Abstract

To solve the pattern recognition problem, a method of synthesized phase objects is suggested. The essence of the suggested method is that synthesized phase objects are used instead of real amplitude objects. The former is object-dependent phase distributions calculated using the iterative Fourier-transform (IFT) algorithm. The method is experimentally studied with a Vander Lugt optical-digital 4F-correlator. We present the comparative analysis of recognition results using conventional and proposed methods, estimate the sensitivity of the latter to distortions of the structure of objects, and determine the applicability limits. It is demonstrated that the proposed method allows one: (а) to simplify the procedure of choice of recognition signs (criteria); (b) to obtain one-type δ-like recognition signals irrespective of the type of objects; (с) to improve signal-to-noise ratio (SNR) for correlation signals by 20 − 30 dB on average. The spatial separation of the Fourier-spectra of objects and optical noises of the correlator by means of the superposition of the phase grating on recognition objects at the recording of holographic filters and at the matched filtering has additionally improved SNR (>10 dB) for correlation signals. To introduce recognition objects in the correlator, we use a SLM LC-R 2500 device. Matched filters are recorded on a self-developing photopolymer.

© 2012 OSA

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References

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2011 (1)

2000 (4)

T. N. Smirnova and O. V. Sakhno, “PPC: self-developing photopolymers for holographic recording,” Proc. SPIE4149, 106–112 (2000).
[CrossRef]

G. M. Karpov, V. V. Obukhovsky, T. N. Smirnova, and V. V. Lemeshko, “Spatial transfer of matter as a method of holographic recording in photoformers,” Opt. Commun.174(5-6), 391–404 (2000).
[CrossRef]

Z. Q. Wang, H. L. Liu, J. H. Guan, and G. G. Mu, “Phase shift joint transform correlator with synthetic discriminant function,” Optik (Stuttg.)111(2), 71–74 (2000).

J. Campos, A. Márquez, M. J. Yzuel, J. A. Davis, D. M. Cottrell, and I. Moreno, “Fully complex synthetic discriminant functions written onto phase-only modulators,” Appl. Opt.39(32), 5965–5970 (2000).
[CrossRef] [PubMed]

1999 (2)

S. C. Verrall, “Windowed binary joint transform correlation with feedback,” Opt. Eng.38(1), 76–88 (1999).
[CrossRef]

D. Roberge, C. Soutar, and B. V. K. Vijaya Kumar, “Optimal trade-off filter for the correlation of fingerprints,” Opt. Eng.38(1), 108–113 (1999).
[CrossRef]

1998 (3)

A. Talukder and D. P. Casasent, “Pose estimation and transformation of faces,” Proc. SPIE3522, 84–95 (1998).
[CrossRef]

A. Talukder and D. P. Casasent, “General methodology for simultaneous representation and discrimination of multiple object classes,” Opt. Eng.37(3), 904–913 (1998).
[CrossRef]

M. M. Matalgah, J. Knopp, and L. Eifler, “Geometric approach for designing optical binary amplitude and binary phase-only filters,” Appl. Opt.37(35), 8233–8246 (1998).
[CrossRef] [PubMed]

1997 (1)

S. Chang, M. Rloux, and J. Domey, “Face recognition with range images and intensity images,” Opt. Eng.36(4), 1106–1112 (1997).
[CrossRef]

1996 (1)

R. S. Kashi, W. Turin, and W. L. Nelson, “On-line handwritten signature verification using stroke direction coding,” Opt. Eng.35(9), 2526–2533 (1996).
[CrossRef]

1995 (1)

V. M. Fitio, L. I. Muravsky, and A. L. Stefansky, “Using of random phase masks for image recognition in optical correlator,” Proc. SPIE2647, 224–234 (1995).
[CrossRef]

1994 (2)

P. K. Rajan and E. S. Raghavan, “Design of synthetic estimation filters using correlation energy minimization,” Opt. Eng.33(6), 1829–1837 (1994).
[CrossRef]

P. Réfrégier, “Application of the stabilizing functional approach to pattern recognition filter,” J. Opt. Soc. Am. A11(4), 1243–1252 (1994).
[CrossRef]

1991 (2)

1990 (2)

M. Fleisher, U. Mahlab, and J. Shamir, “Entropy optimized filter for pattern recognition,” Appl. Opt.29(14), 2091–2098 (1990).
[CrossRef] [PubMed]

O. Tang, E. Jager, and T. T. Tschudi, “Off-axis phase-only filter for pattern recognition,” Opt. Eng.29(11), 1421–1426 (1990).
[CrossRef]

1988 (1)

1984 (1)

1973 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.)35, 237–246 (1972).

1966 (1)

1964 (1)

B. Vander Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory10(2), 139–145 (1964).
[CrossRef]

Campos, J.

Casasent, D.

Casasent, D. P.

A. Talukder and D. P. Casasent, “General methodology for simultaneous representation and discrimination of multiple object classes,” Opt. Eng.37(3), 904–913 (1998).
[CrossRef]

A. Talukder and D. P. Casasent, “Pose estimation and transformation of faces,” Proc. SPIE3522, 84–95 (1998).
[CrossRef]

Chang, S.

S. Chang, M. Rloux, and J. Domey, “Face recognition with range images and intensity images,” Opt. Eng.36(4), 1106–1112 (1997).
[CrossRef]

Cottrell, D. M.

Davis, J. A.

Domey, J.

S. Chang, M. Rloux, and J. Domey, “Face recognition with range images and intensity images,” Opt. Eng.36(4), 1106–1112 (1997).
[CrossRef]

Eifler, L.

Farn, M. W.

Fitio, V. M.

V. M. Fitio, L. I. Muravsky, and A. L. Stefansky, “Using of random phase masks for image recognition in optical correlator,” Proc. SPIE2647, 224–234 (1995).
[CrossRef]

Fleisher, M.

Gallagher, N. C.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.)35, 237–246 (1972).

Goodman, J. W.

Guan, J. H.

Z. Q. Wang, H. L. Liu, J. H. Guan, and G. G. Mu, “Phase shift joint transform correlator with synthetic discriminant function,” Optik (Stuttg.)111(2), 71–74 (2000).

Iezhov, P. V.

Jager, E.

O. Tang, E. Jager, and T. T. Tschudi, “Off-axis phase-only filter for pattern recognition,” Opt. Eng.29(11), 1421–1426 (1990).
[CrossRef]

Karpov, G. M.

G. M. Karpov, V. V. Obukhovsky, T. N. Smirnova, and V. V. Lemeshko, “Spatial transfer of matter as a method of holographic recording in photoformers,” Opt. Commun.174(5-6), 391–404 (2000).
[CrossRef]

Kashi, R. S.

R. S. Kashi, W. Turin, and W. L. Nelson, “On-line handwritten signature verification using stroke direction coding,” Opt. Eng.35(9), 2526–2533 (1996).
[CrossRef]

Kim, J. T.

Knopp, J.

Kuzmenko, A. V.

Lemeshko, V. V.

G. M. Karpov, V. V. Obukhovsky, T. N. Smirnova, and V. V. Lemeshko, “Spatial transfer of matter as a method of holographic recording in photoformers,” Opt. Commun.174(5-6), 391–404 (2000).
[CrossRef]

Liu, B.

Liu, H. L.

Z. Q. Wang, H. L. Liu, J. H. Guan, and G. G. Mu, “Phase shift joint transform correlator with synthetic discriminant function,” Optik (Stuttg.)111(2), 71–74 (2000).

Mahlab, U.

Márquez, A.

Matalgah, M. M.

Moreno, I.

Mu, G. G.

Z. Q. Wang, H. L. Liu, J. H. Guan, and G. G. Mu, “Phase shift joint transform correlator with synthetic discriminant function,” Optik (Stuttg.)111(2), 71–74 (2000).

Muravsky, L. I.

V. M. Fitio, L. I. Muravsky, and A. L. Stefansky, “Using of random phase masks for image recognition in optical correlator,” Proc. SPIE2647, 224–234 (1995).
[CrossRef]

Nelson, W. L.

R. S. Kashi, W. Turin, and W. L. Nelson, “On-line handwritten signature verification using stroke direction coding,” Opt. Eng.35(9), 2526–2533 (1996).
[CrossRef]

Obukhovsky, V. V.

G. M. Karpov, V. V. Obukhovsky, T. N. Smirnova, and V. V. Lemeshko, “Spatial transfer of matter as a method of holographic recording in photoformers,” Opt. Commun.174(5-6), 391–404 (2000).
[CrossRef]

Raghavan, E. S.

P. K. Rajan and E. S. Raghavan, “Design of synthetic estimation filters using correlation energy minimization,” Opt. Eng.33(6), 1829–1837 (1994).
[CrossRef]

Rajan, P. K.

P. K. Rajan and E. S. Raghavan, “Design of synthetic estimation filters using correlation energy minimization,” Opt. Eng.33(6), 1829–1837 (1994).
[CrossRef]

Réfrégier, P.

Rloux, M.

S. Chang, M. Rloux, and J. Domey, “Face recognition with range images and intensity images,” Opt. Eng.36(4), 1106–1112 (1997).
[CrossRef]

Roberge, D.

D. Roberge, C. Soutar, and B. V. K. Vijaya Kumar, “Optimal trade-off filter for the correlation of fingerprints,” Opt. Eng.38(1), 108–113 (1999).
[CrossRef]

Rosen, J.

Sakhno, O. V.

T. N. Smirnova and O. V. Sakhno, “PPC: self-developing photopolymers for holographic recording,” Proc. SPIE4149, 106–112 (2000).
[CrossRef]

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.)35, 237–246 (1972).

Shamir, J.

Smirnova, T. N.

T. N. Smirnova and O. V. Sakhno, “PPC: self-developing photopolymers for holographic recording,” Proc. SPIE4149, 106–112 (2000).
[CrossRef]

G. M. Karpov, V. V. Obukhovsky, T. N. Smirnova, and V. V. Lemeshko, “Spatial transfer of matter as a method of holographic recording in photoformers,” Opt. Commun.174(5-6), 391–404 (2000).
[CrossRef]

Soutar, C.

D. Roberge, C. Soutar, and B. V. K. Vijaya Kumar, “Optimal trade-off filter for the correlation of fingerprints,” Opt. Eng.38(1), 108–113 (1999).
[CrossRef]

Stefansky, A. L.

V. M. Fitio, L. I. Muravsky, and A. L. Stefansky, “Using of random phase masks for image recognition in optical correlator,” Proc. SPIE2647, 224–234 (1995).
[CrossRef]

Talukder, A.

A. Talukder and D. P. Casasent, “General methodology for simultaneous representation and discrimination of multiple object classes,” Opt. Eng.37(3), 904–913 (1998).
[CrossRef]

A. Talukder and D. P. Casasent, “Pose estimation and transformation of faces,” Proc. SPIE3522, 84–95 (1998).
[CrossRef]

Tang, O.

O. Tang, E. Jager, and T. T. Tschudi, “Off-axis phase-only filter for pattern recognition,” Opt. Eng.29(11), 1421–1426 (1990).
[CrossRef]

Tschudi, T. T.

O. Tang, E. Jager, and T. T. Tschudi, “Off-axis phase-only filter for pattern recognition,” Opt. Eng.29(11), 1421–1426 (1990).
[CrossRef]

Turin, W.

R. S. Kashi, W. Turin, and W. L. Nelson, “On-line handwritten signature verification using stroke direction coding,” Opt. Eng.35(9), 2526–2533 (1996).
[CrossRef]

Vander Lugt, B.

B. Vander Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory10(2), 139–145 (1964).
[CrossRef]

Verrall, S. C.

S. C. Verrall, “Windowed binary joint transform correlation with feedback,” Opt. Eng.38(1), 76–88 (1999).
[CrossRef]

Vijaya Kumar, B. V. K.

D. Roberge, C. Soutar, and B. V. K. Vijaya Kumar, “Optimal trade-off filter for the correlation of fingerprints,” Opt. Eng.38(1), 108–113 (1999).
[CrossRef]

Wang, Z. Q.

Z. Q. Wang, H. L. Liu, J. H. Guan, and G. G. Mu, “Phase shift joint transform correlator with synthetic discriminant function,” Optik (Stuttg.)111(2), 71–74 (2000).

Weaver, C. S.

Wyrowsky, F.

Yzuel, M. J.

Appl. Opt. (8)

Chin. Opt. Lett. (1)

IEEE Trans. Inf. Theory (1)

B. Vander Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory10(2), 139–145 (1964).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

G. M. Karpov, V. V. Obukhovsky, T. N. Smirnova, and V. V. Lemeshko, “Spatial transfer of matter as a method of holographic recording in photoformers,” Opt. Commun.174(5-6), 391–404 (2000).
[CrossRef]

Opt. Eng. (7)

O. Tang, E. Jager, and T. T. Tschudi, “Off-axis phase-only filter for pattern recognition,” Opt. Eng.29(11), 1421–1426 (1990).
[CrossRef]

P. K. Rajan and E. S. Raghavan, “Design of synthetic estimation filters using correlation energy minimization,” Opt. Eng.33(6), 1829–1837 (1994).
[CrossRef]

S. Chang, M. Rloux, and J. Domey, “Face recognition with range images and intensity images,” Opt. Eng.36(4), 1106–1112 (1997).
[CrossRef]

S. C. Verrall, “Windowed binary joint transform correlation with feedback,” Opt. Eng.38(1), 76–88 (1999).
[CrossRef]

A. Talukder and D. P. Casasent, “General methodology for simultaneous representation and discrimination of multiple object classes,” Opt. Eng.37(3), 904–913 (1998).
[CrossRef]

R. S. Kashi, W. Turin, and W. L. Nelson, “On-line handwritten signature verification using stroke direction coding,” Opt. Eng.35(9), 2526–2533 (1996).
[CrossRef]

D. Roberge, C. Soutar, and B. V. K. Vijaya Kumar, “Optimal trade-off filter for the correlation of fingerprints,” Opt. Eng.38(1), 108–113 (1999).
[CrossRef]

Opt. Lett. (1)

Optik (Stuttg.) (2)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.)35, 237–246 (1972).

Z. Q. Wang, H. L. Liu, J. H. Guan, and G. G. Mu, “Phase shift joint transform correlator with synthetic discriminant function,” Optik (Stuttg.)111(2), 71–74 (2000).

Proc. SPIE (3)

A. Talukder and D. P. Casasent, “Pose estimation and transformation of faces,” Proc. SPIE3522, 84–95 (1998).
[CrossRef]

T. N. Smirnova and O. V. Sakhno, “PPC: self-developing photopolymers for holographic recording,” Proc. SPIE4149, 106–112 (2000).
[CrossRef]

V. M. Fitio, L. I. Muravsky, and A. L. Stefansky, “Using of random phase masks for image recognition in optical correlator,” Proc. SPIE2647, 224–234 (1995).
[CrossRef]

Other (2)

R. R. Kallman, “Coding intensity images and phase-only images for use in an optical correlator,” USA Patent 5,214,534, May 25 (1993).

P. M. Hirsh, J. A. Jordan, and L. B. Lezem, “Method of making an object-dependent diffuser,” USA Patent 3,619,022, Nov. 9 (1971).

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Figures (8)

Fig. 1
Fig. 1

IFT-algorithm.

Fig. 2
Fig. 2

Distributions for the object f4 (a) and SP-object θ4,1(b): 1. − object; 2. − modulus of the amplitude of the Fourier-spectrum; 3. − autocorrelation signal.

Fig. 3
Fig. 3

(a) Parameters σ 2(A) and |+1(θ)|max (B) versus the number of iterations N; histograms for (b) ϕ 4,1, (c) ϕ 4,13, (d) ϕ 4,45 calculated for the 1st, 13th, and 45th iterations, respectively.

Fig. 4
Fig. 4

(a) Scheme and (b) photo of experimental setup of Vander Lugt optical-digital correlator: CCD1, PC1, k, Fr, P, Bs, SLM, Mr, Sh, MF, L1, A, L2, CCD2 – camera with a computer for the object domain, collimator, Fresnel rhomb, polarizer, beam splitter, spatial light modulator LC-R 2500, mirror, shutter, matched filter, Fourier lens, analyzer, lens, a camera and a computer for the Fourier domain and correlation plane, respectively.

Fig. 5
Fig. 5

Objects f1− f4 (a) and fragments of object f1 (b) for various numbers of rearrangements: 1. – k = 0; 2. – k = 150; 3. – k = 300; 4. – k = 600.

Fig. 6
Fig. 6

Experimental results for object f1 (left) and SP-object θ1,1(right): (a) – dependence of the intensity of the cross-correlation signals on k; (b,c) – shape of correlation signals; (d,e) – shape of Fourier-spectra.

Fig. 7
Fig. 7

(a,b) – fragments of the objects f2 and f4 after phase-only encoding with superposed grating; (c,d) – on-axis Fourier-spectra; (e,f) – off-axis Fourier-spectra.

Fig. 8
Fig. 8

Dependence of the intensity of the correlation signals on the parameter k for object f1 (a) and SP-object θ11 (b) for (1) on-axis and (2) off-axis matched filtering.

Tables (2)

Tables Icon

Table 1 Object and SP-object Parameters

Tables Icon

Table 2 Pattern Recognition Results

Equations (2)

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Θ off (υ,ν)= +1 {exp[i(φ(x,y)+2π(x υ o +y ν o ))]} =Θ(υ,ν)δ(υ υ o ,ν ν o )=Θ(υ υ o ,ν ν o ),
SNR(i,j)= K 4 [(K|i K 2 |)×(K|j K 2 |)] ,

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