Abstract

As a promising three dimensional passive imaging modality, Integral Imaging (II) has been investigated widely within the research community. In virtually all of such investigations, there is an implicit assumption that the collection of elemental images lie on a simple geometric surface (e.g. flat, concave, etc), also known as pickup surface. In this paper, we present a generalized framework for 3D II with arbitrary pickup surface geometry and randomly distributed sensor configuration. In particular, we will study the case of Synthetic Aperture Integral Imaging (SAII) with random location of cameras in space, while all cameras have parallel optical axes but different distances from the 3D scene. We assume that the sensors are randomly distributed in 3D volume of pick up space. For 3D reconstruction, a finite number of sensors with known coordinates are randomly selected from within this volume. The mathematical framework for 3D scene reconstruction is developed based on an affine transform representation of imaging under geometrical optics regime.We demonstrate the feasibility of the methods proposed here by experimental results. To the best of our knowledge, this is the first report on 3D imaging using randomly distributed sensors.

© 2008 Optical Society of America

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2007 (6)

2006 (5)

B. Javidi, S. H. Hong, and O. Matoba, "Multidimensional optical sensor and imaging system," Appl. Opt. 45, 2986-2994 (2006).
[CrossRef]

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

K. Itoh, W. Watanabe, H. Arimoto, and K. Isobe, "Coherence-based 3-D and spectral imaging and laser-scanning microscopy," Proceedings of the IEEE 94, 608-628 (2006).
[CrossRef]

A. Stern and B. Javidi, "Three-dimensional image sensing, visualization, and processing using integral imaging," Proceedings of the IEEE 94, 591-607 (2006).
[CrossRef]

M. Levoy, "Light fields and computional imaging," IEEE Computer 39, 46-55 (2006).

2005 (1)

R. Mart`ınez-Cuenca, G. Saavedra, M. Martnez-Corral, and B. Javidi, "Extended Depth-of-Field 3-D Display and Visualization by Combination of Amplitude-Modulated Microlenses and Deconvolution Tools," IEEE J. Display Technol. 1, 321-327 (2005).
[CrossRef]

2004 (5)

2003 (2)

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]

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. 42, 3326-3333 (2003).
[CrossRef]

2002 (4)

2001 (1)

1999 (1)

F. Okano, J. Arai, H. Hoshino, and I. Yuyama, "Three-dimensional video system based on integral photography," Opt. Eng. 38, 1072-1078 (1999).
[CrossRef]

1998 (1)

1997 (2)

1988 (1)

1980 (1)

T. Okoshi, "Three-dimensional displays," Proceedings of the IEEE 68, 548-564 (1980).
[CrossRef]

1978 (1)

Y. Igarishi, H. Murata, and M. Ueda, "3D display system using a computer-generated integral photograph," Jpn. J. Appl. Phys. 17, 1683-1684 (1978).
[CrossRef]

1931 (1)

1908 (1)

M. G. Lippmann, "La photographie int??egrale," Comptes-rendus de l??Acad??emie des Sciences 146, 446-451 (1908).

Aggoun, A.

R. Zaharia, A. Aggoun, and M. McCormick, "Adaptive 3D-DCT compression algorithm for continuous parallax 3-D integral imaging," Signal Process. Image Commun. 17, 231-242 (2002).
[CrossRef]

Arai, J.

Arimoto, H.

K. Itoh, W. Watanabe, H. Arimoto, and K. Isobe, "Coherence-based 3-D and spectral imaging and laser-scanning microscopy," Proceedings of the IEEE 94, 608-628 (2006).
[CrossRef]

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

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. 42, 3326-3333 (2003).
[CrossRef]

Castro, 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. 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. 42, 3326-3333 (2003).
[CrossRef]

Davies, N.

Frauel, Y.

Hong, S.

Y. Hwang, S. Hong, and B. Javidi, "Free View 3-D Visualization of Occluded Objects by Using Computational Synthetic Aperture Integral Imaging," IEEE J. Display Technol. 3, 64-70 (2007).
[CrossRef]

Hong, S. H.

Hong, S. -H.

Hoshino, H.

Hwang, Y.

Y. Hwang, S. Hong, and B. Javidi, "Free View 3-D Visualization of Occluded Objects by Using Computational Synthetic Aperture Integral Imaging," IEEE J. Display Technol. 3, 64-70 (2007).
[CrossRef]

Igarishi, Y.

Y. Igarishi, H. Murata, and M. Ueda, "3D display system using a computer-generated integral photograph," Jpn. J. Appl. Phys. 17, 1683-1684 (1978).
[CrossRef]

Isobe, K.

K. Itoh, W. Watanabe, H. Arimoto, and K. Isobe, "Coherence-based 3-D and spectral imaging and laser-scanning microscopy," Proceedings of the IEEE 94, 608-628 (2006).
[CrossRef]

Itoh, K.

K. Itoh, W. Watanabe, H. Arimoto, and K. Isobe, "Coherence-based 3-D and spectral imaging and laser-scanning microscopy," Proceedings of the IEEE 94, 608-628 (2006).
[CrossRef]

Ives, H. E.

Jang, J. S.

Jang, J. -S.

Javidi, B.

Y. Hwang, S. Hong, and B. Javidi, "Free View 3-D Visualization of Occluded Objects by Using Computational Synthetic Aperture Integral Imaging," IEEE J. Display Technol. 3, 64-70 (2007).
[CrossRef]

S. Yeom, B. Javidi, and E. Watson, "Photon-counting passive 3D image sensing for reconstruction and recognition of occluded objects," Opt. Express 15, 16189-16195 (2007).
[CrossRef]

A. Castro, Y. Frauel, and B. Javidi, "Integral imaging with large depth of field using an asymmetric phase mask," Opt. Express 15, 10266-10273 (2007).
[CrossRef]

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

B. Javidi, S. H. Hong, and O. Matoba, "Multidimensional optical sensor and imaging system," Appl. Opt. 45, 2986-2994 (2006).
[CrossRef]

A. Stern and B. Javidi, "Three-dimensional image sensing, visualization, and processing using integral imaging," Proceedings of the IEEE 94, 591-607 (2006).
[CrossRef]

R. Mart`ınez-Cuenca, G. Saavedra, M. Martnez-Corral, and B. Javidi, "Extended Depth-of-Field 3-D Display and Visualization by Combination of Amplitude-Modulated Microlenses and Deconvolution Tools," IEEE J. Display Technol. 1, 321-327 (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]

S. -H. Hong and B. Javidi, "Improved resolution 3D object reconstruction using computational integral imaging with time multiplexing," Opt. Express 12, 4579-4588 (2004).
[CrossRef]

Y. Frauel, E. Tajahuerce, O. Matoba, A. Castro, and B. Javidi, "Comparison of passive ranging integral imaging and active imaging digital holography for three-dimensional object recognition," Appl. Opt. 43, 452-462 (2004).
[CrossRef]

S. Yeom, A. Stern, and B. Javidi, "Compression of color integral images using MPEG 2," Opt. Express 12, 1632-1642 (2004).
[CrossRef]

R. Martınez-Cuenca, G. Saavedra, M. Martnez-Corral, and B. Javidi, "Enhanced depth of field integral imaging with sensor resolution constraints," Opt. Express 12, 5237-5242 (2004).
[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]

J. S. Jang and B. Javidi, "Improved viewing resolution of 3-D integral imaging with nonstationary micro-optics," Opt. Lett. 27, 324-326 (2002).
[CrossRef]

J. -S. Jang and B. Javidi, "Three-dimensional synthetic aperture integral imaging," Opt. Lett. 27, 1144-1146 (2002).
[CrossRef]

J. -S. Jang and B. Javidi, "Three-dimensional integral imaging with electronically synthesized lenslet arrays," Opt. Lett. 27, 1767-1769 (2002).
[CrossRef]

H. Arimoto and B. Javidi, "Integral three-dimensional imaging with digital reconstruction," Opt. Lett. 26, 157-159 (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. 42, 3326-3333 (2003).
[CrossRef]

Levoy, M.

M. Levoy, "Light fields and computional imaging," IEEE Computer 39, 46-55 (2006).

Lippmann, M. G.

M. G. Lippmann, "La photographie int??egrale," Comptes-rendus de l??Acad??emie des Sciences 146, 446-451 (1908).

Mart`inez-Cuenca, R.

R. Mart`ınez-Cuenca, G. Saavedra, M. Martnez-Corral, and B. Javidi, "Extended Depth-of-Field 3-D Display and Visualization by Combination of Amplitude-Modulated Microlenses and Deconvolution Tools," IEEE J. Display Technol. 1, 321-327 (2005).
[CrossRef]

Martinez, R.

Martinez-Corral, M.

Martinez-Cuenca, R.

Martnez-Corral, M.

R. Mart`ınez-Cuenca, G. Saavedra, M. Martnez-Corral, and B. Javidi, "Extended Depth-of-Field 3-D Display and Visualization by Combination of Amplitude-Modulated Microlenses and Deconvolution Tools," IEEE J. Display Technol. 1, 321-327 (2005).
[CrossRef]

R. Martınez-Cuenca, G. Saavedra, M. Martnez-Corral, and B. Javidi, "Enhanced depth of field integral imaging with sensor resolution constraints," Opt. Express 12, 5237-5242 (2004).
[CrossRef]

Matoba, O.

McCormick, M.

R. Zaharia, A. Aggoun, and M. McCormick, "Adaptive 3D-DCT compression algorithm for continuous parallax 3-D integral imaging," Signal Process. Image Commun. 17, 231-242 (2002).
[CrossRef]

McCornick, M.

Murata, H.

Y. Igarishi, H. Murata, and M. Ueda, "3D display system using a computer-generated integral photograph," Jpn. J. Appl. Phys. 17, 1683-1684 (1978).
[CrossRef]

Okano, F.

Okoshi, T.

T. Okoshi, "Three-dimensional displays," Proceedings of the IEEE 68, 548-564 (1980).
[CrossRef]

Pons, A.

Saavedra, G.

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. 42, 3326-3333 (2003).
[CrossRef]

Shin, D. -H.

Shin, D.-H.

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. 42, 3326-3333 (2003).
[CrossRef]

Stern, A.

Tajahuerce, E.

Tavakoli, B.

Travis, A. R. L.

A. R. L. Travis, "The display of three dimensional video images," Proc. of the IEEE 85, 1817-1832 (1997).
[CrossRef]

Ueda, M.

Y. Igarishi, H. Murata, and M. Ueda, "3D display system using a computer-generated integral photograph," Jpn. J. Appl. Phys. 17, 1683-1684 (1978).
[CrossRef]

Watanabe, W.

K. Itoh, W. Watanabe, H. Arimoto, and K. Isobe, "Coherence-based 3-D and spectral imaging and laser-scanning microscopy," Proceedings of the IEEE 94, 608-628 (2006).
[CrossRef]

Watson, E.

Yang, L.

Yeom, S.

Yoo, H.

Yuyama, I.

Zaharia, R.

R. Zaharia, A. Aggoun, and M. McCormick, "Adaptive 3D-DCT compression algorithm for continuous parallax 3-D integral imaging," Signal Process. Image Commun. 17, 231-242 (2002).
[CrossRef]

Appl. Opt. (6)

Comptes-rendus de l??Acad??emie des Sciences (1)

M. G. Lippmann, "La photographie int??egrale," Comptes-rendus de l??Acad??emie des Sciences 146, 446-451 (1908).

IEEE Computer (1)

M. Levoy, "Light fields and computional imaging," IEEE Computer 39, 46-55 (2006).

IEEE J. Display Technol. (2)

Y. Hwang, S. Hong, and B. Javidi, "Free View 3-D Visualization of Occluded Objects by Using Computational Synthetic Aperture Integral Imaging," IEEE J. Display Technol. 3, 64-70 (2007).
[CrossRef]

R. Mart`ınez-Cuenca, G. Saavedra, M. Martnez-Corral, and B. Javidi, "Extended Depth-of-Field 3-D Display and Visualization by Combination of Amplitude-Modulated Microlenses and Deconvolution Tools," IEEE J. Display Technol. 1, 321-327 (2005).
[CrossRef]

J. Opt. Soc. Am. (1)

Jpn. J. Appl. Phys. (1)

Y. Igarishi, H. Murata, and M. Ueda, "3D display system using a computer-generated integral photograph," Jpn. J. Appl. Phys. 17, 1683-1684 (1978).
[CrossRef]

Opt. Eng. (2)

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. 42, 3326-3333 (2003).
[CrossRef]

F. Okano, J. Arai, H. Hoshino, and I. Yuyama, "Three-dimensional video system based on integral photography," Opt. Eng. 38, 1072-1078 (1999).
[CrossRef]

Opt. Express (10)

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

A. Castro, Y. Frauel, and B. Javidi, "Integral imaging with large depth of field using an asymmetric phase mask," Opt. Express 15, 10266-10273 (2007).
[CrossRef]

B. Tavakoli, M. DaneshPanah, B. Javidi, and E. Watson, "Performance of 3D integral imaging with position uncertainty," Opt. Express 15, 11889-11902 (2007).
[CrossRef]

D. -H. Shin and H. Yoo, "Image quality enhancement in 3D computational integral imaging by use of interpolation methods," Opt. Express 15, 12039-12049 (2007).
[CrossRef]

H. Yoo and D.-H. Shin "Improved analysis on the signal property of computational integral imaging system," Opt. Express 15, 14107-14114 (2007).
[CrossRef]

S. Yeom, B. Javidi, and E. Watson, "Photon-counting passive 3D image sensing for reconstruction and recognition of occluded objects," Opt. Express 15, 16189-16195 (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]

S. Yeom, A. Stern, and B. Javidi, "Compression of color integral images using MPEG 2," Opt. Express 12, 1632-1642 (2004).
[CrossRef]

S. -H. Hong and B. Javidi, "Improved resolution 3D object reconstruction using computational integral imaging with time multiplexing," Opt. Express 12, 4579-4588 (2004).
[CrossRef]

R. Martınez-Cuenca, G. Saavedra, M. Martnez-Corral, and B. Javidi, "Enhanced depth of field integral imaging with sensor resolution constraints," Opt. Express 12, 5237-5242 (2004).
[CrossRef]

Opt. Lett. (4)

Proc. of the IEEE (1)

A. R. L. Travis, "The display of three dimensional video images," Proc. of the IEEE 85, 1817-1832 (1997).
[CrossRef]

Proceedings of the IEEE (3)

K. Itoh, W. Watanabe, H. Arimoto, and K. Isobe, "Coherence-based 3-D and spectral imaging and laser-scanning microscopy," Proceedings of the IEEE 94, 608-628 (2006).
[CrossRef]

T. Okoshi, "Three-dimensional displays," Proceedings of the IEEE 68, 548-564 (1980).
[CrossRef]

A. Stern and B. Javidi, "Three-dimensional image sensing, visualization, and processing using integral imaging," Proceedings of the IEEE 94, 591-607 (2006).
[CrossRef]

Signal Process. Image Commun. (1)

R. Zaharia, A. Aggoun, and M. McCormick, "Adaptive 3D-DCT compression algorithm for continuous parallax 3-D integral imaging," Signal Process. Image Commun. 17, 231-242 (2002).
[CrossRef]

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