Abstract

In the computational three-dimensional (3D) volumetric reconstruction integral imaging (II) system, volume pixels of the scene are reconstructed by superimposing the inversely mapped elemental images through a computationally simulated optical reconstruction process according to ray optics. Close placement of a 3D object to the lenslet array in the pickup process may result in significant variation in intensity between the adjacent pixels of the reconstructed image, degrading the quality of the image. The intensity differences result from the different number of the superimposed elemental images used for reconstructing the corresponding pixels. In this paper, we propose improvements of the reconstructed image quality in two ways using 1) normalized computational 3D volumetric reconstruction II, and 2) hybrid moving lenslet array technique (MALT). To reduce the intensity irregularities between the pixels, we normalize the intensities of the reconstructed image pixels by the overlapping numbers of the inversely mapped elemental images. To capture the elemental image sets for the MALT process, a stationary 3D object pickup process is performed repeatedly at various locations of the pickup lenslet array’s focal plane, which is perpendicular to the optical axis. With MALT, we are able to enhance the quality of the reconstructed images by increasing the sampling rate. We present experimental results of volume pixel reconstruction to test and verify the performance of the proposed reconstruction algorithm. We have shown that substantial improvement in the visual quality of the 3D reconstruction is obtained using the proposed technique.

©2004 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]

2004 (1)

S. Hong, J.-S. Jang, and B. Javidi, “Three-dimensional volumetric object reconstruction using computational integral imaging,” Optics Express,  12, 483–491 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-483
[Crossref] [PubMed]

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 (3)

2001 (1)

1998 (3)

1994 (1)

N. Davies, M. McCormick, and M. Brewin, “Design and analysis of an image transfer system using microlens array,” Opt. Eng. 33, 3624–3633 (1994).
[Crossref]

1985 (1)

J. W. V. Gissen, M. A Viergever, and C. N. D. Graff, “Improved tomographic reconstruction in seven-pinhole imaging,” IEEE Trans. Med. Imag. MI-4, 91–103 (1985)
[Crossref]

1976 (1)

L. T. Chang, B. Macdonald, and V. Perez-Mendez, “Axial tomography and three dimensional image reconstruction,” IEEE Trans. Nucl. Sci. NS-23, 568–572 (1976)
[Crossref]

1971 (1)

1970 (1)

1968 (1)

1931 (1)

1908 (1)

G. Lippmann, “La photographic intergrale,” C. R. Acad. Sci. 146, 446–451 (1908).

Ambs, P.

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

Arai, J.

Arimoto, H.

Bigue, L.

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

Binet, R.

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

Brady, D. J.

Brewin, M.

N. Davies, M. McCormick, and M. Brewin, “Design and analysis of an image transfer system using microlens array,” Opt. Eng. 33, 3624–3633 (1994).
[Crossref]

Burckhardt, C. B.

Caballero, M. T.

Caulfield, H. J.

Chang, L. T.

L. T. Chang, B. Macdonald, and V. Perez-Mendez, “Axial tomography and three dimensional image reconstruction,” IEEE Trans. Nucl. Sci. NS-23, 568–572 (1976)
[Crossref]

Colineau, J.

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

Davies, N.

N. Davies, M. McCormick, and M. Brewin, “Design and analysis of an image transfer system using microlens array,” Opt. Eng. 33, 3624–3633 (1994).
[Crossref]

Frauel, Y.

Gissen, J. W. V.

J. W. V. Gissen, M. A Viergever, and C. N. D. Graff, “Improved tomographic reconstruction in seven-pinhole imaging,” IEEE Trans. Med. Imag. MI-4, 91–103 (1985)
[Crossref]

Goodman, J. W.

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

Graff, C. N. D.

J. W. V. Gissen, M. A Viergever, and C. N. D. Graff, “Improved tomographic reconstruction in seven-pinhole imaging,” IEEE Trans. Med. Imag. MI-4, 91–103 (1985)
[Crossref]

Hong, S.

S. Hong, J.-S. Jang, and B. Javidi, “Three-dimensional volumetric object reconstruction using computational integral imaging,” Optics Express,  12, 483–491 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-483
[Crossref] [PubMed]

Hoshino, H.

Huignard, J.-P.

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

Isono, H.

Ives, H. E.

Jang, J.-S.

S. Hong, J.-S. Jang, and B. Javidi, “Three-dimensional volumetric object reconstruction using computational integral imaging,” Optics Express,  12, 483–491 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-483
[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]

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]

Javidi, B.

Lehureau, J.-C.

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

Lippmann, G.

G. Lippmann, “La photographic intergrale,” C. R. Acad. Sci. 146, 446–451 (1908).

Macdonald, B.

L. T. Chang, B. Macdonald, and V. Perez-Mendez, “Axial tomography and three dimensional image reconstruction,” IEEE Trans. Nucl. Sci. NS-23, 568–572 (1976)
[Crossref]

Marks, D. L.

Martínez-Corral, M.

McCormick, M.

N. Davies, M. McCormick, and M. Brewin, “Design and analysis of an image transfer system using microlens array,” Opt. Eng. 33, 3624–3633 (1994).
[Crossref]

McMahon, D. H.

Okano, F.

Okoshi, T.

Perez-Mendez, V.

L. T. Chang, B. Macdonald, and V. Perez-Mendez, “Axial tomography and three dimensional image reconstruction,” IEEE Trans. Nucl. Sci. NS-23, 568–572 (1976)
[Crossref]

Pons, A.

Stern, A.

Viergever, M. A

J. W. V. Gissen, M. A Viergever, and C. N. D. Graff, “Improved tomographic reconstruction in seven-pinhole imaging,” IEEE Trans. Med. Imag. MI-4, 91–103 (1985)
[Crossref]

Yuyama, I.

Appl. Opt. (5)

C. R. Acad. Sci. (1)

G. Lippmann, “La photographic intergrale,” C. R. Acad. Sci. 146, 446–451 (1908).

IEEE Trans. Med. Imag. (1)

J. W. V. Gissen, M. A Viergever, and C. N. D. Graff, “Improved tomographic reconstruction in seven-pinhole imaging,” IEEE Trans. Med. Imag. MI-4, 91–103 (1985)
[Crossref]

IEEE Trans. Nucl. Sci. (1)

L. T. Chang, B. Macdonald, and V. Perez-Mendez, “Axial tomography and three dimensional image reconstruction,” IEEE Trans. Nucl. Sci. NS-23, 568–572 (1976)
[Crossref]

J. Opt. Soc. Am. (2)

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

Opt. Eng. (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]

N. Davies, M. McCormick, and M. Brewin, “Design and analysis of an image transfer system using microlens array,” Opt. Eng. 33, 3624–3633 (1994).
[Crossref]

Opt. Lett. (3)

Optics Express (1)

S. Hong, J.-S. Jang, and B. Javidi, “Three-dimensional volumetric object reconstruction using computational integral imaging,” Optics Express,  12, 483–491 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-483
[Crossref] [PubMed]

Other (5)

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

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

T. Okoshi, Three-dimensional imaging techniques (Academic Press, New York, 1976).

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

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Figures (10)

Fig. 1.
Fig. 1. An illustration of optical pickup and display of the II image using MALT. Pickup microlens array and display microlens array move synchronously. (malt.avi: 1.3 MB)

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Fig. 2.
Fig. 2. 3D object used in the experiments.

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Fig. 3.
Fig. 3. Illustration of the lateral coordinates of the elemental image plane and reconstructed image plane for the i-th elemental image set to perform a digital MALT reconstruction. The relative displacement at the elemental image plane is xi /M, and the relative displacement at the reconstructed plane is xi . The magnification factor M is M = z/g.

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Fig. 4.
Fig. 4. Example of two different sets of the elemental images used to reconstruct the 3D scene. Elemental image set 1 (left figure) and 7(right figure) are shown.

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Fig. 5.
Fig. 5. Reconstructed image at display distance z = 7mm with computational II. It is difficult to see the details even in the focused area (in this case, right headlight area)

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Fig. 6.
Fig. 6. The number of the overlapping of the magnified elemental images for the display plane at distance z = 7 mm. Each pixel value of this figure represents the number of the overlapping.

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Fig. 7.
Fig. 7. Reconstructed image after the normalization process at display distance z = 7mm. It is possible to see the details in the focused area (in this case, right headlight area)

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Fig. 8.
Fig. 8. Reconstructed hybrid MALT image after the normalization process at display distance z = 7mm.

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Fig. 9.
Fig. 9. Reconstructed hybrid MALT image after the normalization process (a) at display distance z = 7 mm. (b) at display distance z = 9 mm. (c) at display distance z = 11 mm. (d) at display distance z = 21 mm.

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Fig. 10.
Fig. 10. Movie of the reconstructed 3D volume imagery from the image display plane at z = 6 mm to the image display plane at z = 30 mm with increment of 0.1 mm. (volume.avi: 685 KB)

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Tables (1)

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Table 1. The number of pixels of movement in elemental images at each position

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Equations (4)

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O i pq ( x − x i , y − y i , z ; λ ) = I i pq ( − x − x i M + ( 1 + 1 M ) s x p , − y − y i M + ( 1 + 1 M ) s y q : λ ) , ( z + g ) 2 + [ ( x − s x p ) 2 + ( y − s y q ) 2 ] ( 1 + 1 M ) 2
for { s x ( p − M 2 ) + x i ≤ x ≤ s x ( p + M 2 ) + x i s y ( q − M 2 ) + y i ≤ y ≤ s y ( q + M 2 ) + y i
O i ( x − x i , y − y i , z ; λ ) = ∑ p = 0 m − 1 ∑ q = 0 n − 1 O i pq ( x − x i , y − y i , z ; λ ) ,
O ( x , y , z ; λ ) = ∑ i = 1 k O i ( x − x i , y − y i , z ; λ ) ,

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