Abstract

We discuss and implement a log-polar transform-based distortion-invariant filter for automatic target recognition applications. The log-polar transform is a known space-invariant image representation used in several image vision systems to eliminate the effects of scale and rotation in an image. For in-plane rotation invariance and scale invariance, a log-polar transform-based filter was synthesized. In cases of in-plane rotation invariance, peaks shift horizontally, and in cases of scale invariance, peaks shift vertically. To achieve out-of-plane rotation invariance, log-polar images were used to train the wavelet-modified maximum average correlation height (WaveMACH) filter. The designed filters were implemented in the hybrid digital–optical correlation scheme. It was observed that, for a certain range of rotation and scale differences, the correlation signals merge with the strong dc. To solve this problem a shift was introduced in the log-polar image of the target. The use of a chirp function for dc removal has also been discussed. Correlation peak height and peak-to-sidelobe ratio have been calculated as metrics of goodness of the log-polar transform-based WaveMACH filter. Experimental results are presented.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (Mc-Graw Hill, 1996).
  2. F. T. S. Yu and S. Jutamulia, eds., Optical Pattern Recognition (Cambridge U. Press, 1998).
  3. B. Javidi, ed., Image Recognition and Classification; Algorithms, Systems, and Applications (Dekker, 2002).
    [CrossRef] [PubMed]
  4. B. V. K. Vijaya Kumar, A. Mahalanobis, and R. D. Juday, Correlation Pattern Recognition (Cambridge U. Press, 2005).
    [CrossRef]
  5. B. V. K. Vijaya Kumar and L. Hassebrook, "Performance measures for correlation filters," Appl. Opt. 29, 2997-3006 (1990).
    [CrossRef]
  6. A. Mahalanobis, B. V. K. Vijaya Kumar, S. Song, S. R. F. Sims, and J. F. Epperson, "Unconstrained correlation filters," Appl. Opt. 33, 3751-3759 (1994).
    [CrossRef] [PubMed]
  7. M. Alkanhal, B. V. K. Vijaya Kumar, and A. Mahalanobis, "Improving the false alarm capabilities of the maximum average correlation height correlation filter," Opt. Eng. 39, 1133-1141 (2000).
    [CrossRef] [PubMed]
  8. A. V. Nevel and A. Mahalanobis, "Comparative study of maximum average correlation height filter variants using ladar imagery," Opt. Eng. 42, 541-550 (2003).
    [CrossRef] [PubMed]
  9. S. R. F. Sims and A. Mahalanobis, "Performance evaluation of quadratic correlation filters for target detection and discrimination in infrared imagery," Opt. Eng. 43, 1705-1711 (2004).
    [CrossRef]
  10. S. M. A. Bhuiyan, M. S. Alam, and S. R. F. Sims, "Target detection, classification, and tracking using a maximum average correlation height and polynomial distance classification correlation filter combination," Opt. Eng. 45, 116401 (2006).
    [CrossRef]
  11. R. Young, C. Chatwin, and B. Scott, "High-speed hybrid optical/digital correlator system," Opt. Eng. 32, 2608-2615 (1993).
    [CrossRef] [PubMed]
  12. P. Birch, R. Young, F. Claret-Tournier, D. Budgett, and C. Chatwin, "Computer-generated complex filter for an all-optical and a digital-optical hybrid correlator," Opt. Eng. 41, 105-111 (2002).
    [CrossRef]
  13. A. Bhagatji, N. K Nishchal, V. K. Beri, and A. K. Gupta, "Influence of perturbations in a hybrid digital-optical correlator," Opt. Lasers Eng. 45, 1-11 (2007).
    [CrossRef]
  14. S. Mallat, A Wavelet Tour of Signal Processing, 2nd ed. (Academic, 1999).
  15. H. Schwarzer, S. Teiwes, and F. Wyrowski, "Why is it sensible to use wavelets in matched filtering?" Proc. SPIE 2969, 604-609 (1996).
    [CrossRef]
  16. M. Pohit and K. Singh, "Performance of a wavelet matched filter with optimized dilation designed using simulated annealing algorithm," Opt. Commun. 187, 337-346 (2001).
    [CrossRef]
  17. A. Sinha and K. Singh, "The design of a composite wavelet matched filter for face recognition using breeder genetic algorithm," Opt. Lasers Eng. 43, 1277-1291 (2005).
    [CrossRef]
  18. S. Goyal, N. K. Nishchal, V. K. Beri, and A. K. Gupta, "Wavelet-modified maximum average correlation height filter for rotation invariance that uses chirp encoding in a hybrid digital-optical correlator," Appl. Opt. 45, 4850-4857 (2006).
    [CrossRef] [PubMed]
  19. S. Goyal, N. K. Nishchal, V. K. Beri, and A. K. Gupta, "Wavelet-modified maximum average correlation height filter for out-of-plane rotation invariance," Optik (in press).
  20. A. K. Gupta, N. K. Nishchal, and V. K. Beri, "A hybrid digital-optical correlator for automatic target recognition," Proc. SPIE 6574, 657406 (2007).
    [CrossRef]
  21. P. Bone, R. Young, and C. Chatwin, "Position-, rotation-, scale-, and orientation-invariant multiple object recognition from cluttered scenes," Opt. Eng. 45, 077203 (2006).
    [CrossRef]
  22. C. F. R. Weiman and G. Chaikin, "Logarithmic spiral grids for image processing and display," Comp. Graph. Image Process. 11, 197-226 (1979).
    [CrossRef]
  23. C. M. Pun and M. C. Lee, "Log-polar wavelet energy signatures for rotation and scale invariant texture classification," IEEE Trans. Pattern Anal. Mach. Intell. 25, 590-603 (2003).
    [CrossRef]
  24. J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, "Encoding amplitude information onto phase-only filters," Appl. Opt. 38, 5004-5013 (1999).
    [CrossRef]
  25. J. A. Davis, K. O. Valadez, and D. M. Cottrell, "Encoding amplitude and phase information onto a binary phase-only spatial light modulator," Appl. Opt. 42, 2003-2008 (2003).
    [CrossRef] [PubMed]
  26. G. Metta, A. Gasteratos, and G. Sandini, "Learning to track colored objects with logpolar vision," Mechatronics 14, 989-1006 (2004).

2007 (2)

A. Bhagatji, N. K Nishchal, V. K. Beri, and A. K. Gupta, "Influence of perturbations in a hybrid digital-optical correlator," Opt. Lasers Eng. 45, 1-11 (2007).
[CrossRef]

A. K. Gupta, N. K. Nishchal, and V. K. Beri, "A hybrid digital-optical correlator for automatic target recognition," Proc. SPIE 6574, 657406 (2007).
[CrossRef]

2006 (3)

P. Bone, R. Young, and C. Chatwin, "Position-, rotation-, scale-, and orientation-invariant multiple object recognition from cluttered scenes," Opt. Eng. 45, 077203 (2006).
[CrossRef]

S. M. A. Bhuiyan, M. S. Alam, and S. R. F. Sims, "Target detection, classification, and tracking using a maximum average correlation height and polynomial distance classification correlation filter combination," Opt. Eng. 45, 116401 (2006).
[CrossRef]

S. Goyal, N. K. Nishchal, V. K. Beri, and A. K. Gupta, "Wavelet-modified maximum average correlation height filter for rotation invariance that uses chirp encoding in a hybrid digital-optical correlator," Appl. Opt. 45, 4850-4857 (2006).
[CrossRef] [PubMed]

2005 (1)

A. Sinha and K. Singh, "The design of a composite wavelet matched filter for face recognition using breeder genetic algorithm," Opt. Lasers Eng. 43, 1277-1291 (2005).
[CrossRef]

2004 (2)

G. Metta, A. Gasteratos, and G. Sandini, "Learning to track colored objects with logpolar vision," Mechatronics 14, 989-1006 (2004).

S. R. F. Sims and A. Mahalanobis, "Performance evaluation of quadratic correlation filters for target detection and discrimination in infrared imagery," Opt. Eng. 43, 1705-1711 (2004).
[CrossRef]

2003 (3)

A. V. Nevel and A. Mahalanobis, "Comparative study of maximum average correlation height filter variants using ladar imagery," Opt. Eng. 42, 541-550 (2003).
[CrossRef] [PubMed]

C. M. Pun and M. C. Lee, "Log-polar wavelet energy signatures for rotation and scale invariant texture classification," IEEE Trans. Pattern Anal. Mach. Intell. 25, 590-603 (2003).
[CrossRef]

J. A. Davis, K. O. Valadez, and D. M. Cottrell, "Encoding amplitude and phase information onto a binary phase-only spatial light modulator," Appl. Opt. 42, 2003-2008 (2003).
[CrossRef] [PubMed]

2002 (1)

P. Birch, R. Young, F. Claret-Tournier, D. Budgett, and C. Chatwin, "Computer-generated complex filter for an all-optical and a digital-optical hybrid correlator," Opt. Eng. 41, 105-111 (2002).
[CrossRef]

2001 (1)

M. Pohit and K. Singh, "Performance of a wavelet matched filter with optimized dilation designed using simulated annealing algorithm," Opt. Commun. 187, 337-346 (2001).
[CrossRef]

2000 (1)

M. Alkanhal, B. V. K. Vijaya Kumar, and A. Mahalanobis, "Improving the false alarm capabilities of the maximum average correlation height correlation filter," Opt. Eng. 39, 1133-1141 (2000).
[CrossRef] [PubMed]

1999 (1)

1996 (1)

H. Schwarzer, S. Teiwes, and F. Wyrowski, "Why is it sensible to use wavelets in matched filtering?" Proc. SPIE 2969, 604-609 (1996).
[CrossRef]

1994 (1)

1993 (1)

R. Young, C. Chatwin, and B. Scott, "High-speed hybrid optical/digital correlator system," Opt. Eng. 32, 2608-2615 (1993).
[CrossRef] [PubMed]

1990 (1)

1979 (1)

C. F. R. Weiman and G. Chaikin, "Logarithmic spiral grids for image processing and display," Comp. Graph. Image Process. 11, 197-226 (1979).
[CrossRef]

Appl. Opt. (5)

Comp. Graph. Image Process. (1)

C. F. R. Weiman and G. Chaikin, "Logarithmic spiral grids for image processing and display," Comp. Graph. Image Process. 11, 197-226 (1979).
[CrossRef]

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

C. M. Pun and M. C. Lee, "Log-polar wavelet energy signatures for rotation and scale invariant texture classification," IEEE Trans. Pattern Anal. Mach. Intell. 25, 590-603 (2003).
[CrossRef]

Mechatronics (1)

G. Metta, A. Gasteratos, and G. Sandini, "Learning to track colored objects with logpolar vision," Mechatronics 14, 989-1006 (2004).

Opt. Commun. (1)

M. Pohit and K. Singh, "Performance of a wavelet matched filter with optimized dilation designed using simulated annealing algorithm," Opt. Commun. 187, 337-346 (2001).
[CrossRef]

Opt. Eng. (7)

M. Alkanhal, B. V. K. Vijaya Kumar, and A. Mahalanobis, "Improving the false alarm capabilities of the maximum average correlation height correlation filter," Opt. Eng. 39, 1133-1141 (2000).
[CrossRef] [PubMed]

A. V. Nevel and A. Mahalanobis, "Comparative study of maximum average correlation height filter variants using ladar imagery," Opt. Eng. 42, 541-550 (2003).
[CrossRef] [PubMed]

S. R. F. Sims and A. Mahalanobis, "Performance evaluation of quadratic correlation filters for target detection and discrimination in infrared imagery," Opt. Eng. 43, 1705-1711 (2004).
[CrossRef]

S. M. A. Bhuiyan, M. S. Alam, and S. R. F. Sims, "Target detection, classification, and tracking using a maximum average correlation height and polynomial distance classification correlation filter combination," Opt. Eng. 45, 116401 (2006).
[CrossRef]

R. Young, C. Chatwin, and B. Scott, "High-speed hybrid optical/digital correlator system," Opt. Eng. 32, 2608-2615 (1993).
[CrossRef] [PubMed]

P. Birch, R. Young, F. Claret-Tournier, D. Budgett, and C. Chatwin, "Computer-generated complex filter for an all-optical and a digital-optical hybrid correlator," Opt. Eng. 41, 105-111 (2002).
[CrossRef]

P. Bone, R. Young, and C. Chatwin, "Position-, rotation-, scale-, and orientation-invariant multiple object recognition from cluttered scenes," Opt. Eng. 45, 077203 (2006).
[CrossRef]

Opt. Lasers Eng. (2)

A. Bhagatji, N. K Nishchal, V. K. Beri, and A. K. Gupta, "Influence of perturbations in a hybrid digital-optical correlator," Opt. Lasers Eng. 45, 1-11 (2007).
[CrossRef]

A. Sinha and K. Singh, "The design of a composite wavelet matched filter for face recognition using breeder genetic algorithm," Opt. Lasers Eng. 43, 1277-1291 (2005).
[CrossRef]

Proc. SPIE (2)

H. Schwarzer, S. Teiwes, and F. Wyrowski, "Why is it sensible to use wavelets in matched filtering?" Proc. SPIE 2969, 604-609 (1996).
[CrossRef]

A. K. Gupta, N. K. Nishchal, and V. K. Beri, "A hybrid digital-optical correlator for automatic target recognition," Proc. SPIE 6574, 657406 (2007).
[CrossRef]

Other (6)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (Mc-Graw Hill, 1996).

F. T. S. Yu and S. Jutamulia, eds., Optical Pattern Recognition (Cambridge U. Press, 1998).

B. Javidi, ed., Image Recognition and Classification; Algorithms, Systems, and Applications (Dekker, 2002).
[CrossRef] [PubMed]

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

S. Goyal, N. K. Nishchal, V. K. Beri, and A. K. Gupta, "Wavelet-modified maximum average correlation height filter for out-of-plane rotation invariance," Optik (in press).

S. Mallat, A Wavelet Tour of Signal Processing, 2nd ed. (Academic, 1999).

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 (11)

Fig. 1
Fig. 1

(a) Image of Barbara, (b) log-polar image, (c) shifted log-polar image.

Fig. 2
Fig. 2

Experimental setup used. SF, spatial filter; CL, collimating lens; FT lens, Fourier transform lens; PBS, polarizing beam splitter; SLM, spatial light modulator.

Fig. 3
Fig. 3

Images of tanks. Tank 1 corresponds to the true class image and Tanks 2–4 correspond to false class images.

Fig. 4
Fig. 4

(a)–(d) True class images at angles of in-plane rotation 1°, 90°, 240°, and 330°, respectively, (e) false class image, and (f)–(j) corresponding correlation outputs.

Fig. 5
Fig. 5

(a)–(d) True class images at scale differences 80%, 130%, 150%, and 180%, respectively, (e) false class image, and (f)–(j) corresponding correlation outputs.

Fig. 6
Fig. 6

(a)–(d) True class images at angles of out-of-plane rotation 60°, 150°, 270°, and 330°, respectively, (e) false class image, and (f)–(j) corresponding correlation outputs.

Fig. 7
Fig. 7

(a)–(c) True class images at angles of in-plane rotation 0°, 60°, and 120°, respectively, (d) false class image, and (e)–(h) corresponding correlation outputs obtained after introducing chirp function.

Fig. 8
Fig. 8

(Color online) Plot of correlation peak height versus angle of in-plane rotations with Tank 1 as true class and Tanks 3 and 4 as false class targets.

Fig. 9
Fig. 9

(Color online) Plot of correlation peak height versus percentage scale variations with Tank 1 as true class and Tanks 2 and 3 as false class targets.

Fig. 10
Fig. 10

(Color online) Plot of correlation peak height versus angle of out-of-plane rotations with Tank 1 as true class and Tanks 2 and 4 as false class targets.

Fig. 11
Fig. 11

(Color online) Plot of peak-to-sidelobe ratio versus angle of out-of-plane rotations with Tank 1 as true class and Tanks 2, 3, and 4 as false class targets.

Equations (10)

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

w = log   z ,
z = x + i y ,
r = ( x 2 + y 2 ) 1 / 2 , θ = arctan ( y / x ) .
w = log   r + i θ = u + i v ,
f = S 1 m ,
S = 1 2 i = 1 N ( X i M ) ( X i M ) * ,
h ( x , y ) = [ 1 ( x 2 + y 2 ) ] exp ( x 2 + y 2 2 ) .
H ( u , v ) = 4 π 2 ( u 2 + v 2 ) exp 2 π ( u 2 + v 2 ) .
WaveMACH = S 1 m | H ( u , v ) | 2 .
PSR = peak μ σ ,

Metrics