## Tilted elemental image array generation method for moiré-reduced computer generated integral imaging display |

Optics Express, Vol. 21, Issue 17, pp. 19816-19824 (2013)

http://dx.doi.org/10.1364/OE.21.019816

Acrobat PDF (1609 KB)

### Abstract

In this paper, we propose a tilted elemental image array generation method for computer generated integral imaging display with reduced moiré patterns. The pixels of the tilted elemental image array are divided into border pixels and effective pixels. According to the optimal tilted angle, the effective pixels are arranged with uniform arrangement. Also, a pixel mapping method is proposed. Appropriate experiments are carried out and the experimental results show that not only the color moiré patterns are reduced remarkably, but also the resolution of the reconstructed 3D images are improved through the proposed method.

© 2013 OSA

## 1. Introduction

1. B. Lee, S. Y. Jung, S. W. Min, and J. H. Park, “Three-dimensional display by use of integral photography with dynamically variable image planes,” Opt. Lett. **26**(19), 1481–1482 (2001). [CrossRef] [PubMed]

6. X. Xiao, B. Javidi, M. Martinez-Corral, and A. Stern, “Advances in three-dimensional integral imaging: sensing, display, and applications [Invited],” Appl. Opt. **52**(4), 546–560 (2013). [CrossRef] [PubMed]

7. C. C. Ji, H. Deng, and Q. H. Wang, “Pixel extraction based integral imaging with controllable viewing direction,” J. Opt. **14**(9), 095401 (2012). [CrossRef]

9. S. H. Jiao, X. G. Wang, M. C. Zhou, W. M. Li, T. Hong, D. Nam, J. H. Lee, E. H. Wu, H. T. Wang, and J. Y. Kim, “Multiple ray cluster rendering for interactive integral imaging system,” Opt. Express **21**(8), 10070–10086 (2013). [CrossRef] [PubMed]

10. G. Baasantseren, J. H. Park, K. C. Kwon, and N. Kim, “Viewing angle enhanced integral imaging display using two elemental image masks,” Opt. Express **17**(16), 14405–14417 (2009). [CrossRef] [PubMed]

11. J. H. Jung, S. G. Park, Y. Kim, and B. Lee, “Integral imaging using a color filter pinhole array on a display panel,” Opt. Express **20**(17), 18744–18756 (2012). [CrossRef] [PubMed]

12. I. Amidror, R. D. Hersch, and V. Ostromoukhov, “Spectral analysis and minimization of moiré patterns in color separation,” J. Electron. Imaging **3**(3), 295–317 (1994). [CrossRef]

15. V. Saveljev and S. K. Kim, “Simulation of moiré effect in 3D displays,” J. Opt. Soc. Korea **14**(4), 310–315 (2010). [CrossRef]

16. M. Okui, M. Kobayashi, J. Arai, and F. Okano, “Moire fringe reduction by optical filters in integral three-dimensional imaging on a color flat-panel display,” Appl. Opt. **44**(21), 4475–4483 (2005). [CrossRef] [PubMed]

17. Y. Kim, G. Park, S. W. Cho, J. H. Jung, B. Lee, Y. Choi, and M. G. Lee, “Integral imaging with reduced color moiré pattern by using a slanted lens array,” Proc. SPIE **6803**, 68030L (2008). [CrossRef]

18. K. Yanaka and K. Uehira, “Extended fractional view integral imaging using slanted fly's eye lens,” in *Proceedings of SID Symposium Digest of Technical Papers*, Wiley (Academic, 2011), pp. 1124–1127. [CrossRef]

19. Y. Kim, G. Park, J. H. Jung, J. Kim, and B. Lee, “Color moiré pattern simulation and analysis in three-dimensional integral imaging for finding the moiré-reduced tilted angle of a lens array,” Appl. Opt. **48**(11), 2178–2187 (2009). [CrossRef] [PubMed]

20. Y. Igarashi, H. Murata, and M. Ueda, “3D display system using a computer generated integral photography,” Jpn. J. Appl. Phys. **17**(9), 1683–1684 (1978). [CrossRef]

23. S. W. Min, J. Kim, and B. Lee, “New characteristic equation of three-dimensional integral imaging system and its applications,” Jpn. J. Appl. Phys. **44**(2), L71–L74 (2005). [CrossRef]

24. S. W. Min, K. S. Park, B. Lee, Y. Cho, and M. Hahn, “Enhanced image mapping algorithm for computer-generated integral imaging system,” Jpn. J. Appl. Phys. **45**(28), L744–L747 (2006). [CrossRef]

18. K. Yanaka and K. Uehira, “Extended fractional view integral imaging using slanted fly's eye lens,” in *Proceedings of SID Symposium Digest of Technical Papers*, Wiley (Academic, 2011), pp. 1124–1127. [CrossRef]

28. D. H. Shin and H. Yoo, “Image quality enhancement in 3D computational integral imaging by use of interpolation methods,” Opt. Express **15**(19), 12039–12049 (2007). [CrossRef] [PubMed]

29. H. Yoo, “Axially moving a lenslet array for high-resolution 3D images in computational integral imaging,” Opt. Express **21**(7), 8873–8878 (2013). [CrossRef] [PubMed]

30. W. Li, H. Wang, M. Zhou, S. Wang, S. Jiao, X. Mei, T. Hong, H. Lee, and J. Kim, “Principal observation ray calibration for tiled-lens-array integral imaging display,” in *Proceedings of IEEE Conference on Computer Vision and Pattern Recognition* (Oregon Convention Center, Portland, Oregon, 2013), pp. 1019–1026.

## 2. Principle of the proposed method

### 2.1 Pixel classification in tilted EIA

### 2.2 Generation method of tilted EIA

*φ*has a different effective pixel arrangement. Figure 2(b) shows that each EI with a tilted angle

*θ*has a uniform effective pixel arrangement. We prefer to adopt the tilted angle

*θ*because the titled EIs with the uniform arrangement can be calculated by the same algorithm. In other words, the tilted EIs can be generated more easily by choosing a more suitable tilted angle.

*p*and the micro-lens pitch

*d*into consideration, we combine the color moiré pattern reducing and the effective pixel arrangement uniformity to find out an optimal tilted angle. Assume that

*n*and

*m*represent the pixel numbers within two vertices of the micro-lens in the horizontal direction and vertical direction respectively as shown in Fig. 3. Both

*n*and

*m*are integers that range from 1 to

*d*/

*p*. The distance of the two LCD pixels which are under the two vertices

*r*can be expressed as:We define mismatch error ratio

_{nm}*f*as:where (

_{nm}*θ*,

_{1}*θ*) is the angular range of the moiré pattern reducing. The optimal tilted angle

_{2}*θ*can be calculated by the following relationships:andwhere the

*Findmin*function gives

*A*(

*n′*,

*m′*) the subscripts of the minimum non-negative entry of a matrix. When the values of

*n′*and

*m′*are given,

*θ*can be determined and then the effective pixel arrangement of a tilted EI is also confirmed.

*S*and blue boxes

_{i,j}*G*represent source pixels and target pixels respectively.

_{h,v}*i*,

*j*,

*h*and

*v*are equal to 1, 2, 3, ... . The centers of

*S*

_{1,1}and

*G*

_{1,1}are both on the origin of the coordinate. The input image is rotated by

*θ*around the origin

*o*. We assume the pixel size is unit length. Therefore, the coordinate value of

*G*’s center is (

_{h,v}*h*-1,

*v*-1). Since the direction of rotation is clockwise, transformation formula is given as:

*A*(

*x*

_{1},

*y*

_{1}),

*B*(

*x*

_{2},

*y*

_{2}),

*C*(

*x*

_{3},

*y*

_{3}) and

*D*(

*x*

_{4},

*y*

_{4}) of

*S*are calculated as: If the center of

_{i,j}*G*is inside of

_{h,v}*S*, we set up one to one mapping correspondence between

_{i,j}*G*and

_{h,v}*S*. The relationship between

_{i,j}*G*and

_{h,v}*S*is represented as

_{i,j}*G*=

_{h,v}*S*. We use the method of linear programming and substitute the coordinate value of

_{i,j}*G*’s center,

_{h,v}*A*(

*x*

_{1},

*y*

_{1}),

*B*(

*x*

_{2},

*y*

_{2}),

*C*(

*x*

_{3},

*y*

_{3}), and

*D*(

*x*

_{4},

*y*

_{4}), then the sufficient condition of

*G*=

_{h,v}*S*is given by

_{i,j}## 3. Experimental results and discussion

31. H. Deng, Q. H. Wang, D. H. Li, and F. N. Wang, “Realization of undistorted and orthoscopic integral imaging without black zone in real and virtual fields,” J. Disp. Technol. **7**(5), 255–258 (2011). [CrossRef]

32. Y. Xu, X. R. Wang, Y. Sun, and J. Q. Zhang, “Homogeneous light field model for interactive control of viewing parameters of integral imaging displays,” Opt. Express **20**(13), 14137–14151 (2012). [CrossRef] [PubMed]

*d*= 1.25mm and

*p*= 0.096mm from Table 1. The moiré-reduced angle range, which is measured by software testing and naked-eye observation, is (15°, 25°). According to Eqs. (1)-(4) and the value range, we obtain

*n′*= 12,

*m′*= 5,

*θ*= 22.62°. And then the effective pixels’ arrangement of a tilted EI is also confirmed.

## 4. Conclusion

## Acknowledgments

## References and links

1. | B. Lee, S. Y. Jung, S. W. Min, and J. H. Park, “Three-dimensional display by use of integral photography with dynamically variable image planes,” Opt. Lett. |

2. | A. Stern and B. Javidi, “Three dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE |

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

4. | H. Yoo, “Artifact analysis and image enhancement in three-dimensional computational integral imaging using smooth windowing technique,” Opt. Lett. |

5. | Y. Liu, H. Ren, S. Xu, Y. Chen, L. Rao, T. Ishinabe, and S. T. Wu, “Adaptive focus integral image system design based on fast-response liquid crystal microlens,” J. Disp. Technol. |

6. | X. Xiao, B. Javidi, M. Martinez-Corral, and A. Stern, “Advances in three-dimensional integral imaging: sensing, display, and applications [Invited],” Appl. Opt. |

7. | C. C. Ji, H. Deng, and Q. H. Wang, “Pixel extraction based integral imaging with controllable viewing direction,” J. Opt. |

8. | K. C. Kwon, C. Park, M. U. Erdenebat, J. S. Jeong, J. H. Choi, N. Kim, J. H. Park, Y. T. Lim, and K. H. Yoo, “High speed image space parallel processing for computer-generated integral imaging system,” Opt. Express |

9. | S. H. Jiao, X. G. Wang, M. C. Zhou, W. M. Li, T. Hong, D. Nam, J. H. Lee, E. H. Wu, H. T. Wang, and J. Y. Kim, “Multiple ray cluster rendering for interactive integral imaging system,” Opt. Express |

10. | G. Baasantseren, J. H. Park, K. C. Kwon, and N. Kim, “Viewing angle enhanced integral imaging display using two elemental image masks,” Opt. Express |

11. | J. H. Jung, S. G. Park, Y. Kim, and B. Lee, “Integral imaging using a color filter pinhole array on a display panel,” Opt. Express |

12. | I. Amidror, R. D. Hersch, and V. Ostromoukhov, “Spectral analysis and minimization of moiré patterns in color separation,” J. Electron. Imaging |

13. | R. Börner, “Four autostereoscopic monitors on the level of industrial prototypes,” Displays |

14. | V. Saveljev, J. Y. Son, B. Javidi, S. K. Kim, and D. S. Kim, “Moiré minimization condition in three-dimensional image displays,” J. Disp. Technol. |

15. | V. Saveljev and S. K. Kim, “Simulation of moiré effect in 3D displays,” J. Opt. Soc. Korea |

16. | M. Okui, M. Kobayashi, J. Arai, and F. Okano, “Moire fringe reduction by optical filters in integral three-dimensional imaging on a color flat-panel display,” Appl. Opt. |

17. | Y. Kim, G. Park, S. W. Cho, J. H. Jung, B. Lee, Y. Choi, and M. G. Lee, “Integral imaging with reduced color moiré pattern by using a slanted lens array,” Proc. SPIE |

18. | K. Yanaka and K. Uehira, “Extended fractional view integral imaging using slanted fly's eye lens,” in |

19. | Y. Kim, G. Park, J. H. Jung, J. Kim, and B. Lee, “Color moiré pattern simulation and analysis in three-dimensional integral imaging for finding the moiré-reduced tilted angle of a lens array,” Appl. Opt. |

20. | Y. Igarashi, H. Murata, and M. Ueda, “3D display system using a computer generated integral photography,” Jpn. J. Appl. Phys. |

21. | M. Halle, “Multiple viewpoint rendering,” SIGGRAPH ’98, |

22. | R. Yang, X. Huang, and S. Chen, “Efficient rendering of integral images,” SIGGRAPH’05, |

23. | S. W. Min, J. Kim, and B. Lee, “New characteristic equation of three-dimensional integral imaging system and its applications,” Jpn. J. Appl. Phys. |

24. | S. W. Min, K. S. Park, B. Lee, Y. Cho, and M. Hahn, “Enhanced image mapping algorithm for computer-generated integral imaging system,” Jpn. J. Appl. Phys. |

25. | B. N. R. Lee, Y. Cho, K. S. Park, S. W. Min, J. S. Lim, M. C. Whang, and K. R. Park, “Design and implementation of a fast integral image rendering method,” International Conference on Electronic Commerce 2006, 135–140 (2006). [CrossRef] |

26. | K. S. Park, S. W. Min, and Y. Cho, “Viewpoint vector rendering for efficient elemental image generation,” IEICE – Transactions on Information and Systems E |

27. | S. C. Kang, Z. Z. Stroll, and S. C. Miller, “Small angle image rotation using block transfers,” U.S. patent 4829452 (May 9, 1989). |

28. | D. H. Shin and H. Yoo, “Image quality enhancement in 3D computational integral imaging by use of interpolation methods,” Opt. Express |

29. | H. Yoo, “Axially moving a lenslet array for high-resolution 3D images in computational integral imaging,” Opt. Express |

30. | W. Li, H. Wang, M. Zhou, S. Wang, S. Jiao, X. Mei, T. Hong, H. Lee, and J. Kim, “Principal observation ray calibration for tiled-lens-array integral imaging display,” in |

31. | H. Deng, Q. H. Wang, D. H. Li, and F. N. Wang, “Realization of undistorted and orthoscopic integral imaging without black zone in real and virtual fields,” J. Disp. Technol. |

32. | Y. Xu, X. R. Wang, Y. Sun, and J. Q. Zhang, “Homogeneous light field model for interactive control of viewing parameters of integral imaging displays,” Opt. Express |

**OCIS Codes**

(100.0100) Image processing : Image processing

(100.3010) Image processing : Image reconstruction techniques

(100.6890) Image processing : Three-dimensional image processing

**ToC Category:**

Image Processing

**History**

Original Manuscript: June 19, 2013

Revised Manuscript: August 10, 2013

Manuscript Accepted: August 10, 2013

Published: August 15, 2013

**Citation**

Chao-Chao Ji, Cheng-Gao Luo, Huan Deng, Da-Hai Li, and Qiong-Hua Wang, "Tilted elemental image array generation method for moiré-reduced computer generated integral imaging display," Opt. Express **21**, 19816-19824 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-17-19816

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### References

- B. Lee, S. Y. Jung, S. W. Min, and J. H. Park, “Three-dimensional display by use of integral photography with dynamically variable image planes,” Opt. Lett.26(19), 1481–1482 (2001). [CrossRef] [PubMed]
- A. Stern and B. Javidi, “Three dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE94(3), 591–607 (2006). [CrossRef]
- 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]
- H. Yoo, “Artifact analysis and image enhancement in three-dimensional computational integral imaging using smooth windowing technique,” Opt. Lett.36(11), 2107–2109 (2011). [CrossRef] [PubMed]
- Y. Liu, H. Ren, S. Xu, Y. Chen, L. Rao, T. Ishinabe, and S. T. Wu, “Adaptive focus integral image system design based on fast-response liquid crystal microlens,” J. Disp. Technol.7(12), 674–678 (2011). [CrossRef]
- X. Xiao, B. Javidi, M. Martinez-Corral, and A. Stern, “Advances in three-dimensional integral imaging: sensing, display, and applications [Invited],” Appl. Opt.52(4), 546–560 (2013). [CrossRef] [PubMed]
- C. C. Ji, H. Deng, and Q. H. Wang, “Pixel extraction based integral imaging with controllable viewing direction,” J. Opt.14(9), 095401 (2012). [CrossRef]
- K. C. Kwon, C. Park, M. U. Erdenebat, J. S. Jeong, J. H. Choi, N. Kim, J. H. Park, Y. T. Lim, and K. H. Yoo, “High speed image space parallel processing for computer-generated integral imaging system,” Opt. Express20(2), 732–740 (2012). [CrossRef] [PubMed]
- S. H. Jiao, X. G. Wang, M. C. Zhou, W. M. Li, T. Hong, D. Nam, J. H. Lee, E. H. Wu, H. T. Wang, and J. Y. Kim, “Multiple ray cluster rendering for interactive integral imaging system,” Opt. Express21(8), 10070–10086 (2013). [CrossRef] [PubMed]
- G. Baasantseren, J. H. Park, K. C. Kwon, and N. Kim, “Viewing angle enhanced integral imaging display using two elemental image masks,” Opt. Express17(16), 14405–14417 (2009). [CrossRef] [PubMed]
- J. H. Jung, S. G. Park, Y. Kim, and B. Lee, “Integral imaging using a color filter pinhole array on a display panel,” Opt. Express20(17), 18744–18756 (2012). [CrossRef] [PubMed]
- I. Amidror, R. D. Hersch, and V. Ostromoukhov, “Spectral analysis and minimization of moiré patterns in color separation,” J. Electron. Imaging3(3), 295–317 (1994). [CrossRef]
- R. Börner, “Four autostereoscopic monitors on the level of industrial prototypes,” Displays20(2), 57–64 (1999). [CrossRef]
- V. Saveljev, J. Y. Son, B. Javidi, S. K. Kim, and D. S. Kim, “Moiré minimization condition in three-dimensional image displays,” J. Disp. Technol.1(2), 347–353 (2005). [CrossRef]
- V. Saveljev and S. K. Kim, “Simulation of moiré effect in 3D displays,” J. Opt. Soc. Korea14(4), 310–315 (2010). [CrossRef]
- M. Okui, M. Kobayashi, J. Arai, and F. Okano, “Moire fringe reduction by optical filters in integral three-dimensional imaging on a color flat-panel display,” Appl. Opt.44(21), 4475–4483 (2005). [CrossRef] [PubMed]
- Y. Kim, G. Park, S. W. Cho, J. H. Jung, B. Lee, Y. Choi, and M. G. Lee, “Integral imaging with reduced color moiré pattern by using a slanted lens array,” Proc. SPIE6803, 68030L (2008). [CrossRef]
- K. Yanaka and K. Uehira, “Extended fractional view integral imaging using slanted fly's eye lens,” in Proceedings of SID Symposium Digest of Technical Papers, Wiley (Academic, 2011), pp. 1124–1127. [CrossRef]
- Y. Kim, G. Park, J. H. Jung, J. Kim, and B. Lee, “Color moiré pattern simulation and analysis in three-dimensional integral imaging for finding the moiré-reduced tilted angle of a lens array,” Appl. Opt.48(11), 2178–2187 (2009). [CrossRef] [PubMed]
- Y. Igarashi, H. Murata, and M. Ueda, “3D display system using a computer generated integral photography,” Jpn. J. Appl. Phys.17(9), 1683–1684 (1978). [CrossRef]
- M. Halle, “Multiple viewpoint rendering,” SIGGRAPH ’98, Proceedings of the 25th Annual conference on Computer Graphics and Interactive Techniques, 243–254 (1998).
- R. Yang, X. Huang, and S. Chen, “Efficient rendering of integral images,” SIGGRAPH’05, Proceedings of 32nd Annual conference on Computer Graphics and Interactive Techniques,44 (2005).
- S. W. Min, J. Kim, and B. Lee, “New characteristic equation of three-dimensional integral imaging system and its applications,” Jpn. J. Appl. Phys.44(2), L71–L74 (2005). [CrossRef]
- S. W. Min, K. S. Park, B. Lee, Y. Cho, and M. Hahn, “Enhanced image mapping algorithm for computer-generated integral imaging system,” Jpn. J. Appl. Phys.45(28), L744–L747 (2006). [CrossRef]
- B. N. R. Lee, Y. Cho, K. S. Park, S. W. Min, J. S. Lim, M. C. Whang, and K. R. Park, “Design and implementation of a fast integral image rendering method,” International Conference on Electronic Commerce 2006, 135–140 (2006). [CrossRef]
- K. S. Park, S. W. Min, and Y. Cho, “Viewpoint vector rendering for efficient elemental image generation,” IEICE – Transactions on Information and Systems E90-D, 233–241 (2007).
- S. C. Kang, Z. Z. Stroll, and S. C. Miller, “Small angle image rotation using block transfers,” U.S. patent 4829452 (May 9, 1989).
- D. H. Shin and H. Yoo, “Image quality enhancement in 3D computational integral imaging by use of interpolation methods,” Opt. Express15(19), 12039–12049 (2007). [CrossRef] [PubMed]
- H. Yoo, “Axially moving a lenslet array for high-resolution 3D images in computational integral imaging,” Opt. Express21(7), 8873–8878 (2013). [CrossRef] [PubMed]
- W. Li, H. Wang, M. Zhou, S. Wang, S. Jiao, X. Mei, T. Hong, H. Lee, and J. Kim, “Principal observation ray calibration for tiled-lens-array integral imaging display,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (Oregon Convention Center, Portland, Oregon, 2013), pp. 1019–1026.
- H. Deng, Q. H. Wang, D. H. Li, and F. N. Wang, “Realization of undistorted and orthoscopic integral imaging without black zone in real and virtual fields,” J. Disp. Technol.7(5), 255–258 (2011). [CrossRef]
- Y. Xu, X. R. Wang, Y. Sun, and J. Q. Zhang, “Homogeneous light field model for interactive control of viewing parameters of integral imaging displays,” Opt. Express20(13), 14137–14151 (2012). [CrossRef] [PubMed]

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