Abstract

Independent component analysis (ICA) aims at extracting unknown components from multivariate data assuming that the underlying components are mutually independent. This technique has been successfully applied to the recognition and classification of objects. We present a method that combines the benefits of ICA and the ability of the integral imaging technique to obtain 3D information for the recognition of 3D objects with different orientations. Our recognition is also possible when the 3D objects are partially occluded by intermediate objects.

© 2009 Optical Society of America

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    [CrossRef]
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2007 (2)

R. Martínez-Cuenca, G. Saavedra, A. Pons, B. Javidi, and M. Martínez-Corral, “Facet braiding: a fundamental problem in integral imaging,” Opt. Lett. 32, 1078-1080 (2007).
[CrossRef] [PubMed]

Y. S. Hwang, S.-H. Hong, and B. Javidi, “Free view 3-D visualization of occluded objects by using computational synthetic aperture integral imaging,” J. Disp. Technol. 3, 64-70 (2007).
[CrossRef]

2006 (3)

H. Zheng, D. S. Huang, and L. Shang, “Feature selection in independent component subspace for microarray data classification,” Neurocomputing 69, 2407-2410 (2006).
[CrossRef]

A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE 94, 591-607 (2006).
[CrossRef]

R. Martinez, A. Pons, G. Saavedra, M. Martínez-Corral, and B. Javidi, “Optically-corrected elemental images for undistorted integral image display,” Opt. Express 14, 9657-9663 (2006).
[CrossRef]

2005 (2)

M. Martínez-Corral, B. Javidi, R. Martínez-Cuenca, and G. Saavedra, “Multifacet structure of observed reconstructed integral images,” J. Opt. Soc. Am. A 22, 597-603 (2005).
[CrossRef]

C. Wu, A. Aggoun, M. McCormick, and S. Y. Kung, “Depth measurement from integral images through viewpoint image extraction and a modified multibaseline disparity analysis algorithm,” J. Electron. Imaging 14, 023018 (2005).
[CrossRef]

2004 (5)

2003 (4)

2002 (3)

2001 (1)

1999 (2)

1998 (2)

M. S. Bartlett, H. Martin Lades, and T. J. Sejnowski, “Independent component representations for face recognition,” Proc. SPIE , 3299, 528-539 (1998).
[CrossRef]

J. Arai, F. Okano, H. Hoshino, and I. Yuyama, “Gradient-index lens-array method based on real time integral photography for three-dimensional images,” Appl. Opt. 37, 2034-2045 (1998).
[CrossRef]

1997 (2)

1993 (1)

1982 (1)

H. Murakami and B. Kumar, “Efficient calculation of primary images from a set of images,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-4, 511-515 (1982).
[CrossRef]

1931 (1)

1908 (1)

G. Lippmann, “La photographie integrale,” C. R. Hebd. Seances Acad. Sci. 146, 446-451 (1908).

Adelson, E. H.

Aggoun, A.

C. Wu, A. Aggoun, M. McCormick, and S. Y. Kung, “Depth measurement from integral images through viewpoint image extraction and a modified multibaseline disparity analysis algorithm,” J. Electron. Imaging 14, 023018 (2005).
[CrossRef]

Arai, J.

Arimoto, H.

Bahn, J.-E.

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, J.-E. Bahn, S.-K. Kim, and H. Choi, “Parameters for designing autostereoscopic imaging systems based on lenticular, parallax barrier, and integral photography plates,” Opt. Eng. (Bellingham) 42, 3326-3333 (2003).
[CrossRef]

Bartlett, M. S.

M. S. Bartlett, J. R. Movellan, and T. J. Sejnowski, “Face recognition by independent component analysis,” IEEE Trans. Neural Netw. 13, 1450-1464 (2002).
[CrossRef]

M. S. Bartlett, H. Martin Lades, and T. J. Sejnowski, “Independent component representations for face recognition,” Proc. SPIE , 3299, 528-539 (1998).
[CrossRef]

Chan, A.

Choi, H.

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, J.-E. Bahn, S.-K. Kim, and H. Choi, “Parameters for designing autostereoscopic imaging systems based on lenticular, parallax barrier, and integral photography plates,” Opt. Eng. (Bellingham) 42, 3326-3333 (2003).
[CrossRef]

Choi, Y.-J.

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, J.-E. Bahn, S.-K. Kim, and H. Choi, “Parameters for designing autostereoscopic imaging systems based on lenticular, parallax barrier, and integral photography plates,” Opt. Eng. (Bellingham) 42, 3326-3333 (2003).
[CrossRef]

Der, S.

Dubois, F.

Farid, H.

Frauel, Y.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Goudail, F.

Haneishi, H.

Hong, S.-H.

Y. S. Hwang, S.-H. Hong, and B. Javidi, “Free view 3-D visualization of occluded objects by using computational synthetic aperture integral imaging,” J. Disp. Technol. 3, 64-70 (2007).
[CrossRef]

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]

Hoshino, H.

Hoyer, P. O.

A. Hyvärinen, P. O. Hoyer, and E. Oja, “Sparse code shrinkage: denoising by nonlinear maximum likelihood estimation,” in Advances in Neural Information Processing Systems 11 (NIPS1998) (MIT Press, 1999), pp. 473-479.

Huang, D. S.

H. Zheng, D. S. Huang, and L. Shang, “Feature selection in independent component subspace for microarray data classification,” Neurocomputing 69, 2407-2410 (2006).
[CrossRef]

Hwang, Y. S.

Y. S. Hwang, S.-H. Hong, and B. Javidi, “Free view 3-D visualization of occluded objects by using computational synthetic aperture integral imaging,” J. Disp. Technol. 3, 64-70 (2007).
[CrossRef]

Hyvärinen, A.

A. Hyvärinen, P. O. Hoyer, and E. Oja, “Sparse code shrinkage: denoising by nonlinear maximum likelihood estimation,” in Advances in Neural Information Processing Systems 11 (NIPS1998) (MIT Press, 1999), pp. 473-479.

A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis (Wiley, 2001).
[CrossRef]

Istasse, E.

Ives, H. E.

Jang, J.-S.

Javidi, B.

R. Martínez-Cuenca, G. Saavedra, A. Pons, B. Javidi, and M. Martínez-Corral, “Facet braiding: a fundamental problem in integral imaging,” Opt. Lett. 32, 1078-1080 (2007).
[CrossRef] [PubMed]

Y. S. Hwang, S.-H. Hong, and B. Javidi, “Free view 3-D visualization of occluded objects by using computational synthetic aperture integral imaging,” J. Disp. Technol. 3, 64-70 (2007).
[CrossRef]

R. Martinez, A. Pons, G. Saavedra, M. Martínez-Corral, and B. Javidi, “Optically-corrected elemental images for undistorted integral image display,” Opt. Express 14, 9657-9663 (2006).
[CrossRef]

A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE 94, 591-607 (2006).
[CrossRef]

M. Martínez-Corral, B. Javidi, R. Martínez-Cuenca, and G. Saavedra, “Multifacet structure of observed reconstructed integral images,” J. Opt. Soc. Am. A 22, 597-603 (2005).
[CrossRef]

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]

S. Yeom and B. Javidi, “Three-dimensional distortion-tolerant object recognition using integral imaging,” Opt. Express 12, 5795-5809 (2004).
[CrossRef] [PubMed]

S. Kishk and B. Javidi, “Improved resolution 3D object sensing and recognition using time multiplexed computational integral imaging,” Opt. Express 11, 3528-3541 (2003).
[CrossRef] [PubMed]

A. Stern and B. Javidi, “3-D computational synthetic aperture integral imaging (COMPSAII),” Opt. Express 11, 2446-2451 (2003).
[CrossRef] [PubMed]

J.-S. Jang and B. Javidi, “Large depth-of-focus time-multiplexed three-dimensional integral imaging by use of lenslets with nonuniform focal lengths and aperture sizes,” Opt. Lett. 28, 1924-1926 (2003).
[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]

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]

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

Karhunen, J.

A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis (Wiley, 2001).
[CrossRef]

Kim, S.-K.

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, J.-E. Bahn, S.-K. Kim, and H. Choi, “Parameters for designing autostereoscopic imaging systems based on lenticular, parallax barrier, and integral photography plates,” Opt. Eng. (Bellingham) 42, 3326-3333 (2003).
[CrossRef]

Kishk, S.

Kotynski, R.

Kumar, B.

H. Murakami and B. Kumar, “Efficient calculation of primary images from a set of images,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-4, 511-515 (1982).
[CrossRef]

Kung, S. Y.

C. Wu, A. Aggoun, M. McCormick, and S. Y. Kung, “Depth measurement from integral images through viewpoint image extraction and a modified multibaseline disparity analysis algorithm,” J. Electron. Imaging 14, 023018 (2005).
[CrossRef]

Kwon, H.

Lades, H. Martin

M. S. Bartlett, H. Martin Lades, and T. J. Sejnowski, “Independent component representations for face recognition,” Proc. SPIE , 3299, 528-539 (1998).
[CrossRef]

Lippmann, G.

G. Lippmann, “La photographie integrale,” C. R. Hebd. Seances Acad. Sci. 146, 446-451 (1908).

Mahalanobis, A.

A. Mahalanobis, R. R. Muise, S. R. Stanfill, and A. V. Nevel, “Design and application of quadratic correlation filters for target detection,” IEEE Trans. Aerosp. Electron. Syst. 40, 837-850 (2004).
[CrossRef]

A. Mahalanobis, “A review of correlation filters and their application for scene matching,” in Optoelectronic Devices and Systems for Processing, B.Javidi and K.M.Johnson, eds. (SPIE, 1996), pp. 240-260.

Martinez, R.

Martínez-Corral, M.

Martínez-Cuenca, R.

McCormick, M.

C. Wu, A. Aggoun, M. McCormick, and S. Y. Kung, “Depth measurement from integral images through viewpoint image extraction and a modified multibaseline disparity analysis algorithm,” J. Electron. Imaging 14, 023018 (2005).
[CrossRef]

Minetti, C.

Miyake, Y.

Monnom, O.

Movellan, J. R.

M. S. Bartlett, J. R. Movellan, and T. J. Sejnowski, “Face recognition by independent component analysis,” IEEE Trans. Neural Netw. 13, 1450-1464 (2002).
[CrossRef]

Muise, R. R.

A. Mahalanobis, R. R. Muise, S. R. Stanfill, and A. V. Nevel, “Design and application of quadratic correlation filters for target detection,” IEEE Trans. Aerosp. Electron. Syst. 40, 837-850 (2004).
[CrossRef]

Murakami, H.

H. Murakami and B. Kumar, “Efficient calculation of primary images from a set of images,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-4, 511-515 (1982).
[CrossRef]

Nasrabadi, N.

Nevel, A. V.

A. Mahalanobis, R. R. Muise, S. R. Stanfill, and A. V. Nevel, “Design and application of quadratic correlation filters for target detection,” IEEE Trans. Aerosp. Electron. Syst. 40, 837-850 (2004).
[CrossRef]

Novella Requena, M.

Oja, E.

A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis (Wiley, 2001).
[CrossRef]

A. Hyvärinen, P. O. Hoyer, and E. Oja, “Sparse code shrinkage: denoising by nonlinear maximum likelihood estimation,” in Advances in Neural Information Processing Systems 11 (NIPS1998) (MIT Press, 1999), pp. 473-479.

Okano, F.

Pons, A.

Réfrégier, P.

Saavedra, G.

Sadjadi, F.

F. Sadjadi, Automatic Target Recognition (SPIE, 2000).

Saveljev, V. V.

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, J.-E. Bahn, S.-K. Kim, and H. Choi, “Parameters for designing autostereoscopic imaging systems based on lenticular, parallax barrier, and integral photography plates,” Opt. Eng. (Bellingham) 42, 3326-3333 (2003).
[CrossRef]

Sejnowski, T. J.

M. S. Bartlett, J. R. Movellan, and T. J. Sejnowski, “Face recognition by independent component analysis,” IEEE Trans. Neural Netw. 13, 1450-1464 (2002).
[CrossRef]

M. S. Bartlett, H. Martin Lades, and T. J. Sejnowski, “Independent component representations for face recognition,” Proc. SPIE , 3299, 528-539 (1998).
[CrossRef]

Shang, L.

H. Zheng, D. S. Huang, and L. Shang, “Feature selection in independent component subspace for microarray data classification,” Neurocomputing 69, 2407-2410 (2006).
[CrossRef]

Sokolov, P.

P. Sokolov, Autostereoscopy and Integral Photography by Professor Lippmann's Method (Moscow State U. Press, 1911).

Son, J.-Y.

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, J.-E. Bahn, S.-K. Kim, and H. Choi, “Parameters for designing autostereoscopic imaging systems based on lenticular, parallax barrier, and integral photography plates,” Opt. Eng. (Bellingham) 42, 3326-3333 (2003).
[CrossRef]

Stanfill, S. R.

A. Mahalanobis, R. R. Muise, S. R. Stanfill, and A. V. Nevel, “Design and application of quadratic correlation filters for target detection,” IEEE Trans. Aerosp. Electron. Syst. 40, 837-850 (2004).
[CrossRef]

Stern, A.

A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE 94, 591-607 (2006).
[CrossRef]

A. Stern and B. Javidi, “3-D computational synthetic aperture integral imaging (COMPSAII),” Opt. Express 11, 2446-2451 (2003).
[CrossRef] [PubMed]

Tsumura, N.

Wu, C.

C. Wu, A. Aggoun, M. McCormick, and S. Y. Kung, “Depth measurement from integral images through viewpoint image extraction and a modified multibaseline disparity analysis algorithm,” J. Electron. Imaging 14, 023018 (2005).
[CrossRef]

Yayuma, I.

Yeom, S.

Yuyama, I.

Zheng, H.

H. Zheng, D. S. Huang, and L. Shang, “Feature selection in independent component subspace for microarray data classification,” Neurocomputing 69, 2407-2410 (2006).
[CrossRef]

Appl. Opt. (6)

C. R. Hebd. Seances Acad. Sci. (1)

G. Lippmann, “La photographie integrale,” C. R. Hebd. Seances Acad. Sci. 146, 446-451 (1908).

IEEE Trans. Aerosp. Electron. Syst. (1)

A. Mahalanobis, R. R. Muise, S. R. Stanfill, and A. V. Nevel, “Design and application of quadratic correlation filters for target detection,” IEEE Trans. Aerosp. Electron. Syst. 40, 837-850 (2004).
[CrossRef]

IEEE Trans. Neural Netw. (1)

M. S. Bartlett, J. R. Movellan, and T. J. Sejnowski, “Face recognition by independent component analysis,” IEEE Trans. Neural Netw. 13, 1450-1464 (2002).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

H. Murakami and B. Kumar, “Efficient calculation of primary images from a set of images,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-4, 511-515 (1982).
[CrossRef]

J. Disp. Technol. (1)

Y. S. Hwang, S.-H. Hong, and B. Javidi, “Free view 3-D visualization of occluded objects by using computational synthetic aperture integral imaging,” J. Disp. Technol. 3, 64-70 (2007).
[CrossRef]

J. Electron. Imaging (1)

C. Wu, A. Aggoun, M. McCormick, and S. Y. Kung, “Depth measurement from integral images through viewpoint image extraction and a modified multibaseline disparity analysis algorithm,” J. Electron. Imaging 14, 023018 (2005).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

Neurocomputing (1)

H. Zheng, D. S. Huang, and L. Shang, “Feature selection in independent component subspace for microarray data classification,” Neurocomputing 69, 2407-2410 (2006).
[CrossRef]

Opt. Eng. (Bellingham) (1)

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, J.-E. Bahn, S.-K. Kim, and H. Choi, “Parameters for designing autostereoscopic imaging systems based on lenticular, parallax barrier, and integral photography plates,” Opt. Eng. (Bellingham) 42, 3326-3333 (2003).
[CrossRef]

Opt. Express (5)

Opt. Lett. (4)

Proc. IEEE (1)

A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE 94, 591-607 (2006).
[CrossRef]

Proc. SPIE (1)

M. S. Bartlett, H. Martin Lades, and T. J. Sejnowski, “Independent component representations for face recognition,” Proc. SPIE , 3299, 528-539 (1998).
[CrossRef]

Other (8)

P. Sokolov, Autostereoscopy and Integral Photography by Professor Lippmann's Method (Moscow State U. Press, 1911).

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

A. Hyvärinen, P. O. Hoyer, and E. Oja, “Sparse code shrinkage: denoising by nonlinear maximum likelihood estimation,” in Advances in Neural Information Processing Systems 11 (NIPS1998) (MIT Press, 1999), pp. 473-479.

P. Réfrégier, Noise Theory and Application to Physics (Springer, 2003).

A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis (Wiley, 2001).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

F. Sadjadi, Automatic Target Recognition (SPIE, 2000).

A. Mahalanobis, “A review of correlation filters and their application for scene matching,” in Optoelectronic Devices and Systems for Processing, B.Javidi and K.M.Johnson, eds. (SPIE, 1996), pp. 240-260.

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Figures (14)

Fig. 1
Fig. 1

Experimental optical setup for 3D integral imaging. P is the lens pitch. The lens array produces various perspectives of the 3D scene. A camera captures these various perspectives as 2D elemental images that contain depth information of the 3D scene. A turnable stage allows the acquisition of integral images from various viewing points during the training stage of the system.

Fig. 2
Fig. 2

Diagram of 3D integral imaging system for object recognition using ICA algorithm. W P C A R 5329 × 100 , W I C A R 100 × 100 , x R 5329 × 1 , x test R 5329 × 1 , x P C A R 100 × 1 , x P C A test R 100 × 1 , x I C A R 100 × 1 , x I C A test R 100 × 1 .

Fig. 3
Fig. 3

Sample car object used in our experiments.

Fig. 4
Fig. 4

Cropped sets of 6 × 5 integral images of the six toy cars used in the experiments. Each elemental image is composed of 73 × 73   pixels .

Fig. 5
Fig. 5

Illustration of elemental image decomposition with a given basis image set.

Fig. 6
Fig. 6

First 20 basis images in columns of matrix A (or row of matrix W).

Fig. 7
Fig. 7

Probability of correct decision for toy car object classes from 1–6.

Fig. 8
Fig. 8

Probability of correct decision for toy car object classes 1–6. The car orientation angles vary from 18 ° to 18°.

Fig. 9
Fig. 9

Classification rate for different toy car object classes. From each integral image set used for training sample sizes of 234, 390, 780, and 1560 corresponding to 3, 5, 10, and 20 elemental images are used, respectively.

Fig. 10
Fig. 10

Test results for each of six toy car classes using a training vector from classes 1–6. The cosine angle value is high where the class of the test vector and the class of the training vectors are the same.

Fig. 11
Fig. 11

Test results for each of six toy car classes using a test vector from classes 1–6. The cosine value is high where the class of the test vector and the class of the training vectors are the same.

Fig. 12
Fig. 12

Integral imaging experimental set up with occluded 3D objects.

Fig. 13
Fig. 13

Two integral images of occluded car object for toy car class 4 and toy car class 6, where the class 6 object car is heavily occluded.

Fig. 14
Fig. 14

Classification rate of classifying occluded car objects. From each integral image used for training, the training sample size is 234, 390, 780, and 1560 corresponding to 3, 5, 10, and 20 elemental images, respectively.

Equations (14)

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x = A s ,
s = W x .
kurt ( y ) = E ( y 4 ) 3 [ E ( y 2 ) ] 2 ,
w E [ z ( w T z ) 3 ] 3 w ,
z = D 1 2 U T x ,
w orth i = w i j = 1 i 1 w j , w i w j , w j w j ,
C = 1 n X ¯ X ¯ T ,
C = U λ U T ,
C = 1 n X ¯ T X ¯ .
λ i = λ i ,
u i = X u i n λ i .
x PCA = W PCA T x = U m T x ,
x ICA = W ICA x PCA ,
c = x ICA test x ICA train x ICA test x ICA train ,

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