Abstract

In this paper, we address 3D object visualization and recognition with multi-wavelength digital holography. Color features of 3D objects are obtained by the multiple-wavelengths. Perfect superimposition technique generates reconstructed images of the same size. Statistical pattern recognition techniques: principal component analysis and mixture discriminant analysis analyze multi-spectral information in the reconstructed images. Class-conditional probability density functions are estimated during the training process. Maximum likelihood decision rule categorizes unlabeled images into one of trained-classes. It is shown that a small number of training images is sufficient for the color object classification.

© 2007 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  5. B. Javidi and E. Tajahuerce, "Three-dimensional object recognition by use of digital holography," Opt. Lett. 25, 610-612 (2000).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  8. S. Yeom and B. Javidi, "Three-dimensional object feature extraction and classification with computational holographic imaging," Appl. Opt. 43, 442-451 (2004).
    [CrossRef] [PubMed]
  9. B. Javidi, I. Moon, S. Yeom, and E. Carapezza, "Three-dimensional imaging and recognition of microorganism using single-exposure on-line (SEOL) digital holography," Opt. Express 13, 4492-4506 (2005).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  15. D. Alfieri, G. Coppola, S. D. Nicola, P. Ferraro, A. Finizio, G. Pierattini, and B. Javidi, "Method for superposing reconstructed images from digital holograms of the same object recorded at different distance and wavelength," Opt. Commun. 260, 113-116 (2006).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2007

2006

D. Alfieri, G. Coppola, S. D. Nicola, P. Ferraro, A. Finizio, G. Pierattini, and B. Javidi, "Method for superposing reconstructed images from digital holograms of the same object recorded at different distance and wavelength," Opt. Commun. 260, 113-116 (2006).
[CrossRef]

S. Yeom, I Moon, and B. Javidi, "Real-time 3D sensing, visualization and recognition of dynamic biological micro-organisms," Proc. IEEE 94, 550-566 (2006).
[CrossRef]

J. Maycock, T. Naughton, B. Hennely, J. McDonald, and B. Javidi, "Three-dimensional scene reconstruction of partially occluded objects using digital holograms," Appl. Opt. 45, 2975-2985 (2006).
[CrossRef] [PubMed]

2005

2004

2003

J. Kato, I. Yamaguchi, and T. Matsumura, "Multicolor digital holography with an achromatic phase shifter," Opt. Lett. 27, 1403-1405 (2003).
[CrossRef]

B. J. Frey and N. Jojic, "Transformation-invariant clustering using the EM algorithm," IEEE Trans. on Pattern Anal. Mach. Intell. 25, 1-17 (2003).
[CrossRef]

2002

M. M. Dundar and D. Landgrebe, "A model-based mixture-supervised classification approach in hyperspectral data analysis," IEEE. Trans. Geoscience and remote sensing 40, 2692-2699 (2002).
[CrossRef]

I. Yamaguchi, T. Matsumura, and J. Kato, "Phase-shifting color digital holography," Opt. Lett. 27, 1108-1110 (2002).
[CrossRef]

C. Fraley and A. E. Raftery, "Model-based clustering, discriminant analysis, and density estimation," J. of Am. Stat. Assoc. 97, 611-631 (2002).
[CrossRef]

2001

2000

1996

T. Hastie and R. Tibshirani, "Discriminant analysis by Gaussian mixtures," J. Royal Statistical Society B 58, 155-176 (1996).

1994

1980

Y. Linde, A. Buzo, and R. M. Gray, "An algorithm for vector quantizer design," IEEE Trans. Commun. COM- 2884-95 (1980).
[CrossRef]

Alfieri, D.

D. Alfieri, G. Coppola, S. D. Nicola, P. Ferraro, A. Finizio, G. Pierattini, and B. Javidi, "Method for superposing reconstructed images from digital holograms of the same object recorded at different distance and wavelength," Opt. Commun. 260, 113-116 (2006).
[CrossRef]

P. Ferraro, S. De Nicola, G. Coppola, A. Finizio, D. Alfieri, and G. Pierattini, "Controlling image size as a function of distance and wavelength in Fresnel-transform reconstruction of digital holograms," Opt. Lett. 29, 854-855 (2004).
[CrossRef] [PubMed]

Almoro, P.

Buzo, A.

Y. Linde, A. Buzo, and R. M. Gray, "An algorithm for vector quantizer design," IEEE Trans. Commun. COM- 2884-95 (1980).
[CrossRef]

Carapezza, E.

Castro, M.

Coppola, G.

D. Alfieri, G. Coppola, S. D. Nicola, P. Ferraro, A. Finizio, G. Pierattini, and B. Javidi, "Method for superposing reconstructed images from digital holograms of the same object recorded at different distance and wavelength," Opt. Commun. 260, 113-116 (2006).
[CrossRef]

P. Ferraro, S. De Nicola, G. Coppola, A. Finizio, D. Alfieri, and G. Pierattini, "Controlling image size as a function of distance and wavelength in Fresnel-transform reconstruction of digital holograms," Opt. Lett. 29, 854-855 (2004).
[CrossRef] [PubMed]

De Nicola, S.

Dundar, M. M.

M. M. Dundar and D. Landgrebe, "A model-based mixture-supervised classification approach in hyperspectral data analysis," IEEE. Trans. Geoscience and remote sensing 40, 2692-2699 (2002).
[CrossRef]

Ferraro, P.

D. Alfieri, G. Coppola, S. D. Nicola, P. Ferraro, A. Finizio, G. Pierattini, and B. Javidi, "Method for superposing reconstructed images from digital holograms of the same object recorded at different distance and wavelength," Opt. Commun. 260, 113-116 (2006).
[CrossRef]

P. Ferraro, S. De Nicola, G. Coppola, A. Finizio, D. Alfieri, and G. Pierattini, "Controlling image size as a function of distance and wavelength in Fresnel-transform reconstruction of digital holograms," Opt. Lett. 29, 854-855 (2004).
[CrossRef] [PubMed]

Figueiredo, M. A. T.

M. H. C. Law, M. A. T. Figueiredo, and A. K. Jain, "Simultaneous feature selection and clustering using mixture models," IEEE. Trans. on Pattern Anal. Mach. Intell. 26, 1154-1166 (2004)
[CrossRef]

Finizio, A.

D. Alfieri, G. Coppola, S. D. Nicola, P. Ferraro, A. Finizio, G. Pierattini, and B. Javidi, "Method for superposing reconstructed images from digital holograms of the same object recorded at different distance and wavelength," Opt. Commun. 260, 113-116 (2006).
[CrossRef]

P. Ferraro, S. De Nicola, G. Coppola, A. Finizio, D. Alfieri, and G. Pierattini, "Controlling image size as a function of distance and wavelength in Fresnel-transform reconstruction of digital holograms," Opt. Lett. 29, 854-855 (2004).
[CrossRef] [PubMed]

Fraley, C.

C. Fraley and A. E. Raftery, "Model-based clustering, discriminant analysis, and density estimation," J. of Am. Stat. Assoc. 97, 611-631 (2002).
[CrossRef]

Frauel, Y.

Frey, B. J.

B. J. Frey and N. Jojic, "Transformation-invariant clustering using the EM algorithm," IEEE Trans. on Pattern Anal. Mach. Intell. 25, 1-17 (2003).
[CrossRef]

Garcia, W.

Goudail, F.

A. Mahalanobis and F. Goudail, "Methods for automatic target recognition by use of electro-optic sensors: introduction to the feature Issue," Appl. Opt. 43, 207-209 (2004).
[CrossRef]

F. Goudail and P. Refregier, "Statistical algorithms for target detection in coherent active polarimetric images," J. Opt. Soc. Am. 18, 3049-3060 (2001).
[CrossRef]

Gray, R. M.

Y. Linde, A. Buzo, and R. M. Gray, "An algorithm for vector quantizer design," IEEE Trans. Commun. COM- 2884-95 (1980).
[CrossRef]

Hastie, T.

T. Hastie and R. Tibshirani, "Discriminant analysis by Gaussian mixtures," J. Royal Statistical Society B 58, 155-176 (1996).

Hennely, B.

Jain, A. K.

M. H. C. Law, M. A. T. Figueiredo, and A. K. Jain, "Simultaneous feature selection and clustering using mixture models," IEEE. Trans. on Pattern Anal. Mach. Intell. 26, 1154-1166 (2004)
[CrossRef]

Jang, J.

J. Jang, S. Yeom, and B. Javidi, "Compression of ray information in three-dimensional integral imaging," Opt. Eng.  44, 12700-1~10 (2005).
[CrossRef]

Javidi, B.

D. Alfieri, G. Coppola, S. D. Nicola, P. Ferraro, A. Finizio, G. Pierattini, and B. Javidi, "Method for superposing reconstructed images from digital holograms of the same object recorded at different distance and wavelength," Opt. Commun. 260, 113-116 (2006).
[CrossRef]

J. Maycock, T. Naughton, B. Hennely, J. McDonald, and B. Javidi, "Three-dimensional scene reconstruction of partially occluded objects using digital holograms," Appl. Opt. 45, 2975-2985 (2006).
[CrossRef] [PubMed]

S. Yeom, I Moon, and B. Javidi, "Real-time 3D sensing, visualization and recognition of dynamic biological micro-organisms," Proc. IEEE 94, 550-566 (2006).
[CrossRef]

B. Javidi, I. Moon, S. Yeom, and E. Carapezza, "Three-dimensional imaging and recognition of microorganism using single-exposure on-line (SEOL) digital holography," Opt. Express 13, 4492-4506 (2005).
[CrossRef] [PubMed]

J. Jang, S. Yeom, and B. Javidi, "Compression of ray information in three-dimensional integral imaging," Opt. Eng.  44, 12700-1~10 (2005).
[CrossRef]

S. Yeom and B. Javidi, "Three-dimensional object feature extraction and classification with computational holographic imaging," Appl. Opt. 43, 442-451 (2004).
[CrossRef] [PubMed]

Y. Frauel and B. Javidi, "Neural network for three-dimensional object recognition based on digital holography," Opt. Lett. 26, 1478-1480 (2001).
[CrossRef]

Y. Frauel, E. Tajahuerce, M. Castro, and B. Javidi, "Distortion-tolerant three-dimensional object recognition with digital holography," Appl. Opt. 40, 3887-3893 (2001).
[CrossRef]

B. Javidi and E. Tajahuerce, "Three-dimensional object recognition by use of digital holography," Opt. Lett. 25, 610-612 (2000).
[CrossRef]

Jojic, N.

B. J. Frey and N. Jojic, "Transformation-invariant clustering using the EM algorithm," IEEE Trans. on Pattern Anal. Mach. Intell. 25, 1-17 (2003).
[CrossRef]

Juptner, W.

Kato, J.

Landgrebe, D.

M. M. Dundar and D. Landgrebe, "A model-based mixture-supervised classification approach in hyperspectral data analysis," IEEE. Trans. Geoscience and remote sensing 40, 2692-2699 (2002).
[CrossRef]

Law, M. H. C.

M. H. C. Law, M. A. T. Figueiredo, and A. K. Jain, "Simultaneous feature selection and clustering using mixture models," IEEE. Trans. on Pattern Anal. Mach. Intell. 26, 1154-1166 (2004)
[CrossRef]

Linde, Y.

Y. Linde, A. Buzo, and R. M. Gray, "An algorithm for vector quantizer design," IEEE Trans. Commun. COM- 2884-95 (1980).
[CrossRef]

Mahalanobis, A.

Matsumura, T.

Maycock, J.

McDonald, J.

Moon, I

S. Yeom, I Moon, and B. Javidi, "Real-time 3D sensing, visualization and recognition of dynamic biological micro-organisms," Proc. IEEE 94, 550-566 (2006).
[CrossRef]

Moon, I.

Naughton, T.

Nicola, S. D.

D. Alfieri, G. Coppola, S. D. Nicola, P. Ferraro, A. Finizio, G. Pierattini, and B. Javidi, "Method for superposing reconstructed images from digital holograms of the same object recorded at different distance and wavelength," Opt. Commun. 260, 113-116 (2006).
[CrossRef]

Pierattini, G.

D. Alfieri, G. Coppola, S. D. Nicola, P. Ferraro, A. Finizio, G. Pierattini, and B. Javidi, "Method for superposing reconstructed images from digital holograms of the same object recorded at different distance and wavelength," Opt. Commun. 260, 113-116 (2006).
[CrossRef]

P. Ferraro, S. De Nicola, G. Coppola, A. Finizio, D. Alfieri, and G. Pierattini, "Controlling image size as a function of distance and wavelength in Fresnel-transform reconstruction of digital holograms," Opt. Lett. 29, 854-855 (2004).
[CrossRef] [PubMed]

Raftery, A. E.

C. Fraley and A. E. Raftery, "Model-based clustering, discriminant analysis, and density estimation," J. of Am. Stat. Assoc. 97, 611-631 (2002).
[CrossRef]

Refregier, P.

F. Goudail and P. Refregier, "Statistical algorithms for target detection in coherent active polarimetric images," J. Opt. Soc. Am. 18, 3049-3060 (2001).
[CrossRef]

Sadjadi, F. A.

Saloma, C.

Schnars, U.

Tajahuerce, E.

Tibshirani, R.

T. Hastie and R. Tibshirani, "Discriminant analysis by Gaussian mixtures," J. Royal Statistical Society B 58, 155-176 (1996).

Yamaguchi, I.

Yeom, S.

S. Yeom, I Moon, and B. Javidi, "Real-time 3D sensing, visualization and recognition of dynamic biological micro-organisms," Proc. IEEE 94, 550-566 (2006).
[CrossRef]

B. Javidi, I. Moon, S. Yeom, and E. Carapezza, "Three-dimensional imaging and recognition of microorganism using single-exposure on-line (SEOL) digital holography," Opt. Express 13, 4492-4506 (2005).
[CrossRef] [PubMed]

J. Jang, S. Yeom, and B. Javidi, "Compression of ray information in three-dimensional integral imaging," Opt. Eng.  44, 12700-1~10 (2005).
[CrossRef]

S. Yeom and B. Javidi, "Three-dimensional object feature extraction and classification with computational holographic imaging," Appl. Opt. 43, 442-451 (2004).
[CrossRef] [PubMed]

Appl. Opt.

IEEE Trans. Commun. COM

Y. Linde, A. Buzo, and R. M. Gray, "An algorithm for vector quantizer design," IEEE Trans. Commun. COM- 2884-95 (1980).
[CrossRef]

IEEE Trans. on Pattern Anal. Mach. Intell.

B. J. Frey and N. Jojic, "Transformation-invariant clustering using the EM algorithm," IEEE Trans. on Pattern Anal. Mach. Intell. 25, 1-17 (2003).
[CrossRef]

IEEE. Trans. Geoscience and remote sensing

M. M. Dundar and D. Landgrebe, "A model-based mixture-supervised classification approach in hyperspectral data analysis," IEEE. Trans. Geoscience and remote sensing 40, 2692-2699 (2002).
[CrossRef]

IEEE. Trans. on Pattern Anal. Mach. Intell.

M. H. C. Law, M. A. T. Figueiredo, and A. K. Jain, "Simultaneous feature selection and clustering using mixture models," IEEE. Trans. on Pattern Anal. Mach. Intell. 26, 1154-1166 (2004)
[CrossRef]

J. of Am. Stat. Assoc.

C. Fraley and A. E. Raftery, "Model-based clustering, discriminant analysis, and density estimation," J. of Am. Stat. Assoc. 97, 611-631 (2002).
[CrossRef]

J. Opt. Soc. Am.

F. Goudail and P. Refregier, "Statistical algorithms for target detection in coherent active polarimetric images," J. Opt. Soc. Am. 18, 3049-3060 (2001).
[CrossRef]

J. Royal Statistical Society B

T. Hastie and R. Tibshirani, "Discriminant analysis by Gaussian mixtures," J. Royal Statistical Society B 58, 155-176 (1996).

Opt. Commun.

D. Alfieri, G. Coppola, S. D. Nicola, P. Ferraro, A. Finizio, G. Pierattini, and B. Javidi, "Method for superposing reconstructed images from digital holograms of the same object recorded at different distance and wavelength," Opt. Commun. 260, 113-116 (2006).
[CrossRef]

Opt. Eng

J. Jang, S. Yeom, and B. Javidi, "Compression of ray information in three-dimensional integral imaging," Opt. Eng.  44, 12700-1~10 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. IEEE

S. Yeom, I Moon, and B. Javidi, "Real-time 3D sensing, visualization and recognition of dynamic biological micro-organisms," Proc. IEEE 94, 550-566 (2006).
[CrossRef]

Other

B. Javidi, ed., Optical Imaging Sensors and Systems for Homeland Security Applications (Springer, NewYork, 2005).

A. K. Jain, Fundamentals of digital image processing (Prentice-Hall Inc., 1989).

R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification 2nd ed. (Wiley Interscience, New York, 2001).

K. Fukunaga, Introduction to Statistical Pattern Recognition 2nd ed. (Academic Press, Boston, 1990).

C. M. Bishop, Neural Networks for Pattern Recognition (Oxford University Press, New York, 1995).

G. J. McLachlan, Discriminant analysis and statistical pattern recognition (Wiley, New York, 1992).
[CrossRef]

Supplementary Material (6)

» Media 1: AVI (2157 KB)     
» Media 2: AVI (2157 KB)     
» Media 3: AVI (2157 KB)     
» Media 4: AVI (2157 KB)     
» Media 5: AVI (2157 KB)     
» Media 6: AVI (2157 KB)     

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Figures (8)

Fig. 1.
Fig. 1.

Optical set-up for multi-wavelength digital holography using two lasers, M: mirror, BS: beam splitter, BE: beam-expander, RP: reflecting prism, CCD: charge coupled device.

Fig. 2.
Fig. 2.

EM algorithm

Fig. 3.
Fig. 3.

Movies of 50 reconstructed images from the class 1, (a) (the movie file size: 2.10 MB) λ=632.8 nm [Media 1], (b) (the movie file size: 2.10 MB) λ=532.0 nm [Media 2].

Fig. 4.
Fig. 4.

Movies of 50 reconstructed images from the class 2, (a) (the movie file size: 2.10 MB) λ=632.8 nm [Media 3], (b) (the movie file size: 2.10 MB) λ=532.0 nm [Media 4].

Fig. 5.
Fig. 5.

Movies of 50 reconstructed images from the class 3, (a) (the movie file size: 2.10 MB) λ=632.8 nm [Media 5], (b) (the movie file size: 2.10 MB) λ=532.0 nm [Media 6].

Fig. 6.
Fig. 6.

Color holographic images, (a) object 1, (b) object 2, (c) object 3.

Fig. 7.
Fig. 7.

Classification results when the dimension of y is one, (a) averaged correct classification rates over 100 runs, (b) averaged false classification rates over 100 runs.

Fig. 8.
Fig. 8.

Classification results when the dimension of y is two, (a) averaged correct classification rates over 100 runs, (b) averaged false classification rates over 100 runs.

Equations (15)

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

N x 1 = N x 2 λ 1 λ 2 ,
Δ x 1 = Δ x 2 = d s λ 1 N x 1 Δ x = d s λ 2 N x 2 Δ x ,
y = W p t x = E t x .
MSE ( x ̂ ) = E x x ̂ 2 = i = l + 1 d v i ,
x ̂ = μ x + W P ( y μ y ) = μ x + W P W P t ( x μ x ) ,
p j ( y ) = k = 1 G j P ( w jk ) p ( y w jk ) , j = 1 , , N c ,
p ( y | w jk ) = N ( y ; μ jk , Σ jk ) = 1 2 π Σ jk 1 2 e 1 2 ( y μ jk ) t jk 1 ( y μ jk ) ,
L j = log p j ( y j 1 , , y jn j ) ,
P ̂ ( w jk | y jt ) = N ( y jt ; μ ̂ jk , Σ ̂ jk ) P ̂ ( w jk ) k = 1 G j N ( y jt ; μ ̂ jk , Σ ̂ jk ) P ̂ ( w jk ) ,
μ ̂ jk = t = 1 n j P ̂ ( w jk | y jt ) y jt t = 1 n j P ̂ ( w jk | y jt ) ,
Σ ̂ jk = t = 1 n j P ̂ ( w jk | y jt ) ( y jt μ ̂ jk ) ( y jt μ ̂ jk ) t t = 1 n j P ̂ ( w jk | y jt ) ,
P ̂ ( w jk ) = 1 n j t = 1 n j P ̂ ( w jk | y jt ) ,
y test C j ̂ if j ̂ = arg max j = 1 , , N c p ̂ j ( y test ) ,
r c ( j ) = Number of decision for class j Number of test images in class j ,
r f ( j ) = Number of decision for class j Number of test images in all classes except for class j .

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