Abstract

The performance of nonlinear morphological correlation is investigated and compared with that of conventional linear correlation. In particular, the effects of illumination variations on the morphological correlation output are investigated in detail. The morphological correlation is shown to be invariant to uniform input-image illumination when the input-image illumination is higher than that of the reference. It also provides higher pattern discriminability, sharper peaks, and more-robust detection in the presence of salt-and-pepper noise than does the linear correlation. Computer-simulation results are provided.

© 1999 Optical Society of America

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  1. C. S. Weaver, J. W. Goodman, “A technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
    [CrossRef] [PubMed]
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    [CrossRef]
  3. A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
  4. B. Javidi, J. Wang, “Binary nonlinear joint transform correlation with median and subset median thresholding,” Appl. Opt. 30, 967–976 (1991).
    [CrossRef] [PubMed]
  5. M. S. Alam, M. A. Karim, “Fringe-adjusted joint transform correlation,” Appl. Opt. 32, 3208–3216 (1995).
  6. R. K. Wang, L. Shang, C. R. Chatwin, “Modified fringe-adjusted joint-transform correlation to accommodate noise in the input scene,” Appl. Opt. 35, 286–296 (1996).
    [CrossRef] [PubMed]
  7. T. J. Grycewicz, “Fourier-plane windowing in the binary joint transform correlator for multiple target detection,” Appl. Opt. 34, 3933–3941 (1995).
    [CrossRef] [PubMed]
  8. M. S. Alam, M. A. Karim, “Joint-transform correlation under varying illumination,” Appl. Opt. 32, 4351–4356 (1993).
    [CrossRef] [PubMed]
  9. S. Jutamulia, G. M. Storti, D. A. Gregory, J. C. Kirsch, “Illumination-independent high-efficient joint-transform correlation,” Appl. Opt. 30, 4173–4175 (1991).
    [CrossRef] [PubMed]
  10. B. Javidi, J. Li, A. H. Fazlollahi, J. Horner, “Binary nonlinear joint transform correlator performance with different thresholding methods under unknown illumination conditions,” Appl. Opt. 34, 886–896 (1995).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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  16. P. Maragos, “Optimal morphological approaches to image matching and object detection,” in Second International Conference on Computer Vision (IEEE Computer Society, Washington, D.C., 1988), pp. 695–699.
  17. P. Garcia-Martinex, D. Mas, J. Garcia, C. Ferreira, “Nonlinear morphological correlation: optoelectronic implementation,” Appl. Opt. 37, 2112–2118 (1998).
    [CrossRef]
  18. A. Shemer, D. Mendlovic, G. Shabtay, P. Garcia-Martinez, J. Garcia, “Modified morphological correlation based on bit-map representations,” Appl. Opt. 38, 781–787.
  19. P. D. Wendt, E. J. Coyle, N. C. Gallagher, “Stack filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-34, 898–911 (1986).
    [CrossRef]
  20. E. Ochoa, J. P. Allebach, D. W. Sweeney, “Optical median filtering using threshold decomposition,” Appl. Opt. 26, 252–260 (1987).
    [CrossRef] [PubMed]
  21. B. V. K. Vijaya Kumar, L. Hassebrook, “Performance measures for correlation filters,” Appl. Opt. 29, 2997–3006 (1990).
    [CrossRef]
  22. G. Lu, F. T. S. Yu, “Performance of a phase-transformed input joint transform correlator,” Appl. Opt. 35, 304–313 (1996).
    [CrossRef] [PubMed]
  23. J. L. Horner, J. R. Leger, “Pattern recognition with binary phase-only filters,” Appl. Opt. 24, 609–611 (1985).
    [CrossRef] [PubMed]

1998 (2)

G. S. Pati, K. Singh, “Illumination sensitivity of joint transform correlators using differential processing: computer simulation and experimental studies,” Opt. Commun. 147, 26–32 (1998).
[CrossRef]

P. Garcia-Martinex, D. Mas, J. Garcia, C. Ferreira, “Nonlinear morphological correlation: optoelectronic implementation,” Appl. Opt. 37, 2112–2118 (1998).
[CrossRef]

1997 (1)

G. S. Pati, K. Singh, “Experimental and simulation studies on the performance of binary and gray-valued joint transform correlators under poor illumination conditions and nonoverlapping background noise,” Opt. Eng. 36, 1918–1929 (1997).
[CrossRef]

1996 (2)

1995 (3)

1993 (1)

1991 (3)

1990 (1)

1987 (1)

1986 (1)

P. D. Wendt, E. J. Coyle, N. C. Gallagher, “Stack filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-34, 898–911 (1986).
[CrossRef]

1985 (1)

1984 (1)

F. T. S. Yu, X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[CrossRef]

1966 (1)

1964 (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

Alam, M. S.

M. S. Alam, M. A. Karim, “Fringe-adjusted joint transform correlation,” Appl. Opt. 32, 3208–3216 (1995).

M. S. Alam, M. A. Karim, “Joint-transform correlation under varying illumination,” Appl. Opt. 32, 4351–4356 (1993).
[CrossRef] [PubMed]

Allebach, J. P.

Chatwin, C. R.

Coyle, E. J.

P. D. Wendt, E. J. Coyle, N. C. Gallagher, “Stack filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-34, 898–911 (1986).
[CrossRef]

Dickey, F. M.

Fazlollahi, A. H.

Ferreira, C.

Gallagher, N. C.

P. D. Wendt, E. J. Coyle, N. C. Gallagher, “Stack filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-34, 898–911 (1986).
[CrossRef]

Garcia, J.

Garcia-Martinex, P.

Garcia-Martinez, P.

Goodman, J. W.

C. S. Weaver, J. W. Goodman, “A technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
[CrossRef] [PubMed]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1967), pp. 203–208.

Gregory, D. A.

Grycewicz, T. J.

Hassebrook, L.

Horner, J.

Horner, J. L.

Javidi, B.

Jutamulia, S.

Karim, M. A.

M. S. Alam, M. A. Karim, “Fringe-adjusted joint transform correlation,” Appl. Opt. 32, 3208–3216 (1995).

M. S. Alam, M. A. Karim, “Joint-transform correlation under varying illumination,” Appl. Opt. 32, 4351–4356 (1993).
[CrossRef] [PubMed]

Kirsch, J. C.

Leger, J. R.

Li, J.

Lu, G.

Lu, X. J.

F. T. S. Yu, X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[CrossRef]

Maragos, P.

P. Maragos, “Morphological correlation and mean absolute error,” in ICASSP-89: 1989 International Conference on Acoustic, Speech and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1989), Vol. 3, pp. 1568–1571.

P. Maragos, “Optimal morphological approaches to image matching and object detection,” in Second International Conference on Computer Vision (IEEE Computer Society, Washington, D.C., 1988), pp. 695–699.

Mas, D.

Mendlovic, D.

Ochoa, E.

Pati, G. S.

G. S. Pati, K. Singh, “Illumination sensitivity of joint transform correlators using differential processing: computer simulation and experimental studies,” Opt. Commun. 147, 26–32 (1998).
[CrossRef]

G. S. Pati, K. Singh, “Experimental and simulation studies on the performance of binary and gray-valued joint transform correlators under poor illumination conditions and nonoverlapping background noise,” Opt. Eng. 36, 1918–1929 (1997).
[CrossRef]

Romero, L. A.

Shabtay, G.

Shang, L.

Shemer, A.

Singh, K.

G. S. Pati, K. Singh, “Illumination sensitivity of joint transform correlators using differential processing: computer simulation and experimental studies,” Opt. Commun. 147, 26–32 (1998).
[CrossRef]

G. S. Pati, K. Singh, “Experimental and simulation studies on the performance of binary and gray-valued joint transform correlators under poor illumination conditions and nonoverlapping background noise,” Opt. Eng. 36, 1918–1929 (1997).
[CrossRef]

Storti, G. M.

Sweeney, D. W.

VanderLugt, A.

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

Vijaya Kumar, B. V. K.

Wang, J.

Wang, R. K.

Weaver, C. S.

Wendt, P. D.

P. D. Wendt, E. J. Coyle, N. C. Gallagher, “Stack filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-34, 898–911 (1986).
[CrossRef]

Yu, F. T. S.

G. Lu, F. T. S. Yu, “Performance of a phase-transformed input joint transform correlator,” Appl. Opt. 35, 304–313 (1996).
[CrossRef] [PubMed]

F. T. S. Yu, X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[CrossRef]

Appl. Opt. (14)

M. S. Alam, M. A. Karim, “Fringe-adjusted joint transform correlation,” Appl. Opt. 32, 3208–3216 (1995).

E. Ochoa, J. P. Allebach, D. W. Sweeney, “Optical median filtering using threshold decomposition,” Appl. Opt. 26, 252–260 (1987).
[CrossRef] [PubMed]

B. V. K. Vijaya Kumar, L. Hassebrook, “Performance measures for correlation filters,” Appl. Opt. 29, 2997–3006 (1990).
[CrossRef]

B. Javidi, J. Wang, “Binary nonlinear joint transform correlation with median and subset median thresholding,” Appl. Opt. 30, 967–976 (1991).
[CrossRef] [PubMed]

M. S. Alam, M. A. Karim, “Joint-transform correlation under varying illumination,” Appl. Opt. 32, 4351–4356 (1993).
[CrossRef] [PubMed]

P. Garcia-Martinex, D. Mas, J. Garcia, C. Ferreira, “Nonlinear morphological correlation: optoelectronic implementation,” Appl. Opt. 37, 2112–2118 (1998).
[CrossRef]

A. Shemer, D. Mendlovic, G. Shabtay, P. Garcia-Martinez, J. Garcia, “Modified morphological correlation based on bit-map representations,” Appl. Opt. 38, 781–787.

B. Javidi, J. Li, A. H. Fazlollahi, J. Horner, “Binary nonlinear joint transform correlator performance with different thresholding methods under unknown illumination conditions,” Appl. Opt. 34, 886–896 (1995).
[CrossRef] [PubMed]

T. J. Grycewicz, “Fourier-plane windowing in the binary joint transform correlator for multiple target detection,” Appl. Opt. 34, 3933–3941 (1995).
[CrossRef] [PubMed]

R. K. Wang, L. Shang, C. R. Chatwin, “Modified fringe-adjusted joint-transform correlation to accommodate noise in the input scene,” Appl. Opt. 35, 286–296 (1996).
[CrossRef] [PubMed]

G. Lu, F. T. S. Yu, “Performance of a phase-transformed input joint transform correlator,” Appl. Opt. 35, 304–313 (1996).
[CrossRef] [PubMed]

J. L. Horner, J. R. Leger, “Pattern recognition with binary phase-only filters,” Appl. Opt. 24, 609–611 (1985).
[CrossRef] [PubMed]

S. Jutamulia, G. M. Storti, D. A. Gregory, J. C. Kirsch, “Illumination-independent high-efficient joint-transform correlation,” Appl. Opt. 30, 4173–4175 (1991).
[CrossRef] [PubMed]

C. S. Weaver, J. W. Goodman, “A technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
[CrossRef] [PubMed]

IEEE Trans. Acoust. Speech Signal Process. (1)

P. D. Wendt, E. J. Coyle, N. C. Gallagher, “Stack filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-34, 898–911 (1986).
[CrossRef]

IEEE Trans. Inf. Theory (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

Opt. Commun. (2)

F. T. S. Yu, X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[CrossRef]

G. S. Pati, K. Singh, “Illumination sensitivity of joint transform correlators using differential processing: computer simulation and experimental studies,” Opt. Commun. 147, 26–32 (1998).
[CrossRef]

Opt. Eng. (1)

G. S. Pati, K. Singh, “Experimental and simulation studies on the performance of binary and gray-valued joint transform correlators under poor illumination conditions and nonoverlapping background noise,” Opt. Eng. 36, 1918–1929 (1997).
[CrossRef]

Opt. Lett. (1)

Other (3)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1967), pp. 203–208.

P. Maragos, “Morphological correlation and mean absolute error,” in ICASSP-89: 1989 International Conference on Acoustic, Speech and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1989), Vol. 3, pp. 1568–1571.

P. Maragos, “Optimal morphological approaches to image matching and object detection,” in Second International Conference on Computer Vision (IEEE Computer Society, Washington, D.C., 1988), pp. 695–699.

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Figures (12)

Fig. 1
Fig. 1

Block diagram of JTC-based morphological correlation (after Ref. 17).

Fig. 2
Fig. 2

Input and reference images used in pattern-discriminability evaluation.

Fig. 3
Fig. 3

Output cross-correlation distributions between images in Fig. 2 for (a) LC and (b) MC.

Fig. 4
Fig. 4

Images used in simulations: (a) noise-free target, (b) target in salt-and-pepper noise with a noise density of 0.2, and (c) target in salt-and-pepper noise with a noise density of 0.7.

Fig. 5
Fig. 5

Output correlation distributions between Figs. 4(a) and 4(c): (a) LC, (b) MC.

Fig. 6
Fig. 6

PNR versus noise intensity.

Fig. 7
Fig. 7

Joint input image when α’s ≥ 1.

Fig. 8
Fig. 8

Output correlation distributions when α’s ≥ 1 for (a) MC and (b) LC.

Fig. 9
Fig. 9

Joint input image when 0 < α’s < 1.

Fig. 10
Fig. 10

Output correlation distributions when 0 < α’s < 1 for (a) MC and (b) LC.

Fig. 11
Fig. 11

PCE versus illumination α.

Fig. 12
Fig. 12

PNR versus illumination α.

Equations (27)

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

Cx, y=tx, y * rx, y=hl rh, ltx+h, y+l,
MCx, y=tx, yΘrx, y=hlminrh, l, tx+h, y+l,
tx, y=q=1Q-1 tqx, y,
rx, y=q=1Q-1 rqx, y,
tqx, y=1if tx, yq0otherwise,
rqx, y=1if rx, yq0otherwise.
MCx, y=q=1Q-1 tqx, y * rqx, y=q=1Q-1 Cqx, y,
MSEx, y=m,nRtm+x, n+y-rm, n2,
MAEx, y=m,nR |tm+x, n+y-rm, n|,
SCR=APICPI,
API=hlminrh, l, rh, l2=hl rh, l2.
SCR=hl rh, l2maxx,yhlminrh, l, tx+h, y+l2.
minrh, l, tx+h, y+lrh, l,
maxx,yhlminrh, l, tx+h, y+lhl rh, l.
PCE=|z0, 0|2/Ez,
Ez=xy |zx, y|2.
tx, y=αrx, y.
Cx, y=αhl rh, lrx+h, y+l.
C0, 0=α hl rh, l2.
PCE=|C0, 0|2xy |Cx, y|2=αhl rh, l2xyhl αrx, yrx+h, y+l2=hl rh, l2xyhl rx, yrx+h, y+l2,
MCx, y=hlminrh, l, αrx+h, y+l.
MC0, 0=hlminrh, l, αrh, l=hl rh, l.
PCE=|MC0, 0|2xy |MCx, y|2=hl rh, l2xyhlminrh, l, αrx+h, y+l2.
minrh, l, α1rx+h, y+lminrh, l,α2rx+h, y+l,
MC0, 0=hl th, l=αhl rh, l.
PCE=|MC0, 0|2xy |MCx, y|2=αhl rh, l2xyhlminrh, l, αrx+h, y+l2=hl rh, l2xyhlminrh, lα, rx+h, y+l2=hl rh, l2xyhlminβrh, l, rx+h, y+l2,
PNR=z0, 0xΩyΩ |zx, y|/N,

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