optical Information Processing (Academic, 1994).

F.T. S.Yu and S. Jutamulia, eds., Optical Pattern Recognition (Cambridge U. Press, 1998).

B. Javidi, ed., Image Recognition and Classification: Algorithms, Systems, and Applications (Marcel Dekker, 2002).
[CrossRef]

R. M. Rao and A. S. Bopardikar, Wavelet Transforms: Introduction to Theory and Applications (Addison-Wesley, 1998).

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Figures (12)

Fig. 1
Fig. 1

(a–c) True-class and (d) false-class images used to synthesize the MACH filter.

Fig. 2
Fig. 2

Simulation results. (a), (c), (e) Correlation outputs with the MACH filter. (b), (d), (f) Correlation outputs with the wavelet-modified MACH filter. (a)–(d) correspond to true-class images at angles of 30° and 125°, and (e) and (f) correspond to false-class images.

Fig. 3
Fig. 3

Simulation results. (a), (c), (e) Correlation outputs with the chirp-encoded MACH filter. (b), (d), (f) Correlation outputs with the chirp-encoded wavelet-modified MACH filter. (a)–(d) correspond to true-class images at angles of 30° and 125°, and (e) and (f) correspond to false- class images.

Fig. 4
Fig. 4

(Color online) Simulation results. Correlation peak height versus angle of rotation for (a) chirp-encoded MACH filter and (b) chirp-encoded wavelet-modified MACH filter.

Fig. 5
Fig. 5

(Color online) Simulation results. (a) Plot of the SNR with angle of rotation with the chirp-encoded MACH filter and (b) plot of the SNR with angle of rotation with the chirp-encoded wavelet-modified MACH filter.

Fig. 6
Fig. 6

Images of tank 1 (true class) and tanks 2–5 (false class) used to synthesize the MACH filter.

Fig. 7
Fig. 7

(Color online) Simulated correlation outputs with the chirp-encoded wavelet-modified MACH filter with tank 1 as true class: (a) tanks 2 and 3 as false class and (b) tanks 4 and 5 as false class having different energies.

Fig. 8
Fig. 8

Experimental setup. SF, spatial filter; CL, collimating lens; PBS, polarizing beam splitter; FT, Fourier transform.

Fig. 9
Fig. 9

Experimental results. (a), (c), (e) Correlation outputs with the MACH filter. (b), (d), (f) Correlation outputs with the wavelet-modified MACH filter. (a)–(d) correspond to true-class images at angles of 30° and 125°, and (e) and (f) correspond to false-class images.

Fig. 10
Fig. 10

Experimental results. (a), (c), (e) Correlation output containing only one of the autocorrelation peaks with the chirp-encoded MACH filter. (b), (d), (f) Correlation output containing only one of the autocorrelation peaks with the chirp-encoded wavelet MACH filter. (a)–(d) correspond to true-class images at angles of 30° and 125°, and (e) and (f) correspond to false-class images.

Fig. 11
Fig. 11

Experimental results. (a) Tanks 1–5 at different rotations: first row at 35°, second row at 140°, third row at 210°, and fourth row at 305°. (b) Corresponding correlation peaks with the chirp-encoded wavelet MACH filter.

Fig. 12
Fig. 12

(Color online) Experimental results. (a) On the left-hand side, A shows one of the autocorrelation peaks obtained after use of the chirp-encoded MACH filter. On the right-hand side, B shows one of the autocorrelation peaks obtained after use of the chirp-encoded wavelet-modified MACH filter. (b) Measured correlation peak height obtained in the above two cases. Here, I wmc refers to the intensity when the chirp-encoded wavelet-modified MACH filter was used, and I mc refers to the intensity when the chirp-encoded MACH filter was used to obtain the correlation peaks.

Equations (63)

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

0 ° 360 °
0 °   and   360 °
3 5
8 12   μm
± 1
h ( x )
h a , b ( x ) = 1 a h ( x b a ) .
f ( x )
h a , b ( x )
w f ( a ,   b ) = h a , b * ( x ) f ( x ) d x ,
w f ( a , b )
f ( x )
H a , b ( f ) = exp ( i 2 π f x ) h a , b ( x ) d x = a exp ( i 2 π f b ) H ( a f ) ,
H ( f )
h ( x )
h ( x )
H ( f )
H ( f )
H ( 0 )
H ( f )
h ( x , y ) = [ 1 ( x 2 + y 2 ) ] exp ( x 2 + y 2 2 ) .
H ( u , ν ) = 4 π 2 ( u 2 + ν 2 ) exp [ 2 π ( u 2 + ν 2 ) ] .
h = S 1 m ,
S = 1 N i = 1 N ( X i M ) ( X i M ) + ,
X i
X i
X i
WMF = F * ( u , ν ) | H ( u , ν ) | 2 .
F * ( u , ν )
| H ( u , ν ) | 2
h a , b ( x , y )
| H ( u , ν ) | 2
WMMF = S 1 m | H ( u , ν ) | 2 .
0 °   and   360 °
C ( x , y ) = exp [ i k ( x 2 + y 2 ) / 2 z ] .
k = 2 π / λ
45 × 25
256 × 256
( 0 ° 360 ° )
30 °
+ 30 °
( 0 ° 360 ° )
SNR = | E { η / H } | 2 var { η } .
E { }
var { }
n ( x )
n ( x )
E { η / H }
( λ = 670   nm )
( f = 75   mm )
256 × 256
15   μm × 15   μm
( f = 105   mm )
752 × 582
6.5   μm × 6.25   μm
+ 1
1
190   mm
10 × 10
( I mc )
( I wmc )
0 ° 360 °
0 °   and   360 °

Metrics