Abstract

We introduce a new approach for shift-, scale-, and projection-invariant pattern recognition that combines the harmonic expansion and the synthetic discriminant function approaches by use of a synthetic discriminant function filter with equal-order one-dimensional logarithmic harmonic components. Because projection invariance in one direction is guaranteed by the harmonics, the required number of training images is much fewer than with classical synthetic discriminant function filters.

© 1998 Optical Society of America

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References

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1995 (1)

1990 (2)

1989 (1)

1987 (1)

1986 (3)

1984 (3)

1980 (1)

1976 (1)

Arsenault, H. H.

H. H. Arsenault, Proc. SPIE 613, 239 (1986).
[CrossRef]

Butler, S.

J. Riggins and S. Butler, Opt. Eng. 23, 721 (1984).
[CrossRef]

Casasent, D.

Hester, C. F.

Kiryuschev, I.

Konforti, N.

Lebreton, G.

Mahalanobis, A.

Marom, E.

Maron, E.

Mendlovic, D.

Pochapsky, E.

Psaltis, D.

Réfrégier, Ph.

Riggins, J.

J. Riggins and S. Butler, Opt. Eng. 23, 721 (1984).
[CrossRef]

Szoplik, T.

Vijaya Kumar, B. V. K.

Yao, J.

J. Yao, “Algorithms for optical distortion invariant pattern recognition,” Ph.D. dissertation (Université de Toulon et du Var, La Garde, France, 1997).

Zalevsky, Z.

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Figures (2)

Fig. 1
Fig. 1

Shift-, scale-, and projection-invariance test for the IDLHSDF. (a) F18 aircraft and three scaled projected versions used as input. (b) Correlation between the 1DLHSDF and the true-class inputs from (a).

Fig. 2
Fig. 2

Discrimination capability test for the 1DLHSDF filter. (a) TOR aircraft and three scaled project versions used as input. (b) Correlation between the 1DLHSDF and the false-class inputs from (a).

Equations (7)

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fx, y;x0, y0=N=-fNy;x0, y0xi2π/TN-1/2,
fNy;x0, y0=12T-B-Afx, y;x0, y0×-x-i2π/TN-1/2dx+12T×ABfx, y;x0, y0x-i2π/TN-1/2dx, 
lnB-lnA=T.
hx, y-fNyxi2π/TN-1/2.
h1DLHSDFNx, y=i=1MaihiNx, y,  M=pq,
[Cf1h1DLHSDFNCf2h1DLHSDFNCfMh1DLHSDFN]=[Cf1h1NCf1h2NCf1hMNCf2h1NCf2h2NCf2hMNCfMh1NCfMh2NCfMhMN] [a1*a2*aM*],
Cfih1DLHSDFNβ=a1*Cfih1N+a2*Cfih2N++aM*CfihMN×β exp-i2πTNlnβ=β exp-i2πTNlnβCfih1DLHSDFN,

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