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

Full Article  |  PDF Article

References

  • View by:
  • |

  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]

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.

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 (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)

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

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

Metrics