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

Full Article  |  PDF Article

References

  • View by:
  • |

  1. S. A. Benton, ed., Selected Papers on Three-Dimensional Displays (SPIE Optical Engineering Press, Bellingham, WA, 2001).
  2. D. H. McMahon and H. J. Caulfield, �??A technique for producing wide-angle holographic displays,�?? Appl. Opt. 9, 91-96 (1970).
    [CrossRef] [PubMed]
  3. 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
  4. 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]
  5. M. Martínez-Corral, M. T. Caballero and A. Pons, �??Axial apodization in 4Pi-confocal microscopy by annular binary filters,�?? J. Opt. Soc. Am. A 19, 1532-1536 (2002).
    [CrossRef]
  6. B. Javidi, and F. Okano, eds., Three Dimensional Television, Video, and Display Technologies (Springer, Berlin, 2002)
  7. 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]
  8. 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]
  9. T. Okoshi, Three-dimensional imaging techniques (Academic Press, New York, 1976).
  10. G. Lippmann, �??La photographic intergrale,�?? C. R. Acad. Sci. 146, 446-451 (1908).
  11. H. E. Ives, �??Optical properties of a Lipmann lenticulated sheet,�?? J. Opt. Soc. Am. 21, 171-176 (1931).
    [CrossRef]
  12. D. L. Marks, and D. J. Brady, �??Three-dimensional source reconstruction with a scanned pinhole camera,�?? Opt. Lett. 23, 820-822 (1998)
    [CrossRef]
  13. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, NY, 1996).
  14. . H. Arimoto and B. Javidi, �??Integral three-dimensional imaging with digital reconstruction,�?? Opt. Lett. 26, 157-159 (2001)
    [CrossRef]
  15. 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]
  16. 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]
  17. 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]
  18. 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]
  19. C. B. Burckhardt, �??Optimum parameters and resolution limitation of integral photography,�?? J. Opt. Soc. Am. 58, 71-76 (1968).
    [CrossRef]
  20. T. Okoshi, �??Optimum design and depth resolution of lens sheet and projection type three dimensional displays,�?? Appl. Opt. 10, 2284-2291 (1971).
    [CrossRef] [PubMed]
  21. H. Hoshino, F. Okano, H. Isono and I. Yuyama, �??Analysis of resolution limitation of integral photography,�?? J. Opt. Soc. Am. A 15, 2059-2065 (1998)
    [CrossRef]
  22. 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]
  23. S. Hong, J.-S. Jang and B. Javidi, �??Three-dimensional volumetric object reconstruction using computational integral imaging,�?? Optics Express, 12, 483-491 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-483">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-483</a>
    [CrossRef] [PubMed]

Appl. Opt.

C. R. Acad. Sci.

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

IEEE Trans. Med. Imag.

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.

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.

J. Opt. Soc. Am. A

LEOS 2003

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

Opt. Eng.

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]

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. Lett.

Optics Express

S. Hong, J.-S. Jang and B. Javidi, �??Three-dimensional volumetric object reconstruction using computational integral imaging,�?? Optics Express, 12, 483-491 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-483">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-483</a>
[CrossRef] [PubMed]

Other

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

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).

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

Supplementary Material (2)

» Media 1: AVI (1304 KB)     
» Media 2: AVI (685 KB)     

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


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)

Fig. 2.
Fig. 2.

3D object used in the experiments.

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.

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.

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)

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.

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)

Fig. 8.
Fig. 8.

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

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.

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)

Tables (1)

Tables Icon

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

Equations (4)

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

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 ) ,

Metrics