Abstract

It has recently been demonstrated that object recognition can be formulated as an image-restoration problem. In this approach, which we term impulse restoration, the objective is to restore a delta function that indicates the detected object’s location. We develop solutions based on impulse restoration for the Gaussian-noise case. We propose a new iterative approach, based on the expectation-maximization (EM) algorithm, that simultaneously estimates the background statistics and restores a delta function at the location of the template. We use a Monte Carlo study and localization-receiver-operating-characteristics curves to evaluate the performance of this approach quantitatively and compare it with existing methods. We present experimental results that demonstrate that impulse restoration is a powerful approach for detecting known objects in images severely degraded by noise. Our numerical experiments point out that the proposed EM-based approach is superior to all tested variants of the matched filter. This result demonstrates that accurate modeling and estimation of the background and noise statistics are crucial for realizing the full potential of impulse restoration-based template matching.

© 1998 Optical Society of America

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References

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  1. A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  13. M. Choi, N. Galatsanos, D. Schonfeld, “Image restoration-based template-matching with application to motion estimation,” in Visual Communications Image Processing ’96, R. Ansari, M. Smith, eds., Proc. SPIE2727, 375–386 (1996).
    [CrossRef]
  14. M. Choi, N. Galatsanos, D. Schonfeld, “On the relation of image restoration and template-matching: application to block-matching motion estimation,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing 1996 (Institute of Electrical and Elec-tronics Engineers, Piscataway, N.J., 1996), Vol. IV, pp. 2112–2115.
  15. M. Choi, N. Galatsanos, D. Schonfeld, “Image restoration based template-matching for multi-channel restoration of image sequences,” Presented at the 1996 ASILOMAR Conference, Pacific Grove, Calif., November 1996.
  16. A. P. Dempster, N. M. Laird, D. B. Rubin, “Maximum-likelihood from incomplete data,” J. R. Statist. Soc. B 39, 1–38 (1977).
  17. A. K. Katsaggelos, K.-T. Lay, Digital Image Restoration (Springer-Verlag, Berlin, 1991).
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    [CrossRef] [PubMed]
  19. S. J. Starr, C. E. Metz, L. B. Lusted, D. J. Goodenough, “Visual detection and localization of radiographic images,” Radiol. 116, 533–538 (1975).
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  22. S. Kay, Fundamentals of Statistical Signal Processing, Estimation Theory (Prentice-Hall, Englewood Cliffs, N.J., 1993).
  23. A. Abu-Naser, “Object recognition based on impulse restoration for images in Gaussian noise,” Master’s thesis (Illinois Institute of Technology, Chicago, Ill., 1996).
  24. John G. Proakis, Dimitris G. Manolakis, Digital Signal Processing, Principles, Algorithms, and Applications (Prentice-Hall, Englewood Cliffs, N.J., 1996).

1997 (1)

1996 (2)

1995 (1)

C. R. Chatwin, R. K. Wang, R. C. D. Young, “Assessment of a Wiener filter—synthetic discriminant function for optical correlation,” J. Optics Lasers Eng. 22, 33–51 (1995).
[CrossRef]

1994 (1)

Q. Chen, M. Defrise, F. Decorninck, “Symmetric phase-only matched filtering of Fourier–Mellin transforms for image registration and recognition,” IEEE Trans. Pattern Recogn. Mach. Intell. 12, 1156–1198 (1994).
[CrossRef]

1993 (1)

J. Ben-Arie, K. R. Rao, “A novel approach to template matching by nonorthogonal image expansion,” IEEE Trans. Circuits Syst. Video Technol. 3, 71–84 (1993).
[CrossRef]

1990 (1)

1989 (2)

1985 (1)

1984 (1)

1981 (1)

A. V. Oppenheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

1977 (1)

A. P. Dempster, N. M. Laird, D. B. Rubin, “Maximum-likelihood from incomplete data,” J. R. Statist. Soc. B 39, 1–38 (1977).

1975 (1)

S. J. Starr, C. E. Metz, L. B. Lusted, D. J. Goodenough, “Visual detection and localization of radiographic images,” Radiol. 116, 533–538 (1975).

Abu-Naser, A.

A. Abu-Naser, “Object recognition based on impulse restoration for images in Gaussian noise,” Master’s thesis (Illinois Institute of Technology, Chicago, Ill., 1996).

Andrews, H.

H. Andrews, B. Hunt, Digital Image RestorationPrentice-Hall, Englewood Cliffs, N.J., 1977).

Ben-Arie, J.

J. Ben-Arie, K. R. Rao, “A novel approach to template matching by nonorthogonal image expansion,” IEEE Trans. Circuits Syst. Video Technol. 3, 71–84 (1993).
[CrossRef]

Chatwin, C. R.

C. R. Chatwin, R. K. Wang, R. C. D. Young, “Assessment of a Wiener filter—synthetic discriminant function for optical correlation,” J. Optics Lasers Eng. 22, 33–51 (1995).
[CrossRef]

Chen, Q.

Q. Chen, M. Defrise, F. Decorninck, “Symmetric phase-only matched filtering of Fourier–Mellin transforms for image registration and recognition,” IEEE Trans. Pattern Recogn. Mach. Intell. 12, 1156–1198 (1994).
[CrossRef]

Choi, M.

M. Choi, N. Galatsanos, D. Schonfeld, “Image restoration-based template-matching with application to motion estimation,” in Visual Communications Image Processing ’96, R. Ansari, M. Smith, eds., Proc. SPIE2727, 375–386 (1996).
[CrossRef]

M. Choi, N. Galatsanos, D. Schonfeld, “On the relation of image restoration and template-matching: application to block-matching motion estimation,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing 1996 (Institute of Electrical and Elec-tronics Engineers, Piscataway, N.J., 1996), Vol. IV, pp. 2112–2115.

M. Choi, N. Galatsanos, D. Schonfeld, “Image restoration based template-matching for multi-channel restoration of image sequences,” Presented at the 1996 ASILOMAR Conference, Pacific Grove, Calif., November 1996.

Decorninck, F.

Q. Chen, M. Defrise, F. Decorninck, “Symmetric phase-only matched filtering of Fourier–Mellin transforms for image registration and recognition,” IEEE Trans. Pattern Recogn. Mach. Intell. 12, 1156–1198 (1994).
[CrossRef]

Defrise, M.

Q. Chen, M. Defrise, F. Decorninck, “Symmetric phase-only matched filtering of Fourier–Mellin transforms for image registration and recognition,” IEEE Trans. Pattern Recogn. Mach. Intell. 12, 1156–1198 (1994).
[CrossRef]

Dempster, A. P.

A. P. Dempster, N. M. Laird, D. B. Rubin, “Maximum-likelihood from incomplete data,” J. R. Statist. Soc. B 39, 1–38 (1977).

Dickey, F. M.

Ersoy, O. K.

Galatsanos, N.

M. Choi, N. Galatsanos, D. Schonfeld, “Image restoration-based template-matching with application to motion estimation,” in Visual Communications Image Processing ’96, R. Ansari, M. Smith, eds., Proc. SPIE2727, 375–386 (1996).
[CrossRef]

M. Choi, N. Galatsanos, D. Schonfeld, “On the relation of image restoration and template-matching: application to block-matching motion estimation,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing 1996 (Institute of Electrical and Elec-tronics Engineers, Piscataway, N.J., 1996), Vol. IV, pp. 2112–2115.

M. Choi, N. Galatsanos, D. Schonfeld, “Image restoration based template-matching for multi-channel restoration of image sequences,” Presented at the 1996 ASILOMAR Conference, Pacific Grove, Calif., November 1996.

Gianino, P. D.

Goodenough, D. J.

S. J. Starr, C. E. Metz, L. B. Lusted, D. J. Goodenough, “Visual detection and localization of radiographic images,” Radiol. 116, 533–538 (1975).

Hansche, B. D.

Hassebrook, L.

Horner, J. L.

Hunt, B.

H. Andrews, B. Hunt, Digital Image RestorationPrentice-Hall, Englewood Cliffs, N.J., 1977).

Inbar, H.

Jain, A. K.

A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989).

Javidi, B.

Katsaggelos, A. K.

A. K. Katsaggelos, K.-T. Lay, Digital Image Restoration (Springer-Verlag, Berlin, 1991).

Kay, S.

S. Kay, Fundamentals of Statistical Signal Processing, Estimation Theory (Prentice-Hall, Englewood Cliffs, N.J., 1993).

Kumar, B. V.

Laird, N. M.

A. P. Dempster, N. M. Laird, D. B. Rubin, “Maximum-likelihood from incomplete data,” J. R. Statist. Soc. B 39, 1–38 (1977).

Lay, K.-T.

A. K. Katsaggelos, K.-T. Lay, Digital Image Restoration (Springer-Verlag, Berlin, 1991).

Leger, R. L.

Lim, J. S.

A. V. Oppenheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

Lusted, L. B.

S. J. Starr, C. E. Metz, L. B. Lusted, D. J. Goodenough, “Visual detection and localization of radiographic images,” Radiol. 116, 533–538 (1975).

Manolakis, Dimitris G.

John G. Proakis, Dimitris G. Manolakis, Digital Signal Processing, Principles, Algorithms, and Applications (Prentice-Hall, Englewood Cliffs, N.J., 1996).

Marom, E.

Metz, C. E.

S. J. Starr, C. E. Metz, L. B. Lusted, D. J. Goodenough, “Visual detection and localization of radiographic images,” Radiol. 116, 533–538 (1975).

Oppenheim, A. V.

A. V. Oppenheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

Parchekani, F.

Proakis, John G.

John G. Proakis, Dimitris G. Manolakis, Digital Signal Processing, Principles, Algorithms, and Applications (Prentice-Hall, Englewood Cliffs, N.J., 1996).

Rao, K. R.

J. Ben-Arie, K. R. Rao, “A novel approach to template matching by nonorthogonal image expansion,” IEEE Trans. Circuits Syst. Video Technol. 3, 71–84 (1993).
[CrossRef]

Rubin, D. B.

A. P. Dempster, N. M. Laird, D. B. Rubin, “Maximum-likelihood from incomplete data,” J. R. Statist. Soc. B 39, 1–38 (1977).

Schonfeld, D.

M. Choi, N. Galatsanos, D. Schonfeld, “On the relation of image restoration and template-matching: application to block-matching motion estimation,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing 1996 (Institute of Electrical and Elec-tronics Engineers, Piscataway, N.J., 1996), Vol. IV, pp. 2112–2115.

M. Choi, N. Galatsanos, D. Schonfeld, “Image restoration based template-matching for multi-channel restoration of image sequences,” Presented at the 1996 ASILOMAR Conference, Pacific Grove, Calif., November 1996.

M. Choi, N. Galatsanos, D. Schonfeld, “Image restoration-based template-matching with application to motion estimation,” in Visual Communications Image Processing ’96, R. Ansari, M. Smith, eds., Proc. SPIE2727, 375–386 (1996).
[CrossRef]

Starr, S. J.

S. J. Starr, C. E. Metz, L. B. Lusted, D. J. Goodenough, “Visual detection and localization of radiographic images,” Radiol. 116, 533–538 (1975).

Van Trees, H. L.

H. L. Van Trees, Detection Estimation, and Modulation Theory: Part I (Wiley, New York, 1968).

Wang, R. K.

C. R. Chatwin, R. K. Wang, R. C. D. Young, “Assessment of a Wiener filter—synthetic discriminant function for optical correlation,” J. Optics Lasers Eng. 22, 33–51 (1995).
[CrossRef]

Yaroslavsky, L. P.

Young, R. C. D.

C. R. Chatwin, R. K. Wang, R. C. D. Young, “Assessment of a Wiener filter—synthetic discriminant function for optical correlation,” J. Optics Lasers Eng. 22, 33–51 (1995).
[CrossRef]

Zeng, M.

Zhang, G.

Appl. Opt. (6)

IEEE Trans. Circuits Syst. Video Technol. (1)

J. Ben-Arie, K. R. Rao, “A novel approach to template matching by nonorthogonal image expansion,” IEEE Trans. Circuits Syst. Video Technol. 3, 71–84 (1993).
[CrossRef]

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

Q. Chen, M. Defrise, F. Decorninck, “Symmetric phase-only matched filtering of Fourier–Mellin transforms for image registration and recognition,” IEEE Trans. Pattern Recogn. Mach. Intell. 12, 1156–1198 (1994).
[CrossRef]

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

J. Optics Lasers Eng. (1)

C. R. Chatwin, R. K. Wang, R. C. D. Young, “Assessment of a Wiener filter—synthetic discriminant function for optical correlation,” J. Optics Lasers Eng. 22, 33–51 (1995).
[CrossRef]

J. R. Statist. Soc. B (1)

A. P. Dempster, N. M. Laird, D. B. Rubin, “Maximum-likelihood from incomplete data,” J. R. Statist. Soc. B 39, 1–38 (1977).

Proc. IEEE (1)

A. V. Oppenheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

Radiol. (1)

S. J. Starr, C. E. Metz, L. B. Lusted, D. J. Goodenough, “Visual detection and localization of radiographic images,” Radiol. 116, 533–538 (1975).

Other (10)

H. L. Van Trees, Detection Estimation, and Modulation Theory: Part I (Wiley, New York, 1968).

H. Andrews, B. Hunt, Digital Image RestorationPrentice-Hall, Englewood Cliffs, N.J., 1977).

S. Kay, Fundamentals of Statistical Signal Processing, Estimation Theory (Prentice-Hall, Englewood Cliffs, N.J., 1993).

A. Abu-Naser, “Object recognition based on impulse restoration for images in Gaussian noise,” Master’s thesis (Illinois Institute of Technology, Chicago, Ill., 1996).

John G. Proakis, Dimitris G. Manolakis, Digital Signal Processing, Principles, Algorithms, and Applications (Prentice-Hall, Englewood Cliffs, N.J., 1996).

A. K. Katsaggelos, K.-T. Lay, Digital Image Restoration (Springer-Verlag, Berlin, 1991).

A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989).

M. Choi, N. Galatsanos, D. Schonfeld, “Image restoration-based template-matching with application to motion estimation,” in Visual Communications Image Processing ’96, R. Ansari, M. Smith, eds., Proc. SPIE2727, 375–386 (1996).
[CrossRef]

M. Choi, N. Galatsanos, D. Schonfeld, “On the relation of image restoration and template-matching: application to block-matching motion estimation,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing 1996 (Institute of Electrical and Elec-tronics Engineers, Piscataway, N.J., 1996), Vol. IV, pp. 2112–2115.

M. Choi, N. Galatsanos, D. Schonfeld, “Image restoration based template-matching for multi-channel restoration of image sequences,” Presented at the 1996 ASILOMAR Conference, Pacific Grove, Calif., November 1996.

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Figures (11)

Fig. 1
Fig. 1

Examples of the backgrounds used by the exact LMMSE filter. The object of interest is the tank. The exact LMMSE filter is unrealistic. It was studied only to determine a theoretical upper bound on the performance.

Fig. 2
Fig. 2

2×2 autoregressive image model with causal support.

Fig. 3
Fig. 3

Object templates.

Fig. 4
Fig. 4

Examples of noisy test scenes with the object of interest present (in this case, tank). The noise level is σ=20. In each realization the objects are placed randomly within the scene.

Fig. 5
Fig. 5

Examples of noisy scenes with the object of interest absent (in this case, the tank). The noise level is σ=20.

Fig. 6
Fig. 6

Conditional PDF’s for σ=20 when the tank is the object of interest.

Fig. 7
Fig. 7

LROC curves for σ=20. Overall, the EM-AR algorithm outperforms all but the exact (unrealistic) LMMSE filter, which makes use of the unknown object location. Other methods did outperform the EM-AR algorithm in some specific situations but were inconsistent and did not perform as well overall.

Fig. 8
Fig. 8

Lena scene and the template.

Fig. 9
Fig. 9

Examples of noisy Lena scenes for different noise levels. Clockwise from top left, σ=5, σ=30, σ=50, and σ=100.

Fig. 10
Fig. 10

Plot of the probability of correct localization as a function of noise standard deviation.

Fig. 11
Fig. 11

Examples of the restored impulse for σ=30.

Tables (1)

Tables Icon

Table 1 Mean-Square-Error Values for Different Filters for σ=30

Equations (70)

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g(n)=f(n-n0)+b(n),
g(n)=f(n)*δ(n-n0)+b(n),
g=Fδ+b,
BMSE(δˆ)=E[(δ-δˆ)2],
δˆ=(FtCb-1F+Cδ-1)-1FtCb-1g=(FtCb-1F+I)-1FtCb-1g,
Δˆ(k)=F*(k)G(k)|F(k)|2+NSb(k),k=0, 1,, N-1,
Sb(k)=|G(k)|2-|F(k)|2N,k=0, 1,, N-1.
Sb(k)=max0, |G(k)|2-|F(k)|2N,
k=0, 1,, N-1.
θ={δ, Cb},
θˆML=arg maxθ log p(g | θ)
b(n)=b(n)*α(n)+v(n),
b=Ab+v.
Cb=σv2(I-A)-1(I-A)-t,
p(g|θ)=N(Fδ, FtF+σv2(I-A)-1(I-A)-t).
θˆML=arg maxθ{-log(|FtF+Cb|)-(g-Fδ)t[FtF+Cb]-1(g-Fδ)},
g=Fδ+b=[F; I]δb=Hz,
Q(θ; θ(l))=E{ln[p(z; θ)]|g, θ(l)}
θ(l+1)=arg maxθ[Q(θ; θ(l))].
Mδ|g(l)(k)=F*(k)G(k)|F(k)|2+NS˜b(l)(k),
Mb|g(l)(k)=NS˜b(l)(k)G(k)|F(k)|2+NS˜b(l)(k),
Sb|g(l)(k)=|F(k)|2S˜b(l)(k)|F(k)|2+NS˜b(l)(k),
R¯b(l)α(l+1)=R¯b(l)1=rb(l),
rb(l)=R¯b(l)α(l+1),
Sb(l)(k)=Sb|g(l)(k)+1N|Mb | g(l)(k)|2,
k=0, 1,, N-1.
S˜b(l)(k)=(σv(l))2|1-A(l)(k)|2,
k=0, 1,, N-1.
Δˆ(k)=F*(k)G(k)|F(k)|,k=0, 1, , N-1,
Δˆ(k)=F*(k)G(k)|F(k)||G(k)|,k=0, 1, , N-1,
b(n)=g(n)-f(n-n0),
Sb(k)=|G(k)|2+|F(k)|2.
b(n)=w(n-n0)g(n),
Sb(k)=|G(k)|2*|W(k)|2,
PDL=Tp(x|H1)dx
PF=Tp(x|H0)dx,
MSE=1Ni=1N[δˆ(i)-δ(n0)]2,
p(z; θ)=|2πCz|-1/2 exp(-12ztCz-1z),
ln[p(z; θ)]=-12[ln(|2πCz|)+ztCz-1z]=K-12[ln(|Cz|)+ztCz-1z].
Q(θ; θ(l))=K-12{E[ln(|Cz|)|g; θ(l)]+E(gtCz-1z|g; θ(l))=K-Y(θ; θ(l)).
Y(θ; θ(l))=ln(|Cz|)+trace(Cz-1Rz|g(l)),
Rz|g(l)=E(zzt|g; θ(l))=Cz|g(l)+μz|g(l)(μz|g(l))t.
Y(θ; θ(l))=ln(|Cz|)+trace(Cz-1Cz|g(l))+(μz|g(l))tCz-1μz|g(l).
Cz=I00Cb,Cz|g=Cδ|g00Cb|g,
μz|g=[(μδ|g)t,(μb|g)t]t.
Y(θ; θ(l))=ln|σv2(I-A)-1(I-A)-t|
+traceCδ|g(l)+1σv2(I-A)t(I-A)Cb|g(l)
+(μδ|g(l))tμδ|g(l)+1σv2(μb|g(l))t(I-A)t
×(I-A)μb|g(l).
ln|(I-A)-1(I-A)-t|=ln 1=0.
Y(θ; θ(l))=traceCδ|g+1σv2(I-A)t[Cb|g(l)+μb|g(l)(μb|g(l))t](I-A)+(μδ|g(l))tμδ|g(l)+2N ln σv.
trace{XtAX}=N(xtAx),
trace(XaatXt)=trace(AxxtA)=atXtXa,
Y(θ; θ(l))=traceCδ|g+1σv2(1-α)t×[N·Cb|g(l)+Mb|g(l)(Mb|g(l))t](1-α)+(μδ|g(l))tμδ|g(l)+2N ln σv,
Rb(l)=Cb|g(l)+1NMb|g(l)(Mb|g(l))t+2N ln σv,
Y(θ; θ(l))=traceCδ|g+Nσv2(1-α)t×Rb(l)(1-α)+(μδ|g(l))tμδ|g(l).
Sb(l)(k)=Sb|g(l)(k)+1N|Mb|g(l)(k)|2
fork=0, 1,, N-1,
Rb(l)α(l+1)=Rb(l)1=rb(l),
α(l+1)=[(R¯b(l))tR¯b(l)]-1(R¯b(l))trb(l),
S˜b(l)(k)=(σv(l))2|1-A(l)(k)|2,k=0, 1,, N-1,
(σv(l))2=rb(l)(0)-k=1Mα(l)(k)rb(l)(k),
μz|g=CzHt(HCzHt)-1g=FtCb(FFt+Cb)-1g=μδ|gμb|g.
Mδ|g(l)(k)=F*(k)G(k)|F(k)|2+NSb(l)(k),
Mb|g(l)(k)=NSb(l)(k)G(k)|F(k)|2+NSb(l)(k).
Cz|g=Cδ/g00Cb/g=Cz-CzHt(HCzHt)-1HCz.
Cb/g=Cb-Cb(FFt+Cb)-1Cb.
Sb|g(k)=Sb(k)-Sb2(k)1N|F(k)|2+Sb(k).
Sb|g(l)(k)=|F(k)|2Sb(l)(k)|F(k)|2+NSb(l)(k)
fork=0, 1,, N-1.

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