Abstract

In a computational three-dimensional (3D) volumetric reconstruction integral imaging (II) system, volume pixels (voxels) of the scene are reconstructed plane by plane. Therefore, foreground occluding objects and background occluded objects can be reconstructed separately when there is enough spatial separation between the occluding object and the occluded object. Using volumetric computational II reconstruction, we are able to recognize distorted and occluded objects with correlation based recognition algorithms. We present experimental results which show recognition of 3D rotated and occluded targets in a reconstructed scene. We also show the ability of the proposed technique to recognize distorted and occluded 3D non-training targets.

© 2006 Optical Society of America

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    [CrossRef] [PubMed]
  16. <jrn>. S.-H. Hong and Bahram Javidi, "Three-dimensional visualization of partially occluded objects using integral Imaging," IEEE J. Display Technol. 1, 354-359 (2005).</jrn>
    [CrossRef]
  17. Y. Frauel and B. Javidi, "Digital three-dimensional image correlation by use of computer-reconstructed integral imaging," Appl. Opt. 41, 5488-5496 (2002).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [PubMed]
  23. H. Kwon and N. M. Nasrabadi, "Kernel RX-algorithm: a nonlinear anomaly detector for hyperspectral imagery," IEEE Trans. Geosci. Remote Sens. 43, 388-397 (2005)
    [CrossRef]
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    [CrossRef]
  26. P. Refreigher, V. Laude, and B. Javidi, "Nonlinear joint-transform correlation: an optimal solution for adaptive image discrimination and input noise robustness," Opt. Lett. 19, 405-407 (1994).
  27. A. Mahalanobis, "Review of correlation filters and their application for scene matching," Optoelectronic Devices and Systems for Processing, Critical Reviews of Optical Science Technology, B. Javidi and K. Johnson eds., CR 65, SPIE Press, 240-260 (1996).
  28. B. Javidi, and J. Wang, "Optimum distortion-invariant filter for detecting a noisy distorted target in nonoverlapping background noise," J. Opt. Soc. Am. A 12, 2604-2614 (1995).
    [CrossRef]
  29. F. Goudail and P. Refregier, "Statistical algorithms for target detection in coherent active polarimetric images," J. Opt. Soc. Am. 18, 3049-3060 (2001).
    [CrossRef]
  30. M. T. Prona, A. Mahalanobis, and K. N. Zachery, "LADAR automatic target recognition using correlation filters," Proc.SPIE, Automatic Target Recognition IX,  3718, 388-396 (1999).
  31. 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]

2006 (3)

2005 (2)

S. Yeom, B. Javidi, and E. Watson, "Photon counting passive 3D image sensing for automatic target recognition," Opt. Express 13, 9310-9330 (2005),
[CrossRef] [PubMed]

H. Kwon and N. M. Nasrabadi, "Kernel RX-algorithm: a nonlinear anomaly detector for hyperspectral imagery," IEEE Trans. Geosci. Remote Sens. 43, 388-397 (2005)
[CrossRef]

2004 (2)

2003 (2)

J.-S. Jang and B. Javidi, "Formation of orthoscopic three-dimensional real images in direct pickup one-step integral imaging," Opt. Eng. 42, 1869-1870 (2003).
[CrossRef]

A. Stern and B. Javidi, "Three-dimensional image sensing and reconstruction with time-division multiplexed computational integral imaging," Appl. Opt. 42, 7036-7042 (2003).
[CrossRef] [PubMed]

2002 (4)

2001 (2)

H. Arimoto and B. Javidi, "Integral three-dimensional imaging with digital reconstruction," Opt. Lett. 26, 157-159 (2001)
[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]

1999 (1)

M. T. Prona, A. Mahalanobis, and K. N. Zachery, "LADAR automatic target recognition using correlation filters," Proc.SPIE, Automatic Target Recognition IX,  3718, 388-396 (1999).

1998 (1)

1995 (1)

1994 (1)

1960 (1)

J. L. Turin, "An introduction to matched filters," IRE Trans. Inf. Theor. IT-6311-329 (1960).
[CrossRef]

1931 (1)

1908 (1)

G. Lippmann, "La photographic intergrale," C. R. Acad. Sci. 146, 446-451 (1908).

Arimoto, H.

Bertaux, N.

Frauel, Y.

Goudail, F.

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

Hennely, B.

Hong, S.-H.

Hoshino, H.

Isono, H.

Ives, H. E.

Jang, J.-S.

Javidi, B.

B. Javidi, S.-H. Hong, and O. Matoba, "Multi dimensional optical sensors and imaging systems," Appl. Opt. 45, 2986-2994 (2006).
[CrossRef] [PubMed]

B. Javidi, R. Ponce-Diaz, and S.-H. Hong, "Three-dimensional recognition of occluded objects using volumetric reconstruction," Opt. Lett. 31, 1106-1108 (2006).
[CrossRef] [PubMed]

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, B. Javidi, and E. Watson, "Photon counting passive 3D image sensing for automatic target recognition," Opt. Express 13, 9310-9330 (2005),
[CrossRef] [PubMed]

S.-H. Hong, J.-S. Jang, and B. Javidi, "Three-dimensional volumetric object reconstruction using computational integral imaging," Opt. Express 12, 483-491 (2004),
[CrossRef] [PubMed]

M. Martínez-Corral, B. Javidi, R. Martínez-Cuenca, and G. Saavedra, "Integral imaging with improved depth of field by use of amplitude modulated microlens array," Appl. Opt. 43, 5806-5813 (2004).
[CrossRef] [PubMed]

J.-S. Jang and B. Javidi, "Formation of orthoscopic three-dimensional real images in direct pickup one-step integral imaging," Opt. Eng. 42, 1869-1870 (2003).
[CrossRef]

A. Stern and B. Javidi, "Three-dimensional image sensing and reconstruction with time-division multiplexed computational integral imaging," Appl. Opt. 42, 7036-7042 (2003).
[CrossRef] [PubMed]

O. Matoba, T. J. Naughton, Y. Frauel, N. Bertaux, and B. Javidi, "Real-time three-dimensional object reconstruction by use of a phase-encoded digital hologram," Appl. Opt. 41, 6187-6192 (2002).
[CrossRef] [PubMed]

S.-H. Hong and B. Javidi, "Optimum nonlinear composite filter for distortion-tolerant pattern recognition," Appl. Opt. 41, 2172-2178 (2002).
[CrossRef] [PubMed]

Y. Frauel and B. Javidi, "Digital three-dimensional image correlation by use of computer-reconstructed integral imaging," Appl. Opt. 41, 5488-5496 (2002).
[CrossRef] [PubMed]

J.-S. Jang and B. Javidi, "Improved viewing resolution of three-dimensional integral imaging by use of nonstationary micro-optics," Opt. Lett. 27, 324-326 (2002).
[CrossRef]

H. Arimoto and B. Javidi, "Integral three-dimensional imaging with digital reconstruction," Opt. Lett. 26, 157-159 (2001)
[CrossRef]

B. Javidi, and J. Wang, "Optimum distortion-invariant filter for detecting a noisy distorted target in nonoverlapping background noise," J. Opt. Soc. Am. A 12, 2604-2614 (1995).
[CrossRef]

P. Refreigher, V. Laude, and B. Javidi, "Nonlinear joint-transform correlation: an optimal solution for adaptive image discrimination and input noise robustness," Opt. Lett. 19, 405-407 (1994).

Kwon, H.

H. Kwon and N. M. Nasrabadi, "Kernel RX-algorithm: a nonlinear anomaly detector for hyperspectral imagery," IEEE Trans. Geosci. Remote Sens. 43, 388-397 (2005)
[CrossRef]

Laude, V.

Lippmann, G.

G. Lippmann, "La photographic intergrale," C. R. Acad. Sci. 146, 446-451 (1908).

Mahalanobis, A.

M. T. Prona, A. Mahalanobis, and K. N. Zachery, "LADAR automatic target recognition using correlation filters," Proc.SPIE, Automatic Target Recognition IX,  3718, 388-396 (1999).

Martínez-Corral, M.

Martínez-Cuenca, R.

Matoba, O.

Maycock, J.

McDonald, J.

Nasrabadi, N. M.

H. Kwon and N. M. Nasrabadi, "Kernel RX-algorithm: a nonlinear anomaly detector for hyperspectral imagery," IEEE Trans. Geosci. Remote Sens. 43, 388-397 (2005)
[CrossRef]

Naughton, T.

Naughton, T. J.

Okano, F.

Ponce-Diaz, R.

Prona, M. T.

M. T. Prona, A. Mahalanobis, and K. N. Zachery, "LADAR automatic target recognition using correlation filters," Proc.SPIE, Automatic Target Recognition IX,  3718, 388-396 (1999).

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]

Refreigher, P.

Saavedra, G.

Stern, A.

Turin, J. L.

J. L. Turin, "An introduction to matched filters," IRE Trans. Inf. Theor. IT-6311-329 (1960).
[CrossRef]

Wang, J.

Watson, E.

Yeom, S.

Yuyama, I.

Zachery, K. N.

M. T. Prona, A. Mahalanobis, and K. N. Zachery, "LADAR automatic target recognition using correlation filters," Proc.SPIE, Automatic Target Recognition IX,  3718, 388-396 (1999).

Appl. Opt. (7)

C. R. Acad. Sci. (1)

G. Lippmann, "La photographic intergrale," C. R. Acad. Sci. 146, 446-451 (1908).

IEEE Trans. Geosci. Remote Sens. (1)

H. Kwon and N. M. Nasrabadi, "Kernel RX-algorithm: a nonlinear anomaly detector for hyperspectral imagery," IEEE Trans. Geosci. Remote Sens. 43, 388-397 (2005)
[CrossRef]

IRE Trans. Inf. Theor. (1)

J. L. Turin, "An introduction to matched filters," IRE Trans. Inf. Theor. IT-6311-329 (1960).
[CrossRef]

J. Opt. Soc. Am. (2)

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

H. E. Ives, "Optical properties of a Lipmann lenticulated sheet," J. Opt. Soc. Am. 21, 171-176 (1931).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Eng. (1)

J.-S. Jang and B. Javidi, "Formation of orthoscopic three-dimensional real images in direct pickup one-step integral imaging," Opt. Eng. 42, 1869-1870 (2003).
[CrossRef]

Opt. Express (2)

Opt. Lett. (4)

SPIE, Automatic Target Recognition IX (1)

M. T. Prona, A. Mahalanobis, and K. N. Zachery, "LADAR automatic target recognition using correlation filters," Proc.SPIE, Automatic Target Recognition IX,  3718, 388-396 (1999).

Other (9)

A. Mahalanobis, "Review of correlation filters and their application for scene matching," Optoelectronic Devices and Systems for Processing, Critical Reviews of Optical Science Technology, B. Javidi and K. Johnson eds., CR 65, SPIE Press, 240-260 (1996).

Selected Papers on Automatic Target Recognition, F. Sadjadi, Editor, SPIE- CDROM (1999).

<jrn>. S.-H. Hong and Bahram Javidi, "Three-dimensional visualization of partially occluded objects using integral Imaging," IEEE J. Display Technol. 1, 354-359 (2005).</jrn>
[CrossRef]

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

J. W. Goodman, Introduction to Fourier optics, 2nd edition (McGraw-Hill, New York, 1996).
[PubMed]

S. A. Benton, ed., Selected Papers on Three-Dimensional Displays (SPIE Optical Engineering Press, Bellingham, WA, 2001).

P. Ambs, L. Bigue, R. Binet, J. Colineau, J.-C. Lehureau, and J.-P. Huignard, "Image reconstruction using electro-optic holography," Proc. of the 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS 2003, vol. 1 (IEEE, Piscataway, NJ, 2003) pp. 172-173.

B. Javidi and F. Okano, eds., Three Dimensional Television, Video, and Display Technologies (Springer, Berlin, 2002).

T. Okoshi, Three-dimensional Imaging Techniques (Academic Press, New York, 1976).

Supplementary Material (2)

» Media 1: AVI (381 KB)     
» Media 2: AVI (665 KB)     

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Figures (10)

Fig. 1.
Fig. 1.

Experimental setup for 3D object capturing and computational reconstruction with II system. The full 3D volume image at various distances can be reconstructed separately.

Fig. 2.
Fig. 2.

3D object used in the experiments. The blue car is a true class target, green car is a false object. Vegetation is positioned in front of the cars to partially occlude the background objects.

Fig. 3.
Fig. 3.

One of the elemental images used to reconstruct the training target rotated at an angle of 30° to 60°.

Fig. 4.
Fig. 4.

Seven sets of the reconstructed images from the elemental image sets ranging from z=60 mm to z=72 mm with 1mm increment. These 7 reconstructed image sets are used as training reference images rotated at angles of (a) 30°, (b) 35°, (c) 40°, (d) 45°, (e) 50°, (f) 55°, and (g) 60°.

Fig. 5.
Fig. 5.

Reconstructed images from the elemental images sets rotated at an angle of 45° at (a) z=29 mm, (b) z=45 mm, (c) z=52 mm, and (d) z=69 mm.

Fig. 6.
Fig. 6.

Reconstructed images from the elemental images sets rotated at an angle of 32.5° at (a) z=29 mm, (b) z=45 mm, (d) z=52 mm, and (d) z=69 mm.

Fig. 7.
Fig. 7.

A movie file of the reconstructed images from the elemental images sets rotated at an angle of 45° (381KB).

Fig. 8.
Fig. 8.

A movie file of the reconstructed images from the elemental images sets rotated at an angle of 32.5° (665KB).

Fig. 9.
Fig. 9.

Normalized optimum nonlinear filter output for the reconstructed input scene in Figure 5 with 45° rotated training target and a false object at (a) z=29 mm, (b) z=45 mm, (c) z=52 mm, and (d) z=69 mm.

Fig. 10.
Fig. 10.

Normalized optimum nonlinear filter output for the reconstructed input scene in Figure 6 with 32.5° rotated true class non-training target and a false object at (a) z=29 mm, (b) z=45 mm, (c) z=52 mm, and (d) z=69 mm.

Equations (11)

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

s ( t ) = i = 1 T v i r i ( t τ i ) + n b ( t ) [ w ( t ) i = 1 T v i w ri ( t τ i ) ] + n a ( t ) w ( t ) ,
k = 0 M 1 H ( k ) * R i ( k ) = M C i ,
w n M k = 0 M 1 H ( k ) 2 E N ( k ) 2 + w d M k = 0 M 1 H ( k ) 2 S ( k ) 2 = k = 0 M 1 ( a k 2 + b k 2 ) D ( k ) ,
J k = 0 M 1 ( a k 2 + b k 2 ) D ( k ) + i = 1 T λ 1 i ( M C i k = 0 M 1 a k c ik k = 0 M 1 b k d ik ) + i = 1 T λ 2 i ( 0 k = 0 M 1 a k d ik + k = 0 M 1 b k c ik ) .
a k = i = 1 T ( λ 1 i c ik + λ 2 i d ik ) 2 D ( k ) , b k = i = 1 T ( λ 1 i d ik λ 2 i c ik ) 2 D ( k ) .
λ 1 [ λ 11 λ 12 . . . λ 1 T ] t , λ 2 [ λ 21 λ 22 . . . λ 2 T ] t , C [ C 1 C 2 . . . C T ] t ,
A x , y k = 0 M 1 Re [ R x ( k ) ] Re R y ( k ) + Im [ R x ( k ) ] Im R y ( k ) 2 D ( k ) = k = 0 M 1 c xk c yk + d xk d yk 2 D ( k ) ,
B x , y k = 0 M 1 Im [ R x ( k ) ] Re R y ( k ) Re [ R x ( k ) ] Im R y ( k ) 2 D ( k ) = k = 0 M 1 d xk c yk c xk d yk 2 D ( k ) ,
λ 1 t = M C t ( A + B A 1 B ) 1 , λ 2 t = M C t ( A + B A 1 B ) 1 B A 1 .
a k + j b k = 1 2 D ( k ) i = 1 T [ λ 1 i ( c ik + j d ik ) + λ 2 i ( d ik j c ik ) ] = 1 2 D ( k ) i = 1 T ( λ 1 i j λ 2 i ) ( c ik + j d ik ) .
H ( k ) = i = 1 T ( λ 1 i j λ 2 i ) R i ( k ) ( 1 MT i = 1 T ( Φ b 0 ( k ) { W ( k ) 2 + W ri ( k ) 2 2 W ( k ) 2 d Re [ W ri ( k ) ] } ) + 1 M Φ a 0 ( k ) W ( k ) 2 + 1 T i = 1 T ( m b 2 { W ( k ) 2 + W ri ( k ) 2 2 W ( k ) 2 d Re [ W ri ( k ) ] } + 2 m a m b W ( k ) 2 Re [ 1 W ri ( k ) d ] ) + m a 2 W ( k ) 2 + S ( k ) 2 ) ,

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