Abstract

We present the cylindrical harmonic filter for three-dimensional (3D) discrete correlation between range data. The filter guarantees invariance of the correlation peak intensity under target rotation around z-axis. It can be considered a harmonic decomposition, in cylindrical coordinates, of the 3D Fourier spectrum of the target. Some simulation results confirm the in-plane rotation invariance and the discrimination of the filter.

© 2004 Optical Society of America

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References

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  1. J Guerrero, J. Meneses, and O. Gualdrón. “Object recognition using three-dimensional correlation of range images,” Opt. Eng. 39, 10, 2828–2831. (2000).
    [Crossref]
  2. M. Suk and S. Bhandakar, “Three-dimensional object recognition from range images,” (Tokyo, Tosiyasu Kunni, eds., 1992) Springer Verlag, 308p.
  3. Y.N. Hsu, H.H. Arsenault, and G. April, “Rotation Invariant digital pattern recognition using circular harmonic expansion,” Appl. Opt. 21, 4012–4015 (1982).
    [Crossref] [PubMed]
  4. O. Gualdrón and H. Arsenault. “Improved Invariant Pattern Recognition Methods,” in Real Time Optical Information Processing, (San Diego, B. Javidi and J. Horner. Eds.1994), Academic Press, pp 89–113.
  5. P. García-Martínez, H. Arsenault, and C. Ferreira. “Nonlinear Binary Correlations for Rotation Invariant Pattern Recognition using Circular Harmonic Decomposition,” Proc. SPIE 4419.676–679. (2001)
    [Crossref]

2001 (1)

P. García-Martínez, H. Arsenault, and C. Ferreira. “Nonlinear Binary Correlations for Rotation Invariant Pattern Recognition using Circular Harmonic Decomposition,” Proc. SPIE 4419.676–679. (2001)
[Crossref]

2000 (1)

J Guerrero, J. Meneses, and O. Gualdrón. “Object recognition using three-dimensional correlation of range images,” Opt. Eng. 39, 10, 2828–2831. (2000).
[Crossref]

1982 (1)

April, G.

Arsenault, H.

P. García-Martínez, H. Arsenault, and C. Ferreira. “Nonlinear Binary Correlations for Rotation Invariant Pattern Recognition using Circular Harmonic Decomposition,” Proc. SPIE 4419.676–679. (2001)
[Crossref]

O. Gualdrón and H. Arsenault. “Improved Invariant Pattern Recognition Methods,” in Real Time Optical Information Processing, (San Diego, B. Javidi and J. Horner. Eds.1994), Academic Press, pp 89–113.

Arsenault, H.H.

Bhandakar, S.

M. Suk and S. Bhandakar, “Three-dimensional object recognition from range images,” (Tokyo, Tosiyasu Kunni, eds., 1992) Springer Verlag, 308p.

Ferreira, C.

P. García-Martínez, H. Arsenault, and C. Ferreira. “Nonlinear Binary Correlations for Rotation Invariant Pattern Recognition using Circular Harmonic Decomposition,” Proc. SPIE 4419.676–679. (2001)
[Crossref]

García-Martínez, P.

P. García-Martínez, H. Arsenault, and C. Ferreira. “Nonlinear Binary Correlations for Rotation Invariant Pattern Recognition using Circular Harmonic Decomposition,” Proc. SPIE 4419.676–679. (2001)
[Crossref]

Gualdrón, O.

J Guerrero, J. Meneses, and O. Gualdrón. “Object recognition using three-dimensional correlation of range images,” Opt. Eng. 39, 10, 2828–2831. (2000).
[Crossref]

O. Gualdrón and H. Arsenault. “Improved Invariant Pattern Recognition Methods,” in Real Time Optical Information Processing, (San Diego, B. Javidi and J. Horner. Eds.1994), Academic Press, pp 89–113.

Guerrero, J

J Guerrero, J. Meneses, and O. Gualdrón. “Object recognition using three-dimensional correlation of range images,” Opt. Eng. 39, 10, 2828–2831. (2000).
[Crossref]

Hsu, Y.N.

Meneses, J.

J Guerrero, J. Meneses, and O. Gualdrón. “Object recognition using three-dimensional correlation of range images,” Opt. Eng. 39, 10, 2828–2831. (2000).
[Crossref]

Suk, M.

M. Suk and S. Bhandakar, “Three-dimensional object recognition from range images,” (Tokyo, Tosiyasu Kunni, eds., 1992) Springer Verlag, 308p.

Appl. Opt. (1)

Opt. Eng. (1)

J Guerrero, J. Meneses, and O. Gualdrón. “Object recognition using three-dimensional correlation of range images,” Opt. Eng. 39, 10, 2828–2831. (2000).
[Crossref]

Proc. SPIE (1)

P. García-Martínez, H. Arsenault, and C. Ferreira. “Nonlinear Binary Correlations for Rotation Invariant Pattern Recognition using Circular Harmonic Decomposition,” Proc. SPIE 4419.676–679. (2001)
[Crossref]

Other (2)

M. Suk and S. Bhandakar, “Three-dimensional object recognition from range images,” (Tokyo, Tosiyasu Kunni, eds., 1992) Springer Verlag, 308p.

O. Gualdrón and H. Arsenault. “Improved Invariant Pattern Recognition Methods,” in Real Time Optical Information Processing, (San Diego, B. Javidi and J. Horner. Eds.1994), Academic Press, pp 89–113.

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Figures (4)

Fig. 1.
Fig. 1.

Range data corresponding to an adjustable wrench tool

Fig. 2.
Fig. 2.

Input scene used in the discrimination test of the cylindrical harmonic filter.

Fig. 3.
Fig. 3.

Planes w=-2 -1 0 1 2, taken out of the frequency response of normalized magnitude of the cylindrical harmonic filter |H(ρ,φ,w)| synthesized from the range data in Fig. 1.

Fig. 4.
Fig. 4.

Portion of the discrete planes z=[3,4,5,6], taken out of the normalized intensity of 3D-discrete correlation between data range in Fig. 1 and Fig. 2.

Equations (7)

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s ( x , y , z ) = { t ( Δ X , Δ Y , Δ Z ) Object 0 in other case
H k ( ρ , ϕ , w ) = F k ( ρ , w ) e i k ϕ
F k ( ρ , w ) = 1 2 π n = 0 N 1 F ( ρ , ϕ n , w ) exp ( i m ϕ n ) , ϕ n = 2 π n P
C ( 0 , 0 , 0 ) = l = 0 L 1 m = 0 M 1 n = 0 N 1 [ s = F s ( ρ l , w m ) exp ( i s ( ϕ n + α ) ) ] ρ 1 H k * ( ρ l , w m ) exp ( i k ϕ n )
F ( ρ , ϕ + α , w ) = m = F m ( ρ , w ) e i m ( ϕ + α )
C ( 0 , 0 , 0 ) = l = 0 L 1 m = 0 M 1 s = [ F s ( ρ l , w m ) H k * ( ρ l , w m ) e i s α ρ l n = 0 N 1 exp ( i s ϕ n ) exp ( i k ϕ n ) ]
C ( 0 , 0 , 0 ) = 2 π e i k α l = 0 L 1 m = 0 M 1 F k ( ρ l , w m ) H k * ( ρ l , w m ) ρ l

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