Abstract

In a recent work, we demonstrated the usefulness of the Hilbert transform in identifying the in-plane rotation angle between two objects. Here we use the Hilbert-wavelet bases instead of the Hilbert transform in the determination of the exact angle of rotation. We describe the design of the two-dimensional Hilbert-wavelet filter based on the spectral-factorization method to generate a Hilbert-transform pair of orthogonal wavelet bases. We compare the relative performance of the Hilbert transform and the Hilbert wavelet to identify both in-plane and out-of-plane rotation angles. We demonstrate that the Hilbert wavelet offers better rotation-angle determination than the Hilbert transform. We present correlation based rotated and scaled object identification and tracking using Hilbert or Hilbert-wavelet transformed infrared image sequences. We also demonstrate reduced data handling and improved tracking of distorted objects using the Hilbert-wavelet transform.

© 2003 Optical Society of America

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References

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  1. M. S. Snorrason, H. Ruda, “Image understanding software for hybrid hardware,” Advanced Research Projects Agency (DoD), http://cns-web.bu.edu/pub/snorrason-papers/C9406-finalreport.pdf
  2. M. Boshra, B. Bhanu, “Predicting object recognition performance under data uncertainty, occlusion and clutter,” IEEE international Conference on Image Processing, 3, 556–560, 1998.
  3. K. M. Iftekharuddin, C. Rentala, A. Dani, “Determination of exact rotation angle and discrimination for rotated images,” Opt. Laser Technol. 32, 313–327 (2002).
    [CrossRef]
  4. D. Casasent, D. Psaltis, “Position, rotation and scale invariant optical correlator,” Appl. Opt. 15, 1795–1799 (1976).
    [CrossRef] [PubMed]
  5. B. U. Lee, C. M. Kim, R. H. Park, “Error sensitivity of rotation angles in ICP algorithm,” IEEE Pat. Annal. Mach. Intel. 22, 1205–1208 (2000).
  6. IR image dataset, US Army Aviation and Missile Command (AMCOM, 1999.
  7. S. R. F. Sims, “Putting ATR performance on an equal basis—The measurement of knowledge-based distortion and relevant clutter,” U.S. Army Aviation & Missile Command 18, 2631–2635 (1997).
  8. S. R. F. Sims, “Data compression issues in automatic target recognition and measuring of distortion,” Opt. Eng. 36, 2671–2674 (1997).
    [CrossRef]
  9. C. Stauffer, W. E. L. Grimson, “Adaptive background mixture models for real-time tracking,” IEEE Conference on Computer Vision and Pattern Recognition, Fort Collins, Colo., 2, 246—252 (1999).
  10. S. L. Diab, M. A. Karim, K. M. Iftekharuddin, “Multiobject detection of targets with fine details, scale and translation variation,” Opt. Eng. 37, 876–883 (1998).
    [CrossRef]
  11. G. Ravichandran, D. Casasent, “Generalized in plane rotation invariant minimum average correlation energy filter,” Opt. Eng. 30, 1601–1607 (1991).
    [CrossRef]
  12. K. M. Iftekharuddin, M. A. Razzaque, “Constraints in distortion invariant target recognition system simulation,” in International Conference on Sensor Technology, Y. Zhou, S. Xu, eds., Proc. SPIE, 4414, 20–312000.
  13. J. W. Woods, V. K. Ingle, “Kalman filtering in two dimensions: Further results,” IEEE Trans. Acoustic, Speech, Signal Process. 29, 188–197 (1981).
    [CrossRef]
  14. E. W. Selesnick, “Hilbert Transform Pair of Wavelet bases”, Invited paper for information systems, Signal Process. Lett 8, 170–173 (2001).
    [CrossRef]
  15. N. P. Galatsanos, T. Chin, “Restoration of color images by multi channel Kalman filtering,” IEEE Trans. Signal Process. 39, 2237–2252 (1991).
    [CrossRef]
  16. J. P. Thiran, “Recursive digital filters with maximally flat gropu delay,” IEEE Trans. on Circuit Theory, 18, 659–664 (1971).
    [CrossRef]
  17. S. Mallat, A Wavelet Tour of Signal Processing (AcademicNew York1998).
  18. P. Abry, Ondelettes et Turbulences (Diderot, Paris, 1997).
  19. R. G. Driggers, P. Cox, T. Edwards, Introduction to Infrared and Electro Optical Systems, (Artech House, Norwood, Mass., 1999)

2002 (1)

K. M. Iftekharuddin, C. Rentala, A. Dani, “Determination of exact rotation angle and discrimination for rotated images,” Opt. Laser Technol. 32, 313–327 (2002).
[CrossRef]

2001 (1)

E. W. Selesnick, “Hilbert Transform Pair of Wavelet bases”, Invited paper for information systems, Signal Process. Lett 8, 170–173 (2001).
[CrossRef]

2000 (1)

B. U. Lee, C. M. Kim, R. H. Park, “Error sensitivity of rotation angles in ICP algorithm,” IEEE Pat. Annal. Mach. Intel. 22, 1205–1208 (2000).

1998 (2)

S. L. Diab, M. A. Karim, K. M. Iftekharuddin, “Multiobject detection of targets with fine details, scale and translation variation,” Opt. Eng. 37, 876–883 (1998).
[CrossRef]

M. Boshra, B. Bhanu, “Predicting object recognition performance under data uncertainty, occlusion and clutter,” IEEE international Conference on Image Processing, 3, 556–560, 1998.

1997 (2)

S. R. F. Sims, “Putting ATR performance on an equal basis—The measurement of knowledge-based distortion and relevant clutter,” U.S. Army Aviation & Missile Command 18, 2631–2635 (1997).

S. R. F. Sims, “Data compression issues in automatic target recognition and measuring of distortion,” Opt. Eng. 36, 2671–2674 (1997).
[CrossRef]

1991 (2)

G. Ravichandran, D. Casasent, “Generalized in plane rotation invariant minimum average correlation energy filter,” Opt. Eng. 30, 1601–1607 (1991).
[CrossRef]

N. P. Galatsanos, T. Chin, “Restoration of color images by multi channel Kalman filtering,” IEEE Trans. Signal Process. 39, 2237–2252 (1991).
[CrossRef]

1981 (1)

J. W. Woods, V. K. Ingle, “Kalman filtering in two dimensions: Further results,” IEEE Trans. Acoustic, Speech, Signal Process. 29, 188–197 (1981).
[CrossRef]

1976 (1)

1971 (1)

J. P. Thiran, “Recursive digital filters with maximally flat gropu delay,” IEEE Trans. on Circuit Theory, 18, 659–664 (1971).
[CrossRef]

Abry, P.

P. Abry, Ondelettes et Turbulences (Diderot, Paris, 1997).

Bhanu, B.

M. Boshra, B. Bhanu, “Predicting object recognition performance under data uncertainty, occlusion and clutter,” IEEE international Conference on Image Processing, 3, 556–560, 1998.

Boshra, M.

M. Boshra, B. Bhanu, “Predicting object recognition performance under data uncertainty, occlusion and clutter,” IEEE international Conference on Image Processing, 3, 556–560, 1998.

Casasent, D.

G. Ravichandran, D. Casasent, “Generalized in plane rotation invariant minimum average correlation energy filter,” Opt. Eng. 30, 1601–1607 (1991).
[CrossRef]

D. Casasent, D. Psaltis, “Position, rotation and scale invariant optical correlator,” Appl. Opt. 15, 1795–1799 (1976).
[CrossRef] [PubMed]

Chin, T.

N. P. Galatsanos, T. Chin, “Restoration of color images by multi channel Kalman filtering,” IEEE Trans. Signal Process. 39, 2237–2252 (1991).
[CrossRef]

Cox, P.

R. G. Driggers, P. Cox, T. Edwards, Introduction to Infrared and Electro Optical Systems, (Artech House, Norwood, Mass., 1999)

Dani, A.

K. M. Iftekharuddin, C. Rentala, A. Dani, “Determination of exact rotation angle and discrimination for rotated images,” Opt. Laser Technol. 32, 313–327 (2002).
[CrossRef]

Diab, S. L.

S. L. Diab, M. A. Karim, K. M. Iftekharuddin, “Multiobject detection of targets with fine details, scale and translation variation,” Opt. Eng. 37, 876–883 (1998).
[CrossRef]

Driggers, R. G.

R. G. Driggers, P. Cox, T. Edwards, Introduction to Infrared and Electro Optical Systems, (Artech House, Norwood, Mass., 1999)

Edwards, T.

R. G. Driggers, P. Cox, T. Edwards, Introduction to Infrared and Electro Optical Systems, (Artech House, Norwood, Mass., 1999)

Galatsanos, N. P.

N. P. Galatsanos, T. Chin, “Restoration of color images by multi channel Kalman filtering,” IEEE Trans. Signal Process. 39, 2237–2252 (1991).
[CrossRef]

Grimson, W. E. L.

C. Stauffer, W. E. L. Grimson, “Adaptive background mixture models for real-time tracking,” IEEE Conference on Computer Vision and Pattern Recognition, Fort Collins, Colo., 2, 246—252 (1999).

Iftekharuddin, K. M.

K. M. Iftekharuddin, C. Rentala, A. Dani, “Determination of exact rotation angle and discrimination for rotated images,” Opt. Laser Technol. 32, 313–327 (2002).
[CrossRef]

S. L. Diab, M. A. Karim, K. M. Iftekharuddin, “Multiobject detection of targets with fine details, scale and translation variation,” Opt. Eng. 37, 876–883 (1998).
[CrossRef]

K. M. Iftekharuddin, M. A. Razzaque, “Constraints in distortion invariant target recognition system simulation,” in International Conference on Sensor Technology, Y. Zhou, S. Xu, eds., Proc. SPIE, 4414, 20–312000.

Ingle, V. K.

J. W. Woods, V. K. Ingle, “Kalman filtering in two dimensions: Further results,” IEEE Trans. Acoustic, Speech, Signal Process. 29, 188–197 (1981).
[CrossRef]

Karim, M. A.

S. L. Diab, M. A. Karim, K. M. Iftekharuddin, “Multiobject detection of targets with fine details, scale and translation variation,” Opt. Eng. 37, 876–883 (1998).
[CrossRef]

Kim, C. M.

B. U. Lee, C. M. Kim, R. H. Park, “Error sensitivity of rotation angles in ICP algorithm,” IEEE Pat. Annal. Mach. Intel. 22, 1205–1208 (2000).

Lee, B. U.

B. U. Lee, C. M. Kim, R. H. Park, “Error sensitivity of rotation angles in ICP algorithm,” IEEE Pat. Annal. Mach. Intel. 22, 1205–1208 (2000).

Mallat, S.

S. Mallat, A Wavelet Tour of Signal Processing (AcademicNew York1998).

Park, R. H.

B. U. Lee, C. M. Kim, R. H. Park, “Error sensitivity of rotation angles in ICP algorithm,” IEEE Pat. Annal. Mach. Intel. 22, 1205–1208 (2000).

Psaltis, D.

Ravichandran, G.

G. Ravichandran, D. Casasent, “Generalized in plane rotation invariant minimum average correlation energy filter,” Opt. Eng. 30, 1601–1607 (1991).
[CrossRef]

Razzaque, M. A.

K. M. Iftekharuddin, M. A. Razzaque, “Constraints in distortion invariant target recognition system simulation,” in International Conference on Sensor Technology, Y. Zhou, S. Xu, eds., Proc. SPIE, 4414, 20–312000.

Rentala, C.

K. M. Iftekharuddin, C. Rentala, A. Dani, “Determination of exact rotation angle and discrimination for rotated images,” Opt. Laser Technol. 32, 313–327 (2002).
[CrossRef]

Selesnick, E. W.

E. W. Selesnick, “Hilbert Transform Pair of Wavelet bases”, Invited paper for information systems, Signal Process. Lett 8, 170–173 (2001).
[CrossRef]

Sims, S. R. F.

S. R. F. Sims, “Putting ATR performance on an equal basis—The measurement of knowledge-based distortion and relevant clutter,” U.S. Army Aviation & Missile Command 18, 2631–2635 (1997).

S. R. F. Sims, “Data compression issues in automatic target recognition and measuring of distortion,” Opt. Eng. 36, 2671–2674 (1997).
[CrossRef]

Stauffer, C.

C. Stauffer, W. E. L. Grimson, “Adaptive background mixture models for real-time tracking,” IEEE Conference on Computer Vision and Pattern Recognition, Fort Collins, Colo., 2, 246—252 (1999).

Thiran, J. P.

J. P. Thiran, “Recursive digital filters with maximally flat gropu delay,” IEEE Trans. on Circuit Theory, 18, 659–664 (1971).
[CrossRef]

Woods, J. W.

J. W. Woods, V. K. Ingle, “Kalman filtering in two dimensions: Further results,” IEEE Trans. Acoustic, Speech, Signal Process. 29, 188–197 (1981).
[CrossRef]

Appl. Opt. (1)

IEEE international Conference on Image Processing (1)

M. Boshra, B. Bhanu, “Predicting object recognition performance under data uncertainty, occlusion and clutter,” IEEE international Conference on Image Processing, 3, 556–560, 1998.

IEEE Pat. Annal. Mach. Intel. (1)

B. U. Lee, C. M. Kim, R. H. Park, “Error sensitivity of rotation angles in ICP algorithm,” IEEE Pat. Annal. Mach. Intel. 22, 1205–1208 (2000).

IEEE Trans. Acoustic, Speech, Signal Process. (1)

J. W. Woods, V. K. Ingle, “Kalman filtering in two dimensions: Further results,” IEEE Trans. Acoustic, Speech, Signal Process. 29, 188–197 (1981).
[CrossRef]

IEEE Trans. on Circuit Theory (1)

J. P. Thiran, “Recursive digital filters with maximally flat gropu delay,” IEEE Trans. on Circuit Theory, 18, 659–664 (1971).
[CrossRef]

IEEE Trans. Signal Process. (1)

N. P. Galatsanos, T. Chin, “Restoration of color images by multi channel Kalman filtering,” IEEE Trans. Signal Process. 39, 2237–2252 (1991).
[CrossRef]

Opt. Eng. (3)

S. L. Diab, M. A. Karim, K. M. Iftekharuddin, “Multiobject detection of targets with fine details, scale and translation variation,” Opt. Eng. 37, 876–883 (1998).
[CrossRef]

G. Ravichandran, D. Casasent, “Generalized in plane rotation invariant minimum average correlation energy filter,” Opt. Eng. 30, 1601–1607 (1991).
[CrossRef]

S. R. F. Sims, “Data compression issues in automatic target recognition and measuring of distortion,” Opt. Eng. 36, 2671–2674 (1997).
[CrossRef]

Opt. Laser Technol. (1)

K. M. Iftekharuddin, C. Rentala, A. Dani, “Determination of exact rotation angle and discrimination for rotated images,” Opt. Laser Technol. 32, 313–327 (2002).
[CrossRef]

Signal Process. Lett (1)

E. W. Selesnick, “Hilbert Transform Pair of Wavelet bases”, Invited paper for information systems, Signal Process. Lett 8, 170–173 (2001).
[CrossRef]

U.S. Army Aviation & Missile Command (1)

S. R. F. Sims, “Putting ATR performance on an equal basis—The measurement of knowledge-based distortion and relevant clutter,” U.S. Army Aviation & Missile Command 18, 2631–2635 (1997).

Other (7)

S. Mallat, A Wavelet Tour of Signal Processing (AcademicNew York1998).

P. Abry, Ondelettes et Turbulences (Diderot, Paris, 1997).

R. G. Driggers, P. Cox, T. Edwards, Introduction to Infrared and Electro Optical Systems, (Artech House, Norwood, Mass., 1999)

M. S. Snorrason, H. Ruda, “Image understanding software for hybrid hardware,” Advanced Research Projects Agency (DoD), http://cns-web.bu.edu/pub/snorrason-papers/C9406-finalreport.pdf

K. M. Iftekharuddin, M. A. Razzaque, “Constraints in distortion invariant target recognition system simulation,” in International Conference on Sensor Technology, Y. Zhou, S. Xu, eds., Proc. SPIE, 4414, 20–312000.

C. Stauffer, W. E. L. Grimson, “Adaptive background mixture models for real-time tracking,” IEEE Conference on Computer Vision and Pattern Recognition, Fort Collins, Colo., 2, 246—252 (1999).

IR image dataset, US Army Aviation and Missile Command (AMCOM, 1999.

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Figures (16)

Fig. 1
Fig. 1

Algorithm for image preprocessing.

Fig. 2
Fig. 2

Algorithm for angle determination and tracking.

Fig. 3
Fig. 3

Two-dimensional wavelets.

Fig. 4
Fig. 4

In-plane rotated image database with background.

Fig. 5
Fig. 5

In-plane rotation angle determination for raw images.

Fig. 6
Fig. 6

In-plane rotated image database with background removed.

Fig. 7
Fig. 7

Rotation angle determination without background clutter and noise.

Fig. 8
Fig. 8

Out-of-plane rotated and scaled image database (sequence 1).

Fig. 9
Fig. 9

Rotation angle determination with the Hilbert-wavelet: (a) Rotation angle vs. frame number, (b) correlation vs. Frame number.

Fig. 10
Fig. 10

Rotation angle determination with the Hilbert transform: (a) Rotation angle vs. frame number, (b) correlation vs. Frame number.

Fig. 11
Fig. 11

Out-of-plane rotated and scaled image database (sequence 2).

Fig. 12
Fig. 12

Rotation angle determination with the Hilbert wavelet: (a) Rotation angle vs. frame number, (b) correlation vs. Frame number.

Fig. 13
Fig. 13

Rotation angle determination with the Hilbert transform: (a) Rotation angle vs. frame number, (b) correlation vs. Frame number.

Fig. 14
Fig. 14

Performance Plots: (a) Time taken per frame in s vs. percent of compression, (b) percent of misclassification vs. percent of compression, (c) average correlation values vs. percent of compression.

Fig. 15
Fig. 15

Tracking of objects at different scale and angle with a single reference frame.

Fig. 16
Fig. 16

Improved target tracking with Hilbert-wavelet coefficients.

Equations (46)

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H0zH01/z+H0-zH0-1/z=2,
H1z=1/zH0-1/z,
Y0 expjω=1/2H0 expjω/2X expjω/2+H0-expjω/2X-expjω/2,
Y1 expjω=1/2H1 expjω/2X expjω/2+H1-expjω/2X-expjω/2,
Xr expjω=1/2H0 expjωG0 expjω+H1 expjωG1 expjωX expjω+H0-expjωG0 expjω+H1-expjωG1 expjωX ×-expjω,
G0 expjω=H1-expjω
G1 expjω=-H0-expjω.
H1 expjω=-H0-expjω
H02 expjω-H12 expjω=2.
Xr expjω=1/2XTMg,
XT=X expjωX-expjω, gT=G0 expjωG1 expjω,
M=H0 expjωH1 expjωH0-expjωH1-expjω.
M=2 exp-jωL-10,
G0 expjω=2H1-expjωexp-jωL-1H0 expjωH1-expjω-H0-expjωH1 expjω
G1 expjω=2H0 exp-jωexp-jωL-1H0 expjωH1-expjω-H0-expjωH1-exp(jω.
H0 expjωH1-expjω-H0-expjωH1 expjω=K exp-jωN,
H1 expjω=-H0 expjωexp-jωN,
Az=z-LD1/zDz=z-τ,
H0z=FzDz
G0z=FzZ-1D1/z,
G0z=Fzz-LD1/z/Dz.
Fz=Qz1+z-1k.
sz=z+2+z-1kDzD1/z.
ϕht=2n h0nϕh2t-n,
ψht=2n h1nϕh2t-n.
ψgt=Hψht,
Fu, v=Ffx, y+ifhx, y,
Fft/τ=1/ΓFτω,
At=ft2+fht2.
pt=tan-1fht/ft,
rt=12πdftdt.
ft-mf2fht-mh2dtdtft-mf2fht-mh2dtdt.
ψh,1x, y=ϕhxψhy,
ψh,2x, y=ψhxϕhy,
ψh,3x, y=ψhxψhy,
ψix, y=ψh,ix, y+ψg,ix, y, for i=1, 2, and 3,
ψ1x, y=ψh,ix, y-ψg,ix, y, for l=4, 5, and 6,
ψh1x, y=2n h0nϕh2x-n×n h1nϕh2y-n,
ψh2x, y=2n h1nϕh2x-n×n h0nϕh2y-n,
ψh3x, y=2n h1nϕh2x-n×n h1nϕh2y-n.
ψfx, y=ψhix, y*fx, y,
ψfhx, y=ψgix, y*fx, y,
ψfx, y=Tfx, yfx, y,
ψfhx, y=THfx, yfhx, y,
functioncorrα, β=f-x, -y*jx, y.
corr_coeff=αβ functioncorrα, β.

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