Abstract

Until now, most optical pattern recognition filters have been designed to process one image at a time. However, in image sequences, successive frames are highly correlated, so that it is useful to take this correlation into account while designing the filter. We develop a target tracking processor following this method. The images are assumed to consist of a moving object appearing against a moving background. A model that takes into account two successive frames is designed. From this model we determine the maximum-likelihood processor for tracking the object from one frame to the next. Since this processor is based on correlation operations, it could be implemented on a hybrid optoelectronic system that makes use of the rapidity of optical correlation.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Vander Lugt, “Signal detection by complex filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
    [Crossref]
  2. B. V. K. VijayaKumar, C. Hendrix, D. W. Carlson, “Tradeoffs in the design of correlation filters,” in Optical Pattern Recognition, Critical Reviews Vol. CR40, J. L. Horner, B. Javidi, eds. (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1992), pp. 191–215.
  3. B. Javidi, J. Wang, “Limitation of the classic definition of the correlation signal-to-noise ratio in optical pattern recognition with disjoint signal and scene noise,” Appl. Opt. 31, 6826–6829 (1992).
    [Crossref] [PubMed]
  4. F. Goudail, V. Laude, Ph. Réfrégier, “Influence of non-overlapping noise on regularized linear filters for pattern recognition,” Opt. Lett. 20, 2237–2239 (1995).
    [Crossref]
  5. Ph. Réfrégier, B. Javidi, G. Zhang, “Minimum mean-square-error filter for pattern recognition with spatially disjoint signal and scene noise,” Opt. Lett. 18, 1453–1456 (1993).
    [Crossref] [PubMed]
  6. B. Javidi, Ph. Réfrégier, P. Willet, “Optimum receiver design for pattern recognition with nonoverlapping target and scene noise,” Opt. Lett. 18, 1660–1662 (1993).
    [Crossref] [PubMed]
  7. F. Goudail, Ph. Réfrégier, “Optimal detection of a target with random gray levels on a spatially disjoint noise,” Opt. Lett. 21, 495–497 (1996).
    [Crossref] [PubMed]
  8. R. O. Duda, P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).
  9. W. K. Pratt, “Image detection and registration,” in Digital Image Processing (Wiley, New York, 1978), pp. 562–566.
  10. Ph. Réfrégier, “Optimal trade-off filters for noise robustness, sharpness of the correlation peak and Horner efficiency,” Opt. Lett. 16, 829–831 (1991).
    [Crossref]
  11. J. L. Horner, P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23, 812–816 (1984).
    [Crossref] [PubMed]
  12. S. Tonda, Ph. Réfrégier, “Three-dimensional attitude estimation and tracking with linear normalized optimal filtering,” Opt. Eng. 36, 1145–1151 (1997).
    [Crossref]
  13. O. Germain, Ph. Réfrégier, “Optimal snake-based segmentation of a random luminance target on a spatially disjoint background,” Opt. Lett. 21, 1845–1847 (1996).
    [Crossref] [PubMed]
  14. Ph. Réfrégier, O. Germain, T. Gaidon, “Optimal snake segmentation of target and background with independent gamma density probabilities, application to speckled and preprocessed images,” Opt. Commun. 137, 382–388 (1997).
    [Crossref]
  15. M. Kass, A. Witkin, D. Terzopoulos, “Snakes: active contour models,” Int. J. Comput. Vis. 1, 321–331 (1988).
    [Crossref]

1997 (2)

S. Tonda, Ph. Réfrégier, “Three-dimensional attitude estimation and tracking with linear normalized optimal filtering,” Opt. Eng. 36, 1145–1151 (1997).
[Crossref]

Ph. Réfrégier, O. Germain, T. Gaidon, “Optimal snake segmentation of target and background with independent gamma density probabilities, application to speckled and preprocessed images,” Opt. Commun. 137, 382–388 (1997).
[Crossref]

1996 (2)

1995 (1)

1993 (2)

1992 (1)

1991 (1)

1988 (1)

M. Kass, A. Witkin, D. Terzopoulos, “Snakes: active contour models,” Int. J. Comput. Vis. 1, 321–331 (1988).
[Crossref]

1984 (1)

1964 (1)

A. Vander Lugt, “Signal detection by complex filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[Crossref]

Carlson, D. W.

B. V. K. VijayaKumar, C. Hendrix, D. W. Carlson, “Tradeoffs in the design of correlation filters,” in Optical Pattern Recognition, Critical Reviews Vol. CR40, J. L. Horner, B. Javidi, eds. (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1992), pp. 191–215.

Duda, R. O.

R. O. Duda, P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).

Gaidon, T.

Ph. Réfrégier, O. Germain, T. Gaidon, “Optimal snake segmentation of target and background with independent gamma density probabilities, application to speckled and preprocessed images,” Opt. Commun. 137, 382–388 (1997).
[Crossref]

Germain, O.

Ph. Réfrégier, O. Germain, T. Gaidon, “Optimal snake segmentation of target and background with independent gamma density probabilities, application to speckled and preprocessed images,” Opt. Commun. 137, 382–388 (1997).
[Crossref]

O. Germain, Ph. Réfrégier, “Optimal snake-based segmentation of a random luminance target on a spatially disjoint background,” Opt. Lett. 21, 1845–1847 (1996).
[Crossref] [PubMed]

Gianino, P. D.

Goudail, F.

Hart, P. E.

R. O. Duda, P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).

Hendrix, C.

B. V. K. VijayaKumar, C. Hendrix, D. W. Carlson, “Tradeoffs in the design of correlation filters,” in Optical Pattern Recognition, Critical Reviews Vol. CR40, J. L. Horner, B. Javidi, eds. (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1992), pp. 191–215.

Horner, J. L.

Javidi, B.

Kass, M.

M. Kass, A. Witkin, D. Terzopoulos, “Snakes: active contour models,” Int. J. Comput. Vis. 1, 321–331 (1988).
[Crossref]

Laude, V.

Pratt, W. K.

W. K. Pratt, “Image detection and registration,” in Digital Image Processing (Wiley, New York, 1978), pp. 562–566.

Réfrégier, Ph.

S. Tonda, Ph. Réfrégier, “Three-dimensional attitude estimation and tracking with linear normalized optimal filtering,” Opt. Eng. 36, 1145–1151 (1997).
[Crossref]

Ph. Réfrégier, O. Germain, T. Gaidon, “Optimal snake segmentation of target and background with independent gamma density probabilities, application to speckled and preprocessed images,” Opt. Commun. 137, 382–388 (1997).
[Crossref]

F. Goudail, Ph. Réfrégier, “Optimal detection of a target with random gray levels on a spatially disjoint noise,” Opt. Lett. 21, 495–497 (1996).
[Crossref] [PubMed]

O. Germain, Ph. Réfrégier, “Optimal snake-based segmentation of a random luminance target on a spatially disjoint background,” Opt. Lett. 21, 1845–1847 (1996).
[Crossref] [PubMed]

F. Goudail, V. Laude, Ph. Réfrégier, “Influence of non-overlapping noise on regularized linear filters for pattern recognition,” Opt. Lett. 20, 2237–2239 (1995).
[Crossref]

B. Javidi, Ph. Réfrégier, P. Willet, “Optimum receiver design for pattern recognition with nonoverlapping target and scene noise,” Opt. Lett. 18, 1660–1662 (1993).
[Crossref] [PubMed]

Ph. Réfrégier, B. Javidi, G. Zhang, “Minimum mean-square-error filter for pattern recognition with spatially disjoint signal and scene noise,” Opt. Lett. 18, 1453–1456 (1993).
[Crossref] [PubMed]

Ph. Réfrégier, “Optimal trade-off filters for noise robustness, sharpness of the correlation peak and Horner efficiency,” Opt. Lett. 16, 829–831 (1991).
[Crossref]

Terzopoulos, D.

M. Kass, A. Witkin, D. Terzopoulos, “Snakes: active contour models,” Int. J. Comput. Vis. 1, 321–331 (1988).
[Crossref]

Tonda, S.

S. Tonda, Ph. Réfrégier, “Three-dimensional attitude estimation and tracking with linear normalized optimal filtering,” Opt. Eng. 36, 1145–1151 (1997).
[Crossref]

Vander Lugt, A.

A. Vander Lugt, “Signal detection by complex filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[Crossref]

VijayaKumar, B. V. K.

B. V. K. VijayaKumar, C. Hendrix, D. W. Carlson, “Tradeoffs in the design of correlation filters,” in Optical Pattern Recognition, Critical Reviews Vol. CR40, J. L. Horner, B. Javidi, eds. (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1992), pp. 191–215.

Wang, J.

Willet, P.

Witkin, A.

M. Kass, A. Witkin, D. Terzopoulos, “Snakes: active contour models,” Int. J. Comput. Vis. 1, 321–331 (1988).
[Crossref]

Zhang, G.

Appl. Opt. (2)

IEEE Trans. Inf. Theory (1)

A. Vander Lugt, “Signal detection by complex filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[Crossref]

Int. J. Comput. Vis. (1)

M. Kass, A. Witkin, D. Terzopoulos, “Snakes: active contour models,” Int. J. Comput. Vis. 1, 321–331 (1988).
[Crossref]

Opt. Commun. (1)

Ph. Réfrégier, O. Germain, T. Gaidon, “Optimal snake segmentation of target and background with independent gamma density probabilities, application to speckled and preprocessed images,” Opt. Commun. 137, 382–388 (1997).
[Crossref]

Opt. Eng. (1)

S. Tonda, Ph. Réfrégier, “Three-dimensional attitude estimation and tracking with linear normalized optimal filtering,” Opt. Eng. 36, 1145–1151 (1997).
[Crossref]

Opt. Lett. (6)

Other (3)

R. O. Duda, P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).

W. K. Pratt, “Image detection and registration,” in Digital Image Processing (Wiley, New York, 1978), pp. 562–566.

B. V. K. VijayaKumar, C. Hendrix, D. W. Carlson, “Tradeoffs in the design of correlation filters,” in Optical Pattern Recognition, Critical Reviews Vol. CR40, J. L. Horner, B. Javidi, eds. (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1992), pp. 191–215.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (14)

Fig. 1
Fig. 1

Sketch of two successive images st-1 and st.

Fig. 2
Fig. 2

Superposition of st-1 and of st shifted by -τ.

Fig. 3
Fig. 3

Object that will be used as a reference in all the numerical simulations.

Fig. 4
Fig. 4

Example of two successive images. τ=-10 pixels, and δ=0.

Fig. 5
Fig. 5

Illustration of the method for determining τˆ and gτˆ. The sequence represented in Fig. 4 has been utilized. In the image at left, the top part represents the correlation plane obtained by Eq. (32), and the bottom part is a plot of the maximum of each line of this correlation plane. Arbitrary units have been used for this plot.

Fig. 6
Fig. 6

Computation of the final output plane F(τˆ, μ) [cf. Eq. (26)] from the image sequence of Fig. 4. The assumed value of τ0 is the true one. The top parts of the images represent the output planes obtained by the corresponding processor. The bottom parts are plots of the maximum of each line of these output planes. Arbitrary units have been used for these plots.

Fig. 7
Fig. 7

Example of two successive images. τ=-10 pixels, and δ=0.

Fig. 8
Fig. 8

Result of the processing of the image st in Fig. 7 with several classic pattern recognition filters. The top parts of the images represent the output planes obtained by the corresponding filters. The bottom parts are plots of the maximum of each line of these output planes. Arbitrary units have been used for these plots. OT stands for optimal trade-off, and POF stands for phase-only filter.

Fig. 9
Fig. 9

Computation of the final output plane F(τ0, μ) [cf. Eq. (26)] from the image sequence of Fig. 7. The top parts of the images represent the output planes obtained by the corresponding processor. The bottom parts are plots of the maximum of each line of these output planes. Arbitrary units have been used for these plots.

Fig. 10
Fig. 10

(a) Scene, (b) output plane of the processor B(τ0, μ) [cf. Eq. (21)] when the input image is (a), (c) plot of the maximum of each line of the output plane (b).

Fig. 11
Fig. 11

(a) Scene, (b) output plane of the processor B(τ0, μ) [cf. Eq. (21)] when the input image is (a), (c) plot of the maximum of each line of the output plane (b).

Fig. 12
Fig. 12

(a) Scene, (b) output plane of the processor B(τ0, μ) [cf. Eq. (21)] when the input image is (a), (c) plot of the maximum of each line of the output plane (b).

Fig. 13
Fig. 13

(a) Scene, (b) output plane of the processor B(τ0, μ) [cf. Eq. (33)] when the input image is (a), (c) plot of the maximum of each line of the output plane (b).

Fig. 14
Fig. 14

(a) Scene, (b) output plane of the processor B(τ0, μ) [cf. Eq. (33)] when the input image is (a), (c) plot of the maximum of each line of the output plane (b).

Equations (32)

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

sit-1=ri+(1-wi)bi+ni.
sit=βri-δ+(1-wi-δ)bi-τ+ni,
(δˆ, Mˆ)=arg max(δ, M) P(δ, M|S).
P(δ, M|S)=P(S|δ, M)P(δ, M)/P(S).
(δˆ, Mˆ)=arg max(δ, M) P(S|δ, M).
H(b, β, τ, δ)=P(S|δ, M)=1(2πσ)2Nexp-12σ2×{i|wi=0}(sit-1-bi)2+{i|wi=1}(sit-1-ri)2+{i|wi-δ=0}(sit-bi-τ)2+{i|wi-δ=1}(sit-βri-δ)2,
G(b, β, τ, δ)=-{i|wi=0}(sit-1-bi)2-{i|wi-δ=0}(sit-bi-τ)2-{i|wi-δ=1}(sit-βri-δ)2,
G(b, β, τ, μ)=-{i|wi=0}(sit-1-bi)2-{i|wi-μ=0}(si+τt-bi)2-{i|wi-μ=1}(si+τt-βri-μ)2,
D1={i|wi=0andwi-μ=0},
D2={i|wi=0andwi-μ=1},
D3={i|wi=1andwi-μ=0},
D4={i|wi=1andwi-μ=1}.
G(b, β, τ, μ)=-D1[(sit-1-bi)2+(si+τt-bi)2]-D2[(sit-1-bi)2+(si+τt-βri-μ)2]-D3(si+τt-bi)2-D4(si+τt-βri-μ)2.
Gbi=-2(sit-1-bi)-2(si+τt-bi),
Gbi=0  bˆi=12(sit-1+si+τt),
bˆi=sit-1foriD2si+τtforiD3.
G(bˆ, β, τ, μ)=-12D1(sit-1-si+τt)2-W(si+τt-βri-μ)2,
Gβ=0  βˆ=Wsi+τtri-μWri-μ2.
G(bˆ, βˆ, τ, μ)=F(τ, μ)=-12D1(sit-1-si+τt)2-W(si+τt)2-Wsi+τtri-μ2Wri-μ2.
B(τ, μ)=-W(si+τt)2+Wsi+τtri-μ2Wri-μ2=-[(st)2  *  w]τ+μ+[st  *  r]τ+μ2[r  *  r]02,
A(τ, μ)=-12D1(sit-1-si+τt)2=-12I(sit-1-si+τt)2(1-wi)(1-wi-μ),
giτ=(sit-1-si+τt)2(1-wi).
A(τ, μ)=-12Igiτ+12[gτ  *  w]μ=A1(τ)+A2(τ, μ).
F(τ, μ)=A1(τ)+A2(τ, μ)+B(τ, μ)=-12Igiτ+12[gτ  *  w]μ-[(st)2  *  w]τ+μ+[st  *  r]τ+μ2[r  *  r]02.
F(τ0, μ)=A2(τ0, μ)+B(τ0, μ)=12[gτ0  *  w]μ-[(st)2  *  w]τ0+μ+[st  *  r]τ0+μ2[r  *  r]02.
μˆ=arg maxμ F(τ0, μ).
F(τ0, μ)=[hτ0  *  w]μ+[st  *  r]τ0+μ2[r  *  r]02,
hiτ0=giτ0-(si+τ0t)2.
K(δ)=-[(st)2  *  w]δ+[st  *  r]δ2[r  *  r]02,
A1(τ)=-12Igiτ=-12I(sit-1-si+τt)2(1-wi)=-12I(sit-1)2(1-wi)-12I(si+τt)2(1-wi)+Isit-1(1-wi)si+τt.
τˆ=arg maxτ12[(st)2  *  w]τ+[s¯t-1  *  st]τ,
B(τ0, μ)=W(si+τ0t-ri-μ)2=-[(st)2  *  w]τ0+μ+2[st  *  r]τ0+μ.

Metrics