Abstract

A novel method of 3D object recognition independent of lighting conditions is presented. The recognition model is based on a vector space representation using an orthonormal basis generated by the Lambertian reflectance functions obtained with distant light sources. Changing the lighting conditions corresponds to multiplying the elementary images by a constant factor and because of that, all possible lighting views will be elements that belong to that vector space. The recognition method proposed is based on the calculation of the angle between the vector associated with a certain illuminated 3D object and that subspace. We define the angle in terms of linear correlations to get shift and illumination-invariant detection.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  26. S. Roy, D. Lefebvre, and H. H. Arsenault, "Recognition invariant under unknown affine transformations of intensity," Opt. Commun. 238, 69-77 (2004).
    [CrossRef]
  27. J. D. Foley, A. van Dam, S. K. Feiner, and J. F. Hughes, Computer Graphics, Principle and Practics, 2nd ed. (Addison-Wesley, 1996).
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  30. http://mathworld.wolfram.com/Gram-SchmidtOrthonormalization.html.
  31. http://mathworld.wolfram.com/VectorSpaceProjection.html.

2005

S. K. Zhou and R. Chellappa, "Image-based face recognition under illumination and pose variations," J. Opt. Soc. Am. A. 22, 217-229 (2005).
[CrossRef]

2004

2003

2002

2001

O. Matoba, E. Tajahuerce, and B. Javidi, "Real-time three-dimensional object recognition with multiple perspectives imaging," Appl. Opt. 40, 3318-3325 (2001).
[CrossRef]

E. Tajahuerce, O. Matoba, and B. Javidi, "Shift-invariant three-dimensional object recognition by means of digital holography," Appl. Opt. 40, 3877-3886 (2001).
[CrossRef]

R. Campbell and P. Flynn, "A survey of free-form object representation and recognition techniques," Comput. Vis. Image Underst. 81, 166-210 (2001).
[CrossRef]

P. Parrein, J. Taboury, and P. Chavel, "Evaluation of the shape conformity using correlation of range images," Opt. Commun. 195, 393-397 (2001).
[CrossRef]

2000

1999

1998

E. Paquet, P. García-Martínez, and J. García, "Tridimensional invariant correlation based on phase-coded and sine-coded range images," J. Opt. 29, 35-39 (1998).
[CrossRef]

J. Rosen, "Three-dimensional electro-optical correlation," J. Opt. Soc. Am. A 15, 430-436 (1998).
[CrossRef]

1995

E. Paquet, H. H. Arsenault, and M. Rioux, "Recognition of faces from range images by means of the phase Fourier transform," Pure Appl. Opt. 4, 709-721 (1995).
[CrossRef]

1991

1984

1983

1982

R. Bamler and J. Hofer-Alfeis, "Three- and four-dimensional filter operations by coherent optics," Opt. Acta 29, 747-757 (1982).
[CrossRef]

Arsenault, H. H.

Bamler, R.

R. Bamler and J. Hofer-Alfeis, "Three- and four-dimensional filter operations by coherent optics," Opt. Acta 29, 747-757 (1982).
[CrossRef]

Campbell, R.

R. Campbell and P. Flynn, "A survey of free-form object representation and recognition techniques," Comput. Vis. Image Underst. 81, 166-210 (2001).
[CrossRef]

Chavel, P.

P. Parrein, J. Taboury, and P. Chavel, "Evaluation of the shape conformity using correlation of range images," Opt. Commun. 195, 393-397 (2001).
[CrossRef]

Chellappa, R.

S. K. Zhou and R. Chellappa, "Image-based face recognition under illumination and pose variations," J. Opt. Soc. Am. A. 22, 217-229 (2005).
[CrossRef]

Dickey, F. M.

Esteve-Taboada, J. J.

Feiner, S. K.

J. D. Foley, A. van Dam, S. K. Feiner, and J. F. Hughes, Computer Graphics, Principle and Practics, 2nd ed. (Addison-Wesley, 1996).

Ferreira, C.

Flynn, P.

R. Campbell and P. Flynn, "A survey of free-form object representation and recognition techniques," Comput. Vis. Image Underst. 81, 166-210 (2001).
[CrossRef]

Foley, J. D.

J. D. Foley, A. van Dam, S. K. Feiner, and J. F. Hughes, Computer Graphics, Principle and Practics, 2nd ed. (Addison-Wesley, 1996).

Garcia, J.

García, J.

J. J. Esteve-Taboada and J. García, "Detection and orientation evaluation for three-dimensional objects," Opt. Commun. 217, 123-131 (2003).
[CrossRef]

J. J. Esteve-Taboada and J. García, "Detection and orientation evaluations for three-dimensional objects," Opt. Commun. 217, 123-131 (2002).
[CrossRef]

J. J. Esteve-Taboada, J. García, and C. Ferreira, "Rotations-invariant optical recognition of three-dimensional objects," Appl. Opt. 39, 5998-6005 (2000).
[CrossRef]

E. Paquet, P. García-Martínez, and J. García, "Tridimensional invariant correlation based on phase-coded and sine-coded range images," J. Opt. 29, 35-39 (1998).
[CrossRef]

Garcia-Martinez, P.

García-Martínez, P.

E. Paquet, P. García-Martínez, and J. García, "Tridimensional invariant correlation based on phase-coded and sine-coded range images," J. Opt. 29, 35-39 (1998).
[CrossRef]

Giannessini, J.-C.

Hofer-Alfeis, J.

R. Bamler and J. Hofer-Alfeis, "Three- and four-dimensional filter operations by coherent optics," Opt. Acta 29, 747-757 (1982).
[CrossRef]

Hom, B. K.

B. K. Hom, Robot Vision (MIT Press, 1986).

Hughes, J. F.

J. D. Foley, A. van Dam, S. K. Feiner, and J. F. Hughes, Computer Graphics, Principle and Practics, 2nd ed. (Addison-Wesley, 1996).

Javidi, B.

Kim, T.

Lefebvre, D.

Li, Y.

Ma, S.

Y. Tian, H. T. Tsui, S. Y. Yeung, and S. Ma, "Shape from shading for multiple light sources," J. Opt. Soc. Am. A. 16, 36-52 (1999).
[CrossRef]

Mas, D.

Matoba, O.

Mutoh, K.

Palmer, N.

Paquet, E.

E. Paquet, P. García-Martínez, and J. García, "Tridimensional invariant correlation based on phase-coded and sine-coded range images," J. Opt. 29, 35-39 (1998).
[CrossRef]

E. Paquet, H. H. Arsenault, and M. Rioux, "Recognition of faces from range images by means of the phase Fourier transform," Pure Appl. Opt. 4, 709-721 (1995).
[CrossRef]

Parrein, P.

P. Parrein, J. Taboury, and P. Chavel, "Evaluation of the shape conformity using correlation of range images," Opt. Commun. 195, 393-397 (2001).
[CrossRef]

Poon, T.

Rioux, M.

E. Paquet, H. H. Arsenault, and M. Rioux, "Recognition of faces from range images by means of the phase Fourier transform," Pure Appl. Opt. 4, 709-721 (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-of-plane rotations," Appl. Opt. 42, 4658-4662 (2003).
[CrossRef] [PubMed]

Taboury, J.

P. Parrein, J. Taboury, and P. Chavel, "Evaluation of the shape conformity using correlation of range images," Opt. Commun. 195, 393-397 (2001).
[CrossRef]

Tajahuerce, E.

Takeda, M.

Tian, Y.

Y. Tian, H. T. Tsui, S. Y. Yeung, and S. Ma, "Shape from shading for multiple light sources," J. Opt. Soc. Am. A. 16, 36-52 (1999).
[CrossRef]

Tsui, H. T.

Y. Tian, H. T. Tsui, S. Y. Yeung, and S. Ma, "Shape from shading for multiple light sources," J. Opt. Soc. Am. A. 16, 36-52 (1999).
[CrossRef]

Valles, J. J.

van Dam, A.

J. D. Foley, A. van Dam, S. K. Feiner, and J. F. Hughes, Computer Graphics, Principle and Practics, 2nd ed. (Addison-Wesley, 1996).

Yeom, S.

Yeung, S. Y.

Y. Tian, H. T. Tsui, S. Y. Yeung, and S. Ma, "Shape from shading for multiple light sources," J. Opt. Soc. Am. A. 16, 36-52 (1999).
[CrossRef]

Zhou, S. K.

S. K. Zhou and R. Chellappa, "Image-based face recognition under illumination and pose variations," J. Opt. Soc. Am. A. 22, 217-229 (2005).
[CrossRef]

Appl. Opt.

M. Takeda and K. Mutoh, "Fourier transform profilometry for the automatic measurement of 3D object shapes," Appl. Opt. 22, 3977-3982 (1983).
[CrossRef] [PubMed]

M. Rioux, "Laser range finder based on synchronized scanners," Appl. Opt. 23, 3837-3844 (1984).
[CrossRef] [PubMed]

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

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, "Rotations-invariant optical recognition of three-dimensional objects," Appl. Opt. 39, 5998-6005 (2000).
[CrossRef]

O. Matoba, E. Tajahuerce, and B. Javidi, "Real-time three-dimensional object recognition with multiple perspectives imaging," Appl. Opt. 40, 3318-3325 (2001).
[CrossRef]

E. Tajahuerce, O. Matoba, and B. Javidi, "Shift-invariant three-dimensional object recognition by means of digital holography," Appl. Opt. 40, 3877-3886 (2001).
[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]

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

J. J. Esteve-Taboada, N. Palmer, J.-C. Giannessini, J. Garcia, and C. Ferreira, "Recognition of polychromatic three-dimensional objects," Appl. Opt. 43, 433-441 (2004).
[CrossRef] [PubMed]

Comput. Vis. Image Underst.

R. Campbell and P. Flynn, "A survey of free-form object representation and recognition techniques," Comput. Vis. Image Underst. 81, 166-210 (2001).
[CrossRef]

J. Opt.

E. Paquet, P. García-Martínez, and J. García, "Tridimensional invariant correlation based on phase-coded and sine-coded range images," J. Opt. 29, 35-39 (1998).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. A.

Y. Tian, H. T. Tsui, S. Y. Yeung, and S. Ma, "Shape from shading for multiple light sources," J. Opt. Soc. Am. A. 16, 36-52 (1999).
[CrossRef]

S. K. Zhou and R. Chellappa, "Image-based face recognition under illumination and pose variations," J. Opt. Soc. Am. A. 22, 217-229 (2005).
[CrossRef]

Opt. Acta

R. Bamler and J. Hofer-Alfeis, "Three- and four-dimensional filter operations by coherent optics," Opt. Acta 29, 747-757 (1982).
[CrossRef]

Opt. Commun.

J. J. Esteve-Taboada and J. García, "Detection and orientation evaluations for three-dimensional objects," Opt. Commun. 217, 123-131 (2002).
[CrossRef]

P. Parrein, J. Taboury, and P. Chavel, "Evaluation of the shape conformity using correlation of range images," Opt. Commun. 195, 393-397 (2001).
[CrossRef]

S. Roy, D. Lefebvre, and H. H. Arsenault, "Recognition invariant under unknown affine transformations of intensity," Opt. Commun. 238, 69-77 (2004).
[CrossRef]

J. J. Esteve-Taboada and J. García, "Detection and orientation evaluation for three-dimensional objects," Opt. Commun. 217, 123-131 (2003).
[CrossRef]

Opt. Express

Opt. Lett.

Pure Appl. Opt.

E. Paquet, H. H. Arsenault, and M. Rioux, "Recognition of faces from range images by means of the phase Fourier transform," Pure Appl. Opt. 4, 709-721 (1995).
[CrossRef]

Other

J. D. Foley, A. van Dam, S. K. Feiner, and J. F. Hughes, Computer Graphics, Principle and Practics, 2nd ed. (Addison-Wesley, 1996).

http://mathworld.wolfram.com/Gram-SchmidtOrthonormalization.html.

http://mathworld.wolfram.com/VectorSpaceProjection.html.

B. K. Hom, Robot Vision (MIT Press, 1986).

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Figures (11)

Fig. 1
Fig. 1

(a) 3D object mesh. (b) Sample view of 3D object shaded.

Fig. 2
Fig. 2

Geometrical interpretation of LACIF.

Fig. 3
Fig. 3

Definition of the angle between a vector and the subspace.

Fig. 4
Fig. 4

Vector basis {k a(x, y),[N i (x, y)]}. (a) is k a(x, y) equal to ν0 (x, y), and (b), (c), and (d) are {Ni (x, y)} i=X,Y,Z , respectively.

Fig. 5
Fig. 5

Three versions of the target with different illuminations.

Fig. 6
Fig. 6

(a) Correlation peak profile for Fig. 5 using the proposed method. (b) Correlation peak profile for Fig. 5 using the LACIF.

Fig. 7
Fig. 7

(a) A 3D target. (b) Representation of (a) in the basis defined by {k a(x, y), [N i(x, y)]} with no consideration of shadow effects. (c) Subtraction of (a) from (b).

Fig. 8
Fig. 8

Illumination variation in terms of the position of the point source.

Fig. 9
Fig. 9

Results for all illumination sampling for (a) the proposed LADC method and (b) the LACIF method.

Fig. 10
Fig. 10

(a) Sample noisy image (SNR = 5). (b) Correlation peak value variation. (c) PCE variation.

Fig. 11
Fig. 11

(a) Input scene with true and false objects in a noisy environment (SNR = 1). (b) Output for the proposed method using (a).

Equations (91)

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

I 1 ( x , y , z ) = I a k a ( x , y , z ) ,
I a
k a ( x , y , z )
I 2 ( x , y , z ) = I p k l ( x , y , z ) ( L ( x , y , z ) N ( x , y , z ) ) ,
I p
k l ( x , y , z )
L ( x , y , z )
N ( x , y , z )
I ( x , y , z ) = I a k a ( x , y , z ) + I p k l ( x , y , z ) × ( L ( x , y , z ) N ( x , y , z ) ) .
cos ( L N ) 0
I ( x , y ) = { I a k a ( x , y ) + I d k l ( x , y ) [ L x N x ( x , y ) + L y N y ( x , y ) + L z N z ( x , y ) ] if   ( L N ) 0 I a k a ( x , y ) otherwise ,
{ N i ( x , y ) } i = x , y , z
{ L i } i = x , y , z
N ( x , y )
( k a ( x , y ) , { N i ( x , y ) } i = x , y , z )
f ( x , y ) = c 0 v 0 ( x , y ) + c 1 v 1 ( x , y ) + c 2 v 2 ( x , y ) + ,
f ( x , y )
{ c i } i = 0 , 1 ,
v 0 ( x , y )
v 0 ( x , y ) = { 1 if   f ( x , y ) 0 0 otherwise .
{ v i ( x , y ) } i = 1 , 2 ,
v 0 ( x , y )
f ( x , y )
( | f )
{ | v i } = { v i ( x , y ) }
a ( x , y )
a | b ( a b ) ( 0 , 0 ) = 2 a * ( x , y ) b ( x , y ) d x d y ,
2
{ δ ( x x , y y ) , x , y 2 }
N 1 × N 2
N 1 = N 2 = 256
256 × 256 = 65 , 536
{ v i ( x , y ) }
{ v i ( x , y ) }
f ( x , y )
f ( x , y ) = d 0 v ^ 0 ( x , y ) + d 1 v ^ 1 ( x , y ) + d 2 v ^ 2 ( x , y ) ,
{ v ^ i ( x , y ) }
{ d i }
v i | f
( g ( x , y ) )
( f ( x , y ) )
C LACIF ( g , f ; x , y ) = ( f 0 g ) 2 ( x , y ) N ( v ^ 0 g 2 ) ( x , y ) ( v ^ 0 g ) 2 ( x , y ) ,
v ^ 0 ( x , y )
v 0 ( x , y )
f 0 ( x , y )
f 0 ( x , y ) = f ( x , y ) μ f v 0 ( x , y )
μ f
f ( x , y )
a f ( x , y ) + b
f ( x , y )
g ( x , y )
{ v ^ i ( x , y ) }
( g ( x , y ) )
v 0 ( x , y )
( f ( x , y ) )
{ v 0 ( x , y ) , f ( x , y ) }
{ v ^ i ( x , y ) } i = 0 , 1 ,  
C LACIF ( g , v ^ i ; x , y ) = ( v ^ 1 g ) 2 ( x , y ) N ( v ^ 0 g 2 ) ( x , y ) i 1 ( v ^ i g ) 2 ( x , y ) .
{ N i ( x , y ) }
| v ^ 1
| v ^ 2
| g
| g
| g proj
cos 2 ( θ ) = g proj 2 g 2 ,
g
g proj
| g
| g proj
| g proj i v ^ i | g | v ^ i .
| g
| g | g proj
| g proj = 0
π / 2
g proj ( x , y ) 2 = i | v ^ i | g | 2 = i | v ^ i g | 2 ( x , y ) ,
g ( x , y ) 2 = 2 v 0 ( x , y ) g 2 ( x , y ) = N ( v ^ 0 g 2 ) ( x , y ) ,
v ^ 0 ( x , y ) = v 0 ( x , y ) v 0 | v 0 = v 0 ( x , y ) N .
( g 2 ( x , y ) )
( x , y )
cos 2 ( θ ; g , v ^ i ; x , y ) = i ( v ^ i g ) 2 ( x , y ) N ( v ^ 0 g 2 ) ( x , y ) .
{ N i ( x , y ) } i = X , Y , Z
f ( x , y ) f ( x , y ) + R ( x , y ) ,
f ( x , y )
R ( x , y )
R ( x , y ) = { 0 if    v ^ i ( x , y ) = 0 Gaussian   noise   elsewhere .
PCE ( σ ) = [ cos 2 ( θ ; f , v ^ i , 0 , 0 ) ] 2 2 [ cos 2 ( θ ; f , v ^ i , x , y ) ] 2 d x d y .
PCE ( σ ) = [ cos 2 ( θ ; f , v ^ i , 0 , 0 ) ] 2 [ cos 2 ( θ ; f , v ^ i , 0 , 0 ) ] 2 + ( x , y ) ( 0 , 0 ) [ cos 2 ( θ ; f , v ^ i , x , y ) ] 2 d x d y .
cos 2 ( θ ; f , v ^ i , x , y ) = i [ 2 v ^ i * ( x x , y y ) [ f ( x , y ) + R ( x , y ) ] d x d y ] 2 N 2 v ^ 0 * ( x x , y y ) [ f 2 ( x , y ) + f R ( x , y ) + R 2 ( x , y ) ] d x d y .
cos 2 ( θ ; f , v ^ i , x , y ) = K N 2 v ^ 0 * ( x x , y y ) [ R 2 ( x , y ) ] d x d y K σ 2 ,
K
PCE ( σ ) = [ cos 2 ( θ ; f , v ^ i , 0 , 0 ) ] 2 [ cos 2 ( θ ; f , v ^ i , 0 , 0 ) ] 2 + O ( σ 4 ) .

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