Abstract

Invariant pattern recognition can be achieved by use of harmonic decomposition, for example circular harmonics are used for rotation invariant recognition. A common problem with such methods is that often only a single term of the harmonic decomposition is used, and it does not contain a sufficient amount of the reference energy. Thus discrimination capability is limited, especially in the presence of noise or other disturbances. By using several terms of the harmonic decomposition together this problem can be solved; this can be achieved by the use of code division filter multiplexing. Several harmonic terms are encoded onto a single filter, and the signal is simultaneously correlated with all of them, hence producing enhanced discrimination capabilities. Here two methods are suggested for such encoding. The first involves multiplexing the filters in the Fourier plane, while the second involves multiplexing in the image plane.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y.-N. Hsu, H. H. Arsenault, “Pattern discrimination by multiple circular harmonic components,” Appl. Opt. 23, 841–844 (1984).
    [CrossRef]
  2. H. H. Arsenault, C. Belisle, “Contrast-invariant pattern recognition using circular harmonic components,” Appl. Opt. 24, 2072–2075 (1985).
    [CrossRef] [PubMed]
  3. R. Wu, H. Stark, “Rotation-invariant pattern recognition using a vector reference,” Appl. Opt. 23, 838–840 (1984).
    [CrossRef]
  4. R. Wu, H. Stark, “Rotation-invariant pattern recognition using optimum feature extraction,” Appl. Opt. 24, 179–184 (1985).
    [CrossRef] [PubMed]
  5. L. Shen, Y. Sheng, G. Premont, “Theory and optical implementation of the geometrical approach of multiple circular harmonic filters,” Appl. Opt. 34, 4004–4012 (1995).
    [CrossRef] [PubMed]
  6. Z. Zalevsky, D. Mendlovic, J. Garcia, “Invariant pattern recognition by use of wavelength multiplexing,” Appl. Opt. 36, 1059–1063 (1997).
    [CrossRef] [PubMed]
  7. J. Solomon, Z. Zalevsky, D. Mendlovic, J. Garcia, “Filter multiplexing using spatial code division multiple access approach,” Appl. Opt. 42, 772–777 (2003).
    [CrossRef] [PubMed]
  8. Y.-N. Hsu, H. H. Arsenault, G. April, “Rotation-invariant digital pattern recognition using harmonic expansion,” Appl. Opt. 21, 4012–4015 (1982).
    [CrossRef] [PubMed]
  9. Y.-N. Hsu, H. H. Arsenault, “Optical pattern recognition using harmonic expansion,” Appl. Opt. 21, 4016–4019 (1982).
    [CrossRef] [PubMed]
  10. J. Goodman, Introduction to Fourier Optics2nd ed. (McGraw-Hill, New York, 1996), pp. 254–256.
  11. A. J. Viterbi, CDMA, Principles of Spread Spectrum Communication (Addison-Wesley, Reading, Mass., 1996).
  12. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
  13. S. Girilli, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, R. Meucci, “Whole optical wave fields reconstruction by digital holography,” Opt. Express 9, 294–302 (2001).
    [CrossRef]

2003 (1)

2001 (1)

1997 (1)

1995 (1)

1985 (2)

1984 (2)

1982 (2)

1964 (1)

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

April, G.

Arsenault, H. H.

Belisle, C.

De Nicola, S.

Ferraro, P.

Finizio, A.

Garcia, J.

Girilli, S.

Goodman, J.

J. Goodman, Introduction to Fourier Optics2nd ed. (McGraw-Hill, New York, 1996), pp. 254–256.

Hsu, Y.-N.

Mendlovic, D.

Meucci, R.

Pierattini, G.

Premont, G.

Shen, L.

Sheng, Y.

Solomon, J.

Stark, H.

VanderLugt,

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

Viterbi, A. J.

A. J. Viterbi, CDMA, Principles of Spread Spectrum Communication (Addison-Wesley, Reading, Mass., 1996).

Wu, R.

Zalevsky, Z.

Appl. Opt. (9)

IEEE Trans. Inf. Theory (1)

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

Opt. Express (1)

Other (2)

J. Goodman, Introduction to Fourier Optics2nd ed. (McGraw-Hill, New York, 1996), pp. 254–256.

A. J. Viterbi, CDMA, Principles of Spread Spectrum Communication (Addison-Wesley, Reading, Mass., 1996).

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 (13)

Fig. 1
Fig. 1

4-f setup.

Fig. 2
Fig. 2

4-f setup for optional encoding and retrieval.

Fig. 3
Fig. 3

Input image and harmonic terms.

Fig. 4
Fig. 4

(a) Different jet (F-18) used as test case, (b) original jet (Tornado) but rotated, used as test case.

Fig. 5
Fig. 5

CDMA filter.

Fig. 6
Fig. 6

Filter in the image plane.

Fig. 7
Fig. 7

Output received after convolution of input image with filter.

Fig. 8
Fig. 8

Ideal output of the different filters.

Fig. 9
Fig. 9

Ideal output of the different filters shown in mesh grid.

Fig. 10
Fig. 10

Retrieved output from simulation.

Fig. 11
Fig. 11

Original input correlation results.

Fig. 12
Fig. 12

Output by using image plane CDMA coding.

Fig. 13
Fig. 13

Different filter output by using image plane CDMA coding.

Tables (2)

Tables Icon

Table 1 Correlation Results for Only One CH Componenta

Tables Icon

Table 2 Correlation Results for Three CH Componentsa

Equations (24)

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

gr, θ=m=- gmrexpimθ.
gmr=12π02π gr, θexp-imθdθ.
gr, θ-α=m=- gmrexpimαexpimθ.
Cm=2π 0 |gmr|2rdr.
Cα=m=- Cm expimα.
Sνx, νy=n=14 Fnνx, νyMnνx, νy.
Oνx, νy=Iνx, νySνx, νy=Iνx, νyn=14 Fnνx, νyMnνx, νy.
Riνx, νy=Oνx, νyMiνx, νy =n=14 Iνx, νyFnνx, νyMnνx, νy×Miνx, νy=n=14 Iνx, νyFnνx, νy×Mnνx, νyMiνx, νy.
Riνx, νy=Iνx, νyFiνx, νyMi2νx, νy=Iνx, νyFiνx, νyMiνx, νy.
rix, y=ix, y*fix, y.
ikM=ikM+1==ikM+M-1 k=0, 1, 2, 
flkM=flkM+1==flkM+M-1k=0, 1, 2,; 1=1 M.
sn=l=1M flnmln.
dn=k δkM-n.
mln=q δqM-n+l.
minmjn=δi-j i, j
sn=l flnq δqM-n+l.
rn=indn*sn=jijdjsn-j.
rn=jijk δkM-jl fln-jq δqM-n+l+j.
rn=l,j ijj,q fln-jq δqM-n+l+j×k δkM-j.
rn=l,j ikNj,q fln-kNq δq+k×M-n+l
rn=l ink fln-kMt δtM-n+l.
rn=lin*flnt δtM-n+l
rn=lin*flnmln.

Metrics