Abstract

Generalized correlation filters are proposed to improve recognition of a linearly distorted object embedded in a nonoverlapping background when the input scene is degraded with a linear system and additive noise. Several performance criteria defined for the nonoverlapping signal model are used for the design of filters. The derived filters take into account information about an object to be recognized, disjoint background, noise, and linear degradations of the target and the input scene. Computer simulation results obtained with the proposed filters are discussed and compared with those of various correlation filters in terms of discrimination capability, location errors, and tolerance to input noise.

© 2007 Optical Society of America

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2006 (3)

V. H. Diaz-Ramirez, V. Kober, and J. Alvarez-Borrego "Pattern recognition with an adaptive joint transform correlator," Appl. Opt. 45, 5929-5941 (2006).
[CrossRef]

J. A. González-Fraga, V. Kober, and J. Álvarez-Borrego, "Adaptive synthetic discriminant function filters for pattern recognition," Opt. Eng. 45, 057005 (1-10) (2006).
[CrossRef]

A. Vargas, R. Figueroa, J. Campos, C. San Martín, and J. Marileo, "Reconocimiento de formas con un correlador óptico aplicado a imágenes desenfocadas: invariancia por medio de la selección y fusión de bandas," Rev. Mex. Fis. 53, 199-204 (2006).

2004 (1)

R. Navarro, O. Nestares, and J. J. Valles, "Bayesian pattern recognition in optically degraded noisy images," J. Opt. A 6, 36-42 (2004).
[CrossRef]

2003 (1)

A. Vargas, J. Campos, C. S. Martin, and N. Vera, "Filter design of composite trade-off filter with support regions to obtain invariant pattern recognition with defocused images," Opt. Lasers Eng. 40, 67-79 (2003).
[CrossRef]

2002 (1)

2001 (2)

2000 (1)

F. Chan, N. Towghi, L. Pan, and B. Javidi, "Distortion-tolerant minimum-mean-squared-error filter for detecting noisy targets in environmental degradation," Opt. Eng. 39, 2092-2100 (2000).
[CrossRef]

1999 (1)

1998 (1)

J. Flusser and T. Suk, "Degraded image analysis: an invariant approach," IEEE Trans. Pattern Anal. Mach. Intell. 20, 1-14 (1998).
[CrossRef]

1997 (2)

I. Juvells, S. Vallmitjana, E. Martin-Badosa, and A. Carnicer, "Optical pattern recognition in motion acquired scenes using a binary joint transform correlation," J. Mod. Opt. 44, 313-326 (1997).
[CrossRef]

F. Gaudail and P. Réfrégier, "Optimal target tracking on image sequences with a deterministic background," J. Opt. Soc. Am. A 14, 3197-3207 (1997).
[CrossRef]

1996 (4)

B. Javidi, F. Parchekani, and G. Zhang, "Minimum-mean-square-error filters for detecting a noisy target in background noise," Appl. Opt. 35, 6964-6975 (1996).
[CrossRef] [PubMed]

A. Carnicer, S. Vallmitjana, J. de F. Moneo, and I. Juvells, "Implementation of an algorithm for detecting patterns in defocused scenes using binary joint transform correlation," Opt. Commun. 130, 327-336 (1996).
[CrossRef]

V. Kober and J. Campos, "Accuracy of location measurement of a noisy target in a nonoverlapping background," J. Opt. Soc. Am. A 13, 1653-1666 (1996).
[CrossRef]

J. Flusser, T. Suk, and S. Saic, "Recognition of blurred images by the method of moments," IEEE Trans. Image Process. 5, 533-538 (1996).
[CrossRef] [PubMed]

1994 (2)

B. Javidi and J. Wang, "Design of filters to detect a noisy target in nonoverlapping background noise," J. Opt. Soc. Am. A 11, 2604-2612 (1994).
[CrossRef]

J. Campos, S. Bosch, J. Sallent, and A. Berzal, "Experimental implementation of correlation filters for optical pattern recognition in defocused images," J. Opt. 25, 25-31 (1994).
[CrossRef]

1993 (1)

1992 (2)

1991 (1)

J. Campos, S. Bosch, and J. Sallent, "Optical pattern recognition in defocused images using correlation filters," Opt. Commun. 82, 370-379 (1991).
[CrossRef]

1990 (3)

J. Biemond, R. L. Lagendijk, and R. M. Mersereau, "Iterative methods for image deblurring," Proc. IEEE 78, 856-883 (1990).
[CrossRef]

M. I. Sezan and A. M. Tekalp, "Survey of recent developments in digital image restoration," Opt. Eng. 29, 393-404 (1990).
[CrossRef]

B. V. K. Vijaya-Kumar and L. Hassebrook, "Performance measures for correlation filters," Appl. Opt. 29, 2997-3006 (1990).
[CrossRef]

1987 (1)

1984 (2)

1964 (1)

A. B. VanderLugt, "Signal detection by complex filtering," IEEE Trans. Inf. Theory IT-10, 139-145 (1964).
[CrossRef]

Appl. Opt. (8)

IEEE Trans. Image Process. (1)

J. Flusser, T. Suk, and S. Saic, "Recognition of blurred images by the method of moments," IEEE Trans. Image Process. 5, 533-538 (1996).
[CrossRef] [PubMed]

IEEE Trans. Inf. Theory (1)

A. B. VanderLugt, "Signal detection by complex filtering," IEEE Trans. Inf. Theory IT-10, 139-145 (1964).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

J. Flusser and T. Suk, "Degraded image analysis: an invariant approach," IEEE Trans. Pattern Anal. Mach. Intell. 20, 1-14 (1998).
[CrossRef]

J. Mod. Opt. (1)

I. Juvells, S. Vallmitjana, E. Martin-Badosa, and A. Carnicer, "Optical pattern recognition in motion acquired scenes using a binary joint transform correlation," J. Mod. Opt. 44, 313-326 (1997).
[CrossRef]

J. Opt. (1)

J. Campos, S. Bosch, J. Sallent, and A. Berzal, "Experimental implementation of correlation filters for optical pattern recognition in defocused images," J. Opt. 25, 25-31 (1994).
[CrossRef]

J. Opt. A (1)

R. Navarro, O. Nestares, and J. J. Valles, "Bayesian pattern recognition in optically degraded noisy images," J. Opt. A 6, 36-42 (2004).
[CrossRef]

J. Opt. Soc. Am. A (7)

Opt. Commun. (2)

A. Carnicer, S. Vallmitjana, J. de F. Moneo, and I. Juvells, "Implementation of an algorithm for detecting patterns in defocused scenes using binary joint transform correlation," Opt. Commun. 130, 327-336 (1996).
[CrossRef]

J. Campos, S. Bosch, and J. Sallent, "Optical pattern recognition in defocused images using correlation filters," Opt. Commun. 82, 370-379 (1991).
[CrossRef]

Opt. Eng. (3)

M. I. Sezan and A. M. Tekalp, "Survey of recent developments in digital image restoration," Opt. Eng. 29, 393-404 (1990).
[CrossRef]

F. Chan, N. Towghi, L. Pan, and B. Javidi, "Distortion-tolerant minimum-mean-squared-error filter for detecting noisy targets in environmental degradation," Opt. Eng. 39, 2092-2100 (2000).
[CrossRef]

J. A. González-Fraga, V. Kober, and J. Álvarez-Borrego, "Adaptive synthetic discriminant function filters for pattern recognition," Opt. Eng. 45, 057005 (1-10) (2006).
[CrossRef]

Opt. Lasers Eng. (1)

A. Vargas, J. Campos, C. S. Martin, and N. Vera, "Filter design of composite trade-off filter with support regions to obtain invariant pattern recognition with defocused images," Opt. Lasers Eng. 40, 67-79 (2003).
[CrossRef]

Opt. Lett. (1)

Proc. IEEE (1)

J. Biemond, R. L. Lagendijk, and R. M. Mersereau, "Iterative methods for image deblurring," Proc. IEEE 78, 856-883 (1990).
[CrossRef]

Rev. Mex. Fis. (1)

A. Vargas, R. Figueroa, J. Campos, C. San Martín, and J. Marileo, "Reconocimiento de formas con un correlador óptico aplicado a imágenes desenfocadas: invariancia por medio de la selección y fusión de bandas," Rev. Mex. Fis. 53, 199-204 (2006).

Other (7)

M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (Institute of Physics Publishing, 1998).
[CrossRef]

W. K. Pratt, Digital Image Processing (Wiley, 1991).

L. P. Yaroslavsky, Fundamentals of Digital Optics (Springer, 1996).

J. S. Lim, Two-Dimensional Signal and Image Processing (Prentice-Hall PTR, 1990).

B. V. K. Vijaya-Kumar, A. Mahalanobis, and R. D. Juday, Correlation Pattern Recognition (Cambridge U. Press, 2005).
[CrossRef]

L. P. Yaroslavsky, "The theory of optimal methods for localization of objects in pictures," in Progress in Optics, E.Wolf, ed., Vol. XXXIII (Elsevier, 1993), pp. 145-201.
[CrossRef]

V. Kober, Y. K. Seong, T. S. Choi, and I. A. Ovseyevich, "Trade-off filters for optical pattern recognition with nonoverlapping target and scene noise," Pattern Recog. Image Anal. 10, 149-151 (2000).

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Figures (13)

Fig. 1
Fig. 1

(a) Test real input scene. (b) Test stochastic input scene. (c) Objects used in experiments.

Fig. 2
Fig. 2

Performance of correlation filters in terms of DC when the standard deviation of nonoverlapping background is 0.27 and the mean value is varied for: (a) deterministic scene in Fig. 1a, (b) stochastic scene in Fig. 1b.

Fig. 3
Fig. 3

Test scenes defocused with D = 7 and corrupted additionally by white noise with σ n = 0.12 : (a) scene in Fig. 1a, (b) scene in Fig. 1b.

Fig. 4
Fig. 4

Performance of correlation filters when the input real scene in Fig. 1a is defocused with different values of D: (a) DC versus D, (b) LE versus D.

Fig. 5
Fig. 5

Tolerance of correlation filters for pattern recognition in blurred and noisy real scenes: (a) DC versus σ n with D = 7 , (b) LE versus σ n with D = 7 , (c) DC versus σ n with D = 11 , (d) LE versus σ n with D = 11 .

Fig. 6
Fig. 6

Performance of proposed filters designed with D = 7 for pattern recognition in the deterministic scene blurred with different values of D: (a) DC versus D, (b) LE versus D, (c) DC versus σ n when the scene blurred with D = 3 , (d) LE versus σ n when the scene blurred with D = 3 .

Fig. 7
Fig. 7

Recognition of blurred object in defocused and noisy deterministic scene: (a) DC versus σ n with D = 3 , (b) LE versus σ n with D = 3 , (c) DC versus σ n with D = 7 , (d) LE versus σ n with D = 7 .

Fig. 8
Fig. 8

Performance of correlation filters for pattern recognition in restored deterministic scene, which was originally defocused and corrupted by additive noise: (a) DC versus σ n with D = 7 , (b) LE versus σ n with D = 7 , (c) DC versus σ n with D = 11 , (d) LE versus σ n with D = 11 .

Fig. 9
Fig. 9

Illustration of linear degradation by a uniform target motion in 3   pixels from left to right.

Fig. 10
Fig. 10

Test scenes in Fig. 1 degraded with M = 9 and D = 7 and corrupted additionally by white noise with σ n = 0.12 : (a) deterministic scene, (b) stochastic scene.

Fig. 11
Fig. 11

Performance of correlation filters for recognition of a moving target in the input scene shown in Fig. 1a: (a) DC versus M, (b) LE versus M for the scene.

Fig. 12
Fig. 12

Recognition of a moving object in defocused with D = 7 and noisy deterministic scene: (a) DC versus σ n with M = 5 , (b) LE versus σ n with M = 5 , (c) DC versus σ n with M = 9 , (d) LE versus σ n with M = 9 .

Fig. 13
Fig. 13

Recognition of a moving object in defocused with D = 7 and noisy stochastic scene: (a) DC versus σ n with M = 5 , (b) LE versus σ n with M = 5 , (c) DC versus σ n with M = 9 , (d) LE versus σ n with M = 9 .

Tables (3)

Tables Icon

Table 1 Filter Performance with Respect to DC and LE for Recognition of Target in Degraded Scene

Tables Icon

Table 2 Filter Performance with Respect to DC and LE for Recognition of Target in Noisy and Degraded Scene with D = 11

Tables Icon

Table 3 Filter Performance with Respect to DC and LE for Recognition of Moving Target in Input Scene

Equations (40)

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POE = E { y ( x 0 , x 0 ) } 2 E { [ y ( x , x 0 ) ] 2 ¯ } ,
SNR = E { y ( x 0 , x 0 ) } 2 Var { y ( x , x 0 ) } ¯ ,
s ( x , x 0 ) = [ t ( x x 0 ) + b ( x , x 0 ) ] h LD ( x ) + n ( x ) ,
b ( x , x 0 ) = b ( x ) w ( x , x 0 ) .
E { y ( x , x 0 ) } = 1 2 π [ T ( ω ) + μ b W ( ω ) ] H LD ( ω ) H ( ω ) exp [ j ω ( x x 0 ) ] d ω ,
E { y ( x 0 , x 0 ) } 2 = 1 4 π 2 [ T ( ω ) + μ b W ( ω ) ] H LD ( ω ) H ( ω ) d ω 2 .
E { [ y ( x , x 0 ) ] 2 ¯ } = Var { y ( x , x 0 ) } ¯ + E { y ( x , x 0 ) } 2 ¯ .
Var { y ( x , x 0 ) } ¯ = 1 2 π { [ α 2 π B 0 ( ω ) W ( ω ) 2 ] H LD ( ω ) 2 + N ( ω ) } H ( ω ) 2 d ω ,
E { y ( x , x 0 ) } 2 ¯ = 1 2 π α T ( ω ) + μ b W ( ω ) 2 H LD ( ω ) 2 H ( ω ) 2 d ω ,
E { [ y ( x , x 0 ) ] 2 ¯ } = 1 2 π { α [ T ( ω ) + μ b W ( ω ) 2 + 1 2 π B 0 ( ω ) W ( ω ) 2 ] H LD ( ω ) 2 + N ( ω ) } H ( ω ) 2 d ω .
POE = ( 2 π ) 1 [ T ( ω ) + μ b W ( ω ) ] H LD ( ω ) H ( ω ) d ω 2 { α [ T ( ω ) + μ b W ( ω ) 2 + 1 2 π B 0 ( ω ) W ( ω ) 2 ] H LD ( ω ) 2 + N ( ω ) } H ( ω ) 2 d ω .
GOF LD ( ω ) = { [ T ( ω ) + μ b W ( ω ) ] H LD ( ω ) } * α [ T ( ω ) + μ b W ( ω ) 2 + 1 2 π B 0 ( ω ) W ( ω ) 2 ] H LD ( ω ) 2 + N ( ω ) ,
SNR = [ T ( ω ) + μ b W ( ω ) ] H LD ( ω ) H ( ω ) d ω 2 2 π { [ α 2 π B 0 ( ω ) W ( ω ) 2 ] H LD ( ω ) 2 + N ( ω ) } H ( ω ) 2 d ω .
GMF LD ( ω ) = { [ T ( ω ) + μ b W ( ω ) ] H LD ( ω ) } * [ α 2 π B 0 ( ω ) W ( ω ) 2 ] H LD ( ω ) 2 + N ( ω ) .
η H = E { y ( x , x 0 ) } 2 d x E { s ( x , x 0 ) } 2 d x = [ T ( ω ) + μ b W ( ω ) ] H LD ( ω ) 2 H ( ω ) 2 d ω [ T ( ω ) + μ b W ( ω ) ] H LD ( ω ) 2 d ω .
GPOF LD ( ω ) = [ T ( ω ) + μ b W ( ω ) ] * T ( ω ) + μ b W ( ω ) exp [ j θ H LD ( ω ) ] ,
s ( x , x 0 ) = [ t ( x x 0 ) h TD ( x ) + b ( x ) w TD ( x x 0 ) ] h LD ( x ) + n ( x ) ,
E { y ( x , x 0 ) } = 1 2 π [ T ( ω ) H TD ( ω ) + μ b W TD ( ω ) ] H LD ( ω ) H ( ω ) exp [ j ω ( x x 0 ) ] d ω ,
E { y ( x 0 , x 0 ) } 2 = 1 4 π 2 [ T ( ω ) H TD ( ω ) + μ b W TD ( ω ) ] H LD ( ω ) H ( ω ) d ω 2 .
Var { y ( x , x 0 ) } ¯ = 1 2 π { [ α 2 π B 0 ( ω ) W TD ( ω ) 2 ] H LD ( ω ) 2 + N ( ω ) } H ( ω ) 2 d ω ,
E { y ( x , x 0 ) } 2 ¯ = 1 2 π α T ( ω ) H TD ( ω ) + μ b W TD ( ω ) 2 H LD ( ω ) 2 H ( ω ) 2 d ω .
POE = ( 2 π ) 1 [ T ( ω ) H TD ( ω ) + μ b W TD ( ω ) ] H LD ( ω ) H ( ω ) d ω 2 { α [ T ( ω ) H TD ( ω ) + μ b W TD ( ω ) 2 + 1 2 π B 0 ( ω ) W TD ( ω ) 2 ] H LD ( ω ) 2 + N ( ω ) } H ( ω ) 2 d ω .
GOF LD ̱ TD ( ω ) = { [ T ( ω ) H TD ( ω ) + μ b W TD ( ω ) ] H LD ( ω ) } * α [ T ( ω ) H TD ( ω ) + μ b W TD ( ω ) 2 + 1 2 π B 0 ( ω ) W TD ( ω ) 2 ] H LD ( ω ) 2 + N ( ω ) .
SNR = [ T ( ω ) H TD ( ω ) + μ b W TD ( ω ) ] H LD ( ω ) H ( ω ) d ω 2 2 π { [ α 2 π B 0 ( ω ) W TD ( ω ) 2 ] H LD ( ω ) 2 + N ( ω ) } H ( ω ) 2 d ω .
GMF LD ̱ TD = { [ T ( ω ) H TD ( ω ) + μ b W TD ( ω ) ] H LD ( ω ) } * [ α 2 π B 0 ( ω ) W TD ( ω ) 2 ] H LD ( ω ) 2 + N ( ω ) .
GPOF LD ̱ TD ( ω ) = [ T ( ω ) H TD ( ω ) + μ b W TD ( ω ) ] * T ( ω ) H TD ( ω ) + μ b W TD ( ω ) exp [ j θ H LD ( ω ) ] .
DC = 1 C B ( 0 ) 2 C T ( 0 ) 2 ,
LE = ( x T x ̃ T ) 2 + ( y T y ̃ T ) 2 ,
H W ( ω ) = S s ( ω ) N ( ω ) S s ( ω ) H LD ( ω ) ,
h TM ( x ) = { 1 M , if 0 x M = V T 0 , otherwise } .
Var { y ( x , x 0 ) } = Var { r b ( x , x 0 ) } + Var { r n ( x ) } .
Var { r b ( x , x 0 ) } = E { r b ( x , x 0 ) E { r b ( x , x 0 ) } 2 } = E { b 0 ( x ξ ) w ( x x 0 ξ ) h u ( ξ ) ( b 0 ( x β ) w ( x x 0 β ) h u ( β ) ) * d ξ d β } ,
Var { r b ( x , x 0 ) } = R b ( β ξ ) w ( x x 0 ξ ) h u ( ξ ) ( w ( x x 0 β ) h u ( β ) ) * d ξ d β = [ R b ( γ ) ( h u ( γ ) w ( x x 0 γ ) ) ( h u ( γ ) w ( x x 0 + γ ) ) * ] γ = 0 .
Var { r b ( x , x 0 ) } = 1 2 π B 0 ( ω ) ( 1 2 π H u ( ω ) W ( ω ) exp [ j ( x x 0 ) ω ] ) × ( 1 2 π H u ( ω ) W ( ω ) exp [ j ( x x 0 ) ω ] ) * d ω = 1 ( 2 π ) 3 B 0 ( ω ) H u ( ω 1 ) × H u * ( ω 2 ) W ( ω 1 ω ) W * ( ω 2 ω ) exp [ j ( x x 0 ) ( ω 1 ω 2 ) ] d ω d ω 1 d ω 2 ,
Y b ( ω ) ¯ = [ α 2 π B 0 ( ω ) W ( ω ) 2 ] H u ( ω ) 2 .
Y b ( ω ) ¯ = α 2 π B 0 ( ω ) W ( ω ) 2 .
Var { y ( x , x 0 ) } ¯ = Var { r b ( x , x 0 ) } ¯ + Var { r n ( x ) } = 1 2 π [ ( α 2 π B 0 ( ω ) W ( ω ) 2 ) H LD ( ω ) 2 + N ( ω ) ] H ( ω ) 2 d ω .
E { y ( x , x 0 ) } 2 = [ t ( x x 0 ) + μ b w ( x x 0 ) ] h u ( x ) 2 .
E { y ( x , x 0 ) } 2 d x = 1 2 π T ( ω ) + μ b W ( ω ) 2 H u ( ω ) 2 d ω .
E { y ( x , x 0 ) } 2 ¯ = 1 L E [ y ( x , x 0 ) ] 2 d x = 1 2 π α T ( ω ) + μ b W ( ω ) 2 H LD ( ω ) 2 H ( ω ) 2 d ω .

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