Abstract

A new heuristic filter based on the optimum filter for disjoint noise developed by Javidi and Wang [J. Opt. Soc. Am. A 11, 2604 (1995)] is presented. In this new filter a number of optimum filters built from single training images are combined linearly by use of the synthetic discriminant function (SDF) approach into a distortion-invariant filter for disjoint noise. Like the traditional SDF approach, this summation technique makes it possible to control the height of the correlation peak easily, for example, if a uniform filter response is needed. The filter is compared with the distortion-invariant version of the optimum filter on images with low contrast and high levels of nonoverlapping clutter. The new filter shows good results, demonstrating that it is, with very simple heuristic methods, possible to improve the performance of distortion-invariant filters for nonoverlapping noise.

© 1998 Optical Society of America

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References

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1998 (1)

H. Sjöberg, B. Noharet, L. Wosinski, R. Hey, “A compact optical correlator: preprocessing and filter encoding strategies applied to images with varying illumination,” Opt. Eng. 37, 1316–1324 (1998).
[CrossRef]

1996 (1)

1995 (1)

1994 (2)

J. Figue, Ph. Réfrégier, “Angle determination of airplanes by multicorrelation technique with optimal trade-off synthetic discriminant filters,” Opt. Eng. 33, 1821–1828 (1994).
[CrossRef]

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

1992 (1)

1990 (1)

1987 (1)

1986 (1)

1980 (1)

Arsenault, H.

H. Arsenault, D. Asselin, A. Bergeron, S. Chang, P. Gagne, O. Gualdron, “Towards totally invariant optical pattern recognition,” in Vol. PM12 of SPIE Institute Series, Euro-American Workshop on Optical Pattern Recognition, B. Javidi, Ph. Réfrégier, eds. (SPIE, Bellingham, Wash., 1994), pp. 113–136.

Arsenault, H. H.

Asselin, D.

H. Arsenault, D. Asselin, A. Bergeron, S. Chang, P. Gagne, O. Gualdron, “Towards totally invariant optical pattern recognition,” in Vol. PM12 of SPIE Institute Series, Euro-American Workshop on Optical Pattern Recognition, B. Javidi, Ph. Réfrégier, eds. (SPIE, Bellingham, Wash., 1994), pp. 113–136.

Bergeron, A.

H. Arsenault, D. Asselin, A. Bergeron, S. Chang, P. Gagne, O. Gualdron, “Towards totally invariant optical pattern recognition,” in Vol. PM12 of SPIE Institute Series, Euro-American Workshop on Optical Pattern Recognition, B. Javidi, Ph. Réfrégier, eds. (SPIE, Bellingham, Wash., 1994), pp. 113–136.

Casasent, D.

Chang, S.

H. Arsenault, D. Asselin, A. Bergeron, S. Chang, P. Gagne, O. Gualdron, “Towards totally invariant optical pattern recognition,” in Vol. PM12 of SPIE Institute Series, Euro-American Workshop on Optical Pattern Recognition, B. Javidi, Ph. Réfrégier, eds. (SPIE, Bellingham, Wash., 1994), pp. 113–136.

Figue, J.

J. Figue, Ph. Réfrégier, “Angle determination of airplanes by multicorrelation technique with optimal trade-off synthetic discriminant filters,” Opt. Eng. 33, 1821–1828 (1994).
[CrossRef]

Gagne, P.

H. Arsenault, D. Asselin, A. Bergeron, S. Chang, P. Gagne, O. Gualdron, “Towards totally invariant optical pattern recognition,” in Vol. PM12 of SPIE Institute Series, Euro-American Workshop on Optical Pattern Recognition, B. Javidi, Ph. Réfrégier, eds. (SPIE, Bellingham, Wash., 1994), pp. 113–136.

Gualdron, O.

O. Gualdron, H. H. Arsenault, “Optimum rotation-invariant filter for disjoint-noise scenes,” Appl. Opt. 35, 2507–2513 (1996).
[CrossRef] [PubMed]

H. Arsenault, D. Asselin, A. Bergeron, S. Chang, P. Gagne, O. Gualdron, “Towards totally invariant optical pattern recognition,” in Vol. PM12 of SPIE Institute Series, Euro-American Workshop on Optical Pattern Recognition, B. Javidi, Ph. Réfrégier, eds. (SPIE, Bellingham, Wash., 1994), pp. 113–136.

Hester, C. F.

Hey, R.

H. Sjöberg, B. Noharet, L. Wosinski, R. Hey, “A compact optical correlator: preprocessing and filter encoding strategies applied to images with varying illumination,” Opt. Eng. 37, 1316–1324 (1998).
[CrossRef]

Javidi, B.

Kumar, B.

Mahalanobis, A.

Noharet, B.

H. Sjöberg, B. Noharet, L. Wosinski, R. Hey, “A compact optical correlator: preprocessing and filter encoding strategies applied to images with varying illumination,” Opt. Eng. 37, 1316–1324 (1998).
[CrossRef]

Réfrégier, Ph.

J. Figue, Ph. Réfrégier, “Angle determination of airplanes by multicorrelation technique with optimal trade-off synthetic discriminant filters,” Opt. Eng. 33, 1821–1828 (1994).
[CrossRef]

Ph. Réfrégier, “Filter design for optical pattern recognition: multicriteria optimization approach,” Opt. Lett. 15, 854–865 (1990).
[CrossRef] [PubMed]

Sjöberg, H.

H. Sjöberg, B. Noharet, L. Wosinski, R. Hey, “A compact optical correlator: preprocessing and filter encoding strategies applied to images with varying illumination,” Opt. Eng. 37, 1316–1324 (1998).
[CrossRef]

Wang, J.

Wosinski, L.

H. Sjöberg, B. Noharet, L. Wosinski, R. Hey, “A compact optical correlator: preprocessing and filter encoding strategies applied to images with varying illumination,” Opt. Eng. 37, 1316–1324 (1998).
[CrossRef]

Appl. Opt. (4)

J. Opt. Soc. A (1)

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

J. Opt. Soc. Am. A (2)

Opt. Eng. (2)

H. Sjöberg, B. Noharet, L. Wosinski, R. Hey, “A compact optical correlator: preprocessing and filter encoding strategies applied to images with varying illumination,” Opt. Eng. 37, 1316–1324 (1998).
[CrossRef]

J. Figue, Ph. Réfrégier, “Angle determination of airplanes by multicorrelation technique with optimal trade-off synthetic discriminant filters,” Opt. Eng. 33, 1821–1828 (1994).
[CrossRef]

Opt. Lett. (1)

Other (1)

H. Arsenault, D. Asselin, A. Bergeron, S. Chang, P. Gagne, O. Gualdron, “Towards totally invariant optical pattern recognition,” in Vol. PM12 of SPIE Institute Series, Euro-American Workshop on Optical Pattern Recognition, B. Javidi, Ph. Réfrégier, eds. (SPIE, Bellingham, Wash., 1994), pp. 113–136.

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Figures (9)

Fig. 1
Fig. 1

Original image and one example from each test set: (a) the starting image, (b) example from test set 1, and (c) example from test set 2.

Fig. 2
Fig. 2

(a) Correlation-peak intensity and correlation-noise level for the six input images. The circles represent the correlation-peak values, and the crosses the maximum correlation-noise levels. (b) PCR’s for the six input images.

Fig. 3
Fig. 3

Performance of the SDF optimum filter evaluated on test set 1 (without clutter): (a) Correlation-peak intensity and correlation noise level for the 41 test images. The circles represent the correlation-peak values, and the crosses the maximum correlation noise levels. (b) PCR’s for the 41 test images.

Fig. 4
Fig. 4

Performance of the SDF optimum filter evaluated on test set 1 (without clutter): (a) Correlation-peak intensity and correlation- noise level for the 41 test images. The circles represent the correlation-peak values, and the crosses the maximum correlation-noise levels. (b) PCR’s for the 41 test images.

Fig. 5
Fig. 5

Performance of the SDF optimum filter evaluated on test set 2 (with clutter): (a) Correlation-peak intensity and correlation-noise level for the 41 test images. The circles represent the correlation-peak values, and the crosses the maximum correlation-noise levels. (b) PCR’s for the 41 test images.

Fig. 6
Fig. 6

Performance of the SDF optimum filter evaluated on its training set (without clutter): (a) Correlation-peak intensity and correlation-noise level for the 41 training images. The circles represent the correlation-peak values, and the crosses the maximum correlation-noise levels. (b) PCR’s for the 41 training images.

Fig. 7
Fig. 7

Performance of the composite optimum filter evaluated on test set 1 (without clutter): (a) Correlation-peak intensity and correlation-noise level for the 41 test images. The circles represent the correlation-peak values, and the crosses the maximum correlation- noise levels. (b) PCR’s for the 41 test images.

Fig. 8
Fig. 8

Performance of the composite optimum filter evaluated on test set 2 (with clutter): (a) Correlation-peak intensity and correlation- noise level for the 41 test images. The circles represent the correlation-peak values, and the crosses the maximum correlation noise levels. (b) PCR’s for the 41 test images.

Fig. 9
Fig. 9

Performance of the MACE filter evaluated on (a) test set 1, i.e., without clutter (circles represent the correlation-peak values and crosses the maximum correlation-noise levels) and (b) on one representative image from test set 2 (correlation intensity).

Tables (1)

Tables Icon

Table 1 Summary of the Filter Performance with Test Set 2

Equations (9)

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H MACE = Dx x t Dx - 1 c ,
H i = X i * + mW i * | X i + mW i | 2 + 1 2 π   | W i | 2   *   N ,
h = x f a .
x t h = c .
a = x t x f - 1 c .
H opt * ω = i = 1 N R i ω + m b W 1 i ω i = 1 N   | R i ω + m b W 1 i ω | 2 + 1 2 π   W 2 i ω   *   N b 0 ω + 1 2 π   | W r ω | 2   *   N a 0 ω ,
W 1 i ω = | W 0 ω | 2 W 0 0 - W ri ω ,
W 2 i ω = | W 0 ω | 2 + | W ri ω | 2 - 2 | W 0 ω | 2 W ri ω W 0 0 ,
H opt * ω = i = 1 N R i ω + m b W 1 i ω i = 1 N | R i ω + m b W 1 i ω | 2 + 1 2 π   W 2 i ω   *   N b 0 ω .

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