## 3D integral imaging display by smart pseudoscopic-to-orthoscopic conversion (SPOC) |

Optics Express, Vol. 18, Issue 25, pp. 25573-25583 (2010)

http://dx.doi.org/10.1364/OE.18.025573

Acrobat PDF (1297 KB)

### Abstract

*Previously, we reported a digital technique for formation of real, non-distorted, orthoscopic integral images by direct pickup*. However the technique was constrained to the case of symmetric image capture and display systems. Here, we report a more general algorithm which allows the pseudoscopic to orthoscopic transformation with full control over the display parameters so that one can generate a set of synthetic elemental images that suits the characteristics of the Integral-Imaging monitor and permits control over the depth and size of the reconstructed 3D scene.

© 2010 OSA

## 1. Introduction

2. S.-H. Hong, J.-S. Jang, and B. Javidi, “Three-dimensional volumetric object reconstruction using computational integral imaging,” Opt. Express **12**(3), 483–491 (2004). [CrossRef] [PubMed]

3. J.-H. Park, K. Hong, and B. Lee, “Recent progress in three-dimensional information processing based on integral imaging,” Appl. Opt. **48**(34), H77–H94 (2009). [CrossRef] [PubMed]

4. B. Javidi, R. Ponce-Díaz, and S.-H. Hong, “Three-dimensional recognition of occluded objects by using computational integral imaging,” Opt. Lett. **31**(8), 1106–1108 (2006). [CrossRef] [PubMed]

6. S. Yeom, B. Javidi, and E. Watson, “Photon counting passive 3D image sensing for automatic target recognition,” Opt. Express **13**(23), 9310–9330 (2005). [CrossRef] [PubMed]

7. F. Okano, H. Hoshino, J. Arai, and I. Yuyama, “Real-time pickup method for a three-dimensional image based on integral photography,” Appl. Opt. **36**(7), 1598–1603 (1997). [CrossRef] [PubMed]

8. M. Martínez-Corral, B. Javidi, R. Martínez-Cuenca, and G. Saavedra, “Formation of real, orthoscopic integral images by smart pixel mapping,” Opt. Express **13**(23), 9175–9180 (2005). [CrossRef] [PubMed]

8. M. Martínez-Corral, B. Javidi, R. Martínez-Cuenca, and G. Saavedra, “Formation of real, orthoscopic integral images by smart pixel mapping,” Opt. Express **13**(23), 9175–9180 (2005). [CrossRef] [PubMed]

9. D.-H. Shin, C.-W. Tan, B.-G. Lee, J.-J. Lee, and E.-S. Kim, “Resolution-enhanced three-dimensional image reconstruction by use of smart pixel mapping in computational integral imaging,” Appl. Opt. **47**(35), 6656–6665 (2008). [CrossRef] [PubMed]

10. M. Zhang, Y. Piao, and E.-S. Kim, “Occlusion-removed scheme using depth-reversed method in computational integral imaging,” Appl. Opt. **49**(14), 2571–2580 (2010). [CrossRef]

11. T.-Ch. Wei, D.-H. Shin, and B.-G. Lee, “Resolution-enhanced reconstruction of 3D object using depth-reversed elemental images for partially occluded object recognition,” J. Opt. Soc. Korea **13**(1), 139–145 (2009). [CrossRef]

12. D.-H. Shin, B.-G. Lee, and E.-S. Kim, “Modified smart pixel mapping method for displaying orthoscopic 3D images in integral imaging,” Opt. Lasers Eng. **47**(11), 1189–1194 (2009). [CrossRef]

13. J. Arai, H. Kawai, M. Kawakita, and F. Okano, “Depth-control method for integral imaging,” Opt. Lett. **33**(3), 279–281 (2008). [CrossRef] [PubMed]

14. D.-Ch. Hwang, J.-S. Park, S.-Ch. Kim, D.-H. Shin, and E.-S. Kim, “Magnification of 3D reconstructed images in integral imaging using an intermediate-view reconstruction technique,” Appl. Opt. **45**(19), 4631–4637 (2006). [CrossRef] [PubMed]

## 2. The smart pseudoscopic-to-orthoscopic conversion algorithm

*D*from the display MLA; (ii) we assign arbitrary pitch,

*p*

_{S}, and gap,

*g*

_{S}, to the synthetic PA –note that this selection will determine also the size of the final image; and (iii) we fix, also arbitrarily, the number of pixels,

*n*

_{S}, per synthetic elemental image and the total number of elemental images,

*N*

_{S}.

*d*

_{S}determines the position of the reference plane of the image displayed by the InI display monitor. A smart selection of

*d*

_{S}will permit, when displaying the SEIs in an actual InI display monitor, the observation of either orthoscopic real or virtual 3D images. A positive value of

*d*

_{S}corresponds to a floating real 3D image. A negative value corresponds to a virtual reconstruction.

*x*

_{S}, of the center of the

*m*

^{th}pixel of the

*j*

^{th}SEI through its corresponding pinhole (blue dotted line in Fig. 1). The coordinate of the pixel can be written asThe back-projection through the pinhole permits us to calculate the intersection of the blue line with the reference plane:and also the interface with the display MLA:The index of capture microlens where the blue dotted line impacts can be calculated asThe last step is to find the mapping pixel. To this end, we calculate the coordinate of the point that is the conjugate, through the impact microlens, of point Δ

_{o}Finaly, we can calculate the index of the

*l*

^{th}pixel within the

*i*

^{th}elemental cell asThus, the pixel values of the SEIs can be obtained from the captured integral image by the mapping

## 3. Revisiting two typical cases of the *pseudoscopic to orthoscopic* (PO) conversion

### 3.1. The method proposed by Okano et al

7. F. Okano, H. Hoshino, J. Arai, and I. Yuyama, “Real-time pickup method for a three-dimensional image based on integral photography,” Appl. Opt. **36**(7), 1598–1603 (1997). [CrossRef] [PubMed]

*g*

_{S}

*= g*

_{D}

*-2f*

^{2}

*/*(

*d*

_{D}

*-f*) from a MLA similar to the one used in the capture. This procedure permits the reconstruction of virtual, orthoscopic 3D scenes. Note however that

15. H. Navarro, R. Martínez-Cuenca, A. Molina-Martín, M. Martínez-Corral, G. Saavedra, and B. Javidi, “Method to remedy image degradations due to facet braiding in 3D integral imaging monitors,” J. Display Technol. **6**(10), 404–411 (2010). [CrossRef]

### 3.2. **The symmetric case**

*g*

_{S}=

*g*

_{D},

*p*

_{S}=

*p*

_{D}and

*n*

_{S}=

*n*

_{D}, but now

*D*=

*2d*

_{D}(and therefore and

*d*

_{S}=

*d*

_{D}), besidesThis leads to the result Note that these equations are the same as the ones reported in [8

8. M. Martínez-Corral, B. Javidi, R. Martínez-Cuenca, and G. Saavedra, “Formation of real, orthoscopic integral images by smart pixel mapping,” Opt. Express **13**(23), 9175–9180 (2005). [CrossRef] [PubMed]

## 4. Demonstration of the SPOC and experimental results

16. J. S. Jang and B. Javidi, “Three-dimensional synthetic aperture integral imaging,” Opt. Lett. **27**(13), 1144–1146 (2002). [CrossRef]

_{,}and

_{.}. Then we fixed the synthetic parameters to:

15. H. Navarro, R. Martínez-Cuenca, A. Molina-Martín, M. Martínez-Corral, G. Saavedra, and B. Javidi, “Method to remedy image degradations due to facet braiding in 3D integral imaging monitors,” J. Display Technol. **6**(10), 404–411 (2010). [CrossRef]

17. J. Arai, H. Kawai, and F. Okano, “Microlens arrays for integral imaging system,” Appl. Opt. **45**(36), 9066–9078 (2006). [CrossRef] [PubMed]

15. H. Navarro, R. Martínez-Cuenca, A. Molina-Martín, M. Martínez-Corral, G. Saavedra, and B. Javidi, “Method to remedy image degradations due to facet braiding in 3D integral imaging monitors,” J. Display Technol. **6**(10), 404–411 (2010). [CrossRef]

## 5. Conclusions

*ready to be displayed in an InI monitor in which the pitch, the microlenses focal length, the number of pixels per elemental cell, the depth position of the reference plane, and even the grid geometry of the MLA can be selected to fit the conditions of the display architecture.*

## Acknowledgements

## References and Links

1. | G. Lippmann, “Epreuves reversibles donnant la sensation du relief,” J. Phys. |

2. | S.-H. Hong, J.-S. Jang, and B. Javidi, “Three-dimensional volumetric object reconstruction using computational integral imaging,” Opt. Express |

3. | J.-H. Park, K. Hong, and B. Lee, “Recent progress in three-dimensional information processing based on integral imaging,” Appl. Opt. |

4. | B. Javidi, R. Ponce-Díaz, and S.-H. Hong, “Three-dimensional recognition of occluded objects by using computational integral imaging,” Opt. Lett. |

5. | B. Heigl, R. Koch, M. Pollefeys, J. Denzler, and L. Van Gool, “Plenoptic Modeling and Rendering from Image sequences taken by hand-held Camera,” Proc. DAGM, 94–101 (1999). |

6. | S. Yeom, B. Javidi, and E. Watson, “Photon counting passive 3D image sensing for automatic target recognition,” Opt. Express |

7. | F. Okano, H. Hoshino, J. Arai, and I. Yuyama, “Real-time pickup method for a three-dimensional image based on integral photography,” Appl. Opt. |

8. | M. Martínez-Corral, B. Javidi, R. Martínez-Cuenca, and G. Saavedra, “Formation of real, orthoscopic integral images by smart pixel mapping,” Opt. Express |

9. | D.-H. Shin, C.-W. Tan, B.-G. Lee, J.-J. Lee, and E.-S. Kim, “Resolution-enhanced three-dimensional image reconstruction by use of smart pixel mapping in computational integral imaging,” Appl. Opt. |

10. | M. Zhang, Y. Piao, and E.-S. Kim, “Occlusion-removed scheme using depth-reversed method in computational integral imaging,” Appl. Opt. |

11. | T.-Ch. Wei, D.-H. Shin, and B.-G. Lee, “Resolution-enhanced reconstruction of 3D object using depth-reversed elemental images for partially occluded object recognition,” J. Opt. Soc. Korea |

12. | D.-H. Shin, B.-G. Lee, and E.-S. Kim, “Modified smart pixel mapping method for displaying orthoscopic 3D images in integral imaging,” Opt. Lasers Eng. |

13. | J. Arai, H. Kawai, M. Kawakita, and F. Okano, “Depth-control method for integral imaging,” Opt. Lett. |

14. | D.-Ch. Hwang, J.-S. Park, S.-Ch. Kim, D.-H. Shin, and E.-S. Kim, “Magnification of 3D reconstructed images in integral imaging using an intermediate-view reconstruction technique,” Appl. Opt. |

15. | H. Navarro, R. Martínez-Cuenca, A. Molina-Martín, M. Martínez-Corral, G. Saavedra, and B. Javidi, “Method to remedy image degradations due to facet braiding in 3D integral imaging monitors,” J. Display Technol. |

16. | J. S. Jang and B. Javidi, “Three-dimensional synthetic aperture integral imaging,” Opt. Lett. |

17. | J. Arai, H. Kawai, and F. Okano, “Microlens arrays for integral imaging system,” Appl. Opt. |

**OCIS Codes**

(100.6890) Image processing : Three-dimensional image processing

(110.4190) Imaging systems : Multiple imaging

(110.6880) Imaging systems : Three-dimensional image acquisition

(120.2040) Instrumentation, measurement, and metrology : Displays

**ToC Category:**

Imaging Systems

**History**

Original Manuscript: September 22, 2010

Revised Manuscript: October 27, 2010

Manuscript Accepted: October 27, 2010

Published: November 22, 2010

**Citation**

H. Navarro, R. Martínez-Cuenca, G. Saavedra, M. Martínez-Corral, and B. Javidi, "3D integral imaging display by smart
pseudoscopic-to-orthoscopic conversion (SPOC)," Opt. Express **18**, 25573-25583 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-25-25573

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### References

- G. Lippmann, “Epreuves reversibles donnant la sensation du relief,” J. Phys. 7, 821–825 (1908).
- S.-H. Hong, J.-S. Jang, and B. Javidi, “Three-dimensional volumetric object reconstruction using computational integral imaging,” Opt. Express 12(3), 483–491 (2004). [CrossRef] [PubMed]
- J.-H. Park, K. Hong, and B. Lee, “Recent progress in three-dimensional information processing based on integral imaging,” Appl. Opt. 48(34), H77–H94 (2009). [CrossRef] [PubMed]
- B. Javidi, R. Ponce-Díaz, and S.-H. Hong, “Three-dimensional recognition of occluded objects by using computational integral imaging,” Opt. Lett. 31(8), 1106–1108 (2006). [CrossRef] [PubMed]
- B. Heigl, R. Koch, M. Pollefeys, J. Denzler, and L. Van Gool, “Plenoptic Modeling and Rendering from Image sequences taken by hand-held Camera,” Proc. DAGM, 94–101 (1999).
- S. Yeom, B. Javidi, and E. Watson, “Photon counting passive 3D image sensing for automatic target recognition,” Opt. Express 13(23), 9310–9330 (2005). [CrossRef] [PubMed]
- F. Okano, H. Hoshino, J. Arai, and I. Yuyama, “Real-time pickup method for a three-dimensional image based on integral photography,” Appl. Opt. 36(7), 1598–1603 (1997). [CrossRef] [PubMed]
- M. Martínez-Corral, B. Javidi, R. Martínez-Cuenca, and G. Saavedra, “Formation of real, orthoscopic integral images by smart pixel mapping,” Opt. Express 13(23), 9175–9180 (2005). [CrossRef] [PubMed]
- D.-H. Shin, C.-W. Tan, B.-G. Lee, J.-J. Lee, and E.-S. Kim, “Resolution-enhanced three-dimensional image reconstruction by use of smart pixel mapping in computational integral imaging,” Appl. Opt. 47(35), 6656–6665 (2008). [CrossRef] [PubMed]
- M. Zhang, Y. Piao, and E.-S. Kim, “Occlusion-removed scheme using depth-reversed method in computational integral imaging,” Appl. Opt. 49(14), 2571–2580 (2010). [CrossRef]
- T.-Ch. Wei, D.-H. Shin, and B.-G. Lee, “Resolution-enhanced reconstruction of 3D object using depth-reversed elemental images for partially occluded object recognition,” J. Opt. Soc. Korea 13(1), 139–145 (2009). [CrossRef]
- D.-H. Shin, B.-G. Lee, and E.-S. Kim, “Modified smart pixel mapping method for displaying orthoscopic 3D images in integral imaging,” Opt. Lasers Eng. 47(11), 1189–1194 (2009). [CrossRef]
- J. Arai, H. Kawai, M. Kawakita, and F. Okano, “Depth-control method for integral imaging,” Opt. Lett. 33(3), 279–281 (2008). [CrossRef] [PubMed]
- D.-Ch. Hwang, J.-S. Park, S.-Ch. Kim, D.-H. Shin, and E.-S. Kim, “Magnification of 3D reconstructed images in integral imaging using an intermediate-view reconstruction technique,” Appl. Opt. 45(19), 4631–4637 (2006). [CrossRef] [PubMed]
- H. Navarro, R. Martínez-Cuenca, A. Molina-Martín, M. Martínez-Corral, G. Saavedra, and B. Javidi, “Method to remedy image degradations due to facet braiding in 3D integral imaging monitors,” J. Display Technol. 6(10), 404–411 (2010). [CrossRef]
- J. S. Jang and B. Javidi, “Three-dimensional synthetic aperture integral imaging,” Opt. Lett. 27(13), 1144–1146 (2002). [CrossRef]
- J. Arai, H. Kawai, and F. Okano, “Microlens arrays for integral imaging system,” Appl. Opt. 45(36), 9066–9078 (2006). [CrossRef] [PubMed]

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