Abstract

A scale invariant 3D object detection method based on phase Fourier transform (PhFT) is addressed. Three-dimensionality is expressed in terms of range images. The PhFT of a range image gives information about the orientations of the surfaces in the 3D object. When the object is scaled, the PhFT becomes a distribution multiplied by a constant factor which is related to the scale factor. Then 3D scale invariant detection can be solved as illumination invariant detection process. Several correlation operations based on vector space representation are applied. Results show the tolerance of detection method to scale besides discrimination against false objects.

© 2007 Optical Society of America

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References

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2006 (1)

2005 (2)

2004 (2)

J. J. Esteve-Taboada, N. Palmer, J.- Ch. Giannesini, J. García, and C. Ferreira, “Recognition of polychromatic three-dimensional objects,” Appl. Opt. 43, 433–441 (2004).
[Crossref] [PubMed]

S. Roy, D. Lefebvre, and H. H. Arsenault, “Recognition invariant under unknown affine transformations of intensity,” Opt. Commun. 238, 69–77 (2004).
[Crossref]

2003 (4)

J. García, J. J. Vallés, and C. Ferreira, “Detection of three-dimensional objects under arbitrary rotations based on range images,” Opt. Express. 11, 3352–3358 (2003).
[Crossref] [PubMed]

S. Chang, M. Rioux, and C. P. Grover, “Range face recognition based on the phase Fourier transform,” Opt. Commun. 222, 143–153 (2003).
[Crossref]

Y. Li and J. Rosen, “Scale invariant recognition of three-dimensional objects by use of a quasi-correlator,” Appl. Opt. 42, 811–819 (2003).
[Crossref] [PubMed]

D. Lefebvre, H. H. Arsenault, and S. Roy, “Nonlinear filter for pattern recognition invariant to illumination and to out-ot-plane rotations,” Appl. Opt. 42, 4658–4662 (2003).
[Crossref] [PubMed]

2002 (2)

J. J. Esteve-Taboada, J. García, and C. Ferreira, “Optical recognition of three-dimensional objects with scale invariance using classical convergent correlator,” Opt. Eng. 41, 1324–1330 (2002).
[Crossref]

D. Lefebvre, H. H. Arsenault, P. Garcia-Martinez, and C. Ferreira, “Recognition of unsegmented targets invariant under transformations of intensity,” Appl. Opt. 41, 6135–6142 (2002).
[Crossref] [PubMed]

2000 (3)

1999 (2)

1998 (3)

E. Paquet, P. Garcia-Martinez, and J. Garcia, “Tridimensional invariant correlation based on phase-coded and sine-coded range images,” J. Opt. 29, 35–39 (1998).
[Crossref]

J. Rosen, “Three-dimensional joint transform correlator,” Appl. Opt. 37, 7538–7544 (1998).
[Crossref]

J. Rosen, “Three-dimensional electro-optical correlation,” J. Opt. Soc. Am. A 15, 430–436 (1998).
[Crossref]

1995 (1)

E. Paquet, M. Rioux, and H. H. Arsenault, “Invariant pattern recognition for range images using the phase Fourier transform and a neural network,” Opt. Eng. 34, 1178–1183 (1995).
[Crossref]

1991 (1)

1984 (1)

1983 (1)

Arsenault, H. H.

Carapezza, E.

Chang, S.

S. Chang, M. Rioux, and C. P. Grover, “Range face recognition based on the phase Fourier transform,” Opt. Commun. 222, 143–153 (2003).
[Crossref]

Dickey, F. M.

Esteve-Taboada, J. J.

Ferreira, C.

Garcia, J.

J. J. Esteve-Taboada, D. Mas, and J. Garcia, “Three-dimensional object recognition by Fourier transform profilometry,” Appl. Opt. 38, 4760–4765 (1999).
[Crossref]

E. Paquet, P. Garcia-Martinez, and J. Garcia, “Tridimensional invariant correlation based on phase-coded and sine-coded range images,” J. Opt. 29, 35–39 (1998).
[Crossref]

García, J.

Garcia-Martinez, P.

D. Lefebvre, H. H. Arsenault, P. Garcia-Martinez, and C. Ferreira, “Recognition of unsegmented targets invariant under transformations of intensity,” Appl. Opt. 41, 6135–6142 (2002).
[Crossref] [PubMed]

E. Paquet, P. Garcia-Martinez, and J. Garcia, “Tridimensional invariant correlation based on phase-coded and sine-coded range images,” J. Opt. 29, 35–39 (1998).
[Crossref]

García-Martínez, P.

Giannesini, J.- Ch.

Grover, C. P.

S. Chang, M. Rioux, and C. P. Grover, “Range face recognition based on the phase Fourier transform,” Opt. Commun. 222, 143–153 (2003).
[Crossref]

Javidi, B.

Kim, T.

Lefebvre, D.

Li, Y.

Mas, D.

Moon, I.

Mutoh, K.

Palmer, N.

Paquet, E.

E. Paquet, P. Garcia-Martinez, and J. Garcia, “Tridimensional invariant correlation based on phase-coded and sine-coded range images,” J. Opt. 29, 35–39 (1998).
[Crossref]

E. Paquet, M. Rioux, and H. H. Arsenault, “Invariant pattern recognition for range images using the phase Fourier transform and a neural network,” Opt. Eng. 34, 1178–1183 (1995).
[Crossref]

Poon, T.

Rioux, M.

S. Chang, M. Rioux, and C. P. Grover, “Range face recognition based on the phase Fourier transform,” Opt. Commun. 222, 143–153 (2003).
[Crossref]

E. Paquet, M. Rioux, and H. H. Arsenault, “Invariant pattern recognition for range images using the phase Fourier transform and a neural network,” Opt. Eng. 34, 1178–1183 (1995).
[Crossref]

M. Rioux, “Laser range finder based on synchronized scanners,” Appl. Opt. 23, 3837–3844 (1984).
[Crossref] [PubMed]

Romero, L. A.

Rosen, J.

Roy, S.

S. Roy, D. Lefebvre, and H. H. Arsenault, “Recognition invariant under unknown affine transformations of intensity,” Opt. Commun. 238, 69–77 (2004).
[Crossref]

D. Lefebvre, H. H. Arsenault, and S. Roy, “Nonlinear filter for pattern recognition invariant to illumination and to out-ot-plane rotations,” Appl. Opt. 42, 4658–4662 (2003).
[Crossref] [PubMed]

Tajahuerce, E.

Takeda, M.

Vallés, J. J.

J. J. Vallés, J. García, P. García-Martínez, and H. H. Arsenault, “Three-dimensional object detection under arbitrary lighting conditions,” Appl. Opt. 45, 5237–5247 (2006).
[Crossref] [PubMed]

J. García, J. J. Vallés, and C. Ferreira, “Detection of three-dimensional objects under arbitrary rotations based on range images,” Opt. Express. 11, 3352–3358 (2003).
[Crossref] [PubMed]

Yeom, S.

Appl. Opt. (12)

J. Rosen, “Three-dimensional joint transform correlator,” Appl. Opt. 37, 7538–7544 (1998).
[Crossref]

T. Poon and T. Kim, “Optical image recognition of three-dimensional objects,” Appl. Opt. 38, 370–381 (1999).
[Crossref]

M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22, 3977–3882 (1983).
[Crossref] [PubMed]

J. J. Esteve-Taboada, D. Mas, and J. Garcia, “Three-dimensional object recognition by Fourier transform profilometry,” Appl. Opt. 38, 4760–4765 (1999).
[Crossref]

J. J. Esteve-Taboada, J. García, and C. Ferreira, “Rotation invariant optical recognition of three-dimensional objectes,” Appl. Opt. 39, 5998–5352 (2000).
[Crossref]

J. J. Esteve-Taboada, N. Palmer, J.- Ch. Giannesini, J. García, and C. Ferreira, “Recognition of polychromatic three-dimensional objects,” Appl. Opt. 43, 433–441 (2004).
[Crossref] [PubMed]

M. Rioux, “Laser range finder based on synchronized scanners,” Appl. Opt. 23, 3837–3844 (1984).
[Crossref] [PubMed]

Y. Li and J. Rosen, “Scale invariant recognition of three-dimensional objects by use of a quasi-correlator,” Appl. Opt. 42, 811–819 (2003).
[Crossref] [PubMed]

D. Lefebvre, H. H. Arsenault, P. Garcia-Martinez, and C. Ferreira, “Recognition of unsegmented targets invariant under transformations of intensity,” Appl. Opt. 41, 6135–6142 (2002).
[Crossref] [PubMed]

H. H. Arsenault and P. García-Martínez, “Intensity-invariant nonlinear filtering for detection in camouflage” Appl. Opt. 44, 5483–5490 (2005).
[Crossref] [PubMed]

D. Lefebvre, H. H. Arsenault, and S. Roy, “Nonlinear filter for pattern recognition invariant to illumination and to out-ot-plane rotations,” Appl. Opt. 42, 4658–4662 (2003).
[Crossref] [PubMed]

J. J. Vallés, J. García, P. García-Martínez, and H. H. Arsenault, “Three-dimensional object detection under arbitrary lighting conditions,” Appl. Opt. 45, 5237–5247 (2006).
[Crossref] [PubMed]

J. Opt. (1)

E. Paquet, P. Garcia-Martinez, and J. Garcia, “Tridimensional invariant correlation based on phase-coded and sine-coded range images,” J. Opt. 29, 35–39 (1998).
[Crossref]

J. Opt. Soc. Am. A (1)

Opt. Commun. (2)

S. Chang, M. Rioux, and C. P. Grover, “Range face recognition based on the phase Fourier transform,” Opt. Commun. 222, 143–153 (2003).
[Crossref]

S. Roy, D. Lefebvre, and H. H. Arsenault, “Recognition invariant under unknown affine transformations of intensity,” Opt. Commun. 238, 69–77 (2004).
[Crossref]

Opt. Eng. (2)

E. Paquet, M. Rioux, and H. H. Arsenault, “Invariant pattern recognition for range images using the phase Fourier transform and a neural network,” Opt. Eng. 34, 1178–1183 (1995).
[Crossref]

J. J. Esteve-Taboada, J. García, and C. Ferreira, “Optical recognition of three-dimensional objects with scale invariance using classical convergent correlator,” Opt. Eng. 41, 1324–1330 (2002).
[Crossref]

Opt. Express (1)

Opt. Express. (1)

J. García, J. J. Vallés, and C. Ferreira, “Detection of three-dimensional objects under arbitrary rotations based on range images,” Opt. Express. 11, 3352–3358 (2003).
[Crossref] [PubMed]

Opt. Lett. (3)

Other (1)

B. Javidi, ed., Image Recognition and Classification: Algorithms, Systems, and Applications, (Marcel Dekker, New York, 2002).
[Crossref]

Supplementary Material (1)

» Media 1: AVI (1094 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

(a). Range image of a diamond shaped object. (b). PhFT amplitude of Fig. 1(a). (c)Scaled version of Fig. 1(a). (d) PhFT amplitude of Fig. 1(c).

Fig. 2.
Fig. 2.

(a). Range image. (b). PhFT amplitude of Fig. 2(a). (c) Scaled range image. (d) PhFT amplitude of Fig. 2(c)

Fig. 3.
Fig. 3.

(a). LACIF value for different scale factors (b). Multimedia file (1.09MB). Scaled Range Targets (c). Profile 1-D with the LACIF correlation peak value [Media 1]

Fig. 4.
Fig. 4.

(a). Target range image. (b). False range image. (c). LACIF peak value for different scaled targets of Fig. 4(a). (d). Idem for the false target.

Equations (15)

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P ( x , y ) = exp [ imz ( x , y ) ]
P h F T z ( u , v ) = F 2 D { exp [ i z ( x , y ) ] }
P h F T z ( u , v ) k 2 P h F T z ( u , v )
P h F T z ( u , v ) α P h F T z ( u , v ) + β ( u , v )
P h F T z o ( u , v ) = P h F T z ( u , v ) μ f ( u , v )
P h F T z ( u , v ) α P hFT z o ( u , v ) + β ( u , v )
PhFT z ' ( u , v ) = α " ϕ 1 ( u , v ) + β " ϕ 2 ( u , v )
C L A C I F ( u , v ) = ( P h F T s ( u , v ) ϕ 2 ( u , v ) ) 2 N ( P h F T s ( u , v ) 2 ϕ 1 ( u , v ) ) ( P h F T s ϕ 1 ( u , v ) ) 2
f ( x , y ) = ( a x + b y + c ) w ( x , y )
P h F T f ( u , v ) = F T { e i , f ( x , y ) } = 2 e i ( a x + b y + c ) w ( x , y ) e i 2 π ( u x + v y ) d x d y
= ( x , y ) w e i . ( a x + b y + c ) e i 2 π ( u x + v y ) d x d y + ( x , y ) w e i 2 π ( u x + v y ) d x d y
= e i c δ ( u a 2 π , v b 2 π ) W ( u , v )
f ( x , y ) = ( a x + b y + c ) w ( x k , y k )
PhFT f ' ( u , v ) = k 2 e i c δ ( u a 2 π , v b 2 π ) W ( k u , k v )
P h F T f ' ( u , v ) k 2 e i c δ ( u a 2 π , v b 2 π ) W ( u , v ) = k 2 P h F T f ( u , v )

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