Effect of Pickup Position Uncertainty in Three-Dimensional Computational Integral Imaging

  • Mehdi DaneshPanah
  • Behnoosh Tavakoli
  • Bahram Javidi
  • Edward A. Watson


This chapter will review the relevant investigations analyzing the performance of Integral Imaging (II) technique under pickup position uncertainty. Theoretical and simulation results for the sensitivity of Synthetic Aperture Integral Imaging (SAII) to the accuracy of pickup position measurements are provided. SAII is a passive three-dimensional, multi-view imaging technique that, unlike digital holography, operates under incoherent or natural illumination. In practical SAII applications, there is always an uncertainty associated with the position at which each sensor captures the elemental image. In this chapter, we theoretically analyze and quantify image degradation due to measurements’ uncertainty in terms of Mean Square Error (MSE) metric. Experimental results are also presented that support the theory. We show that in SAII, with a given uncertainty in the sensor locations, the high spatial frequency content of the 3-D reconstructed images are most degraded. We also show an inverse relationship between the reconstruction distance and degradation metric.


Mean Square Error Full Width Half Maximum Average Mean Square Error Elemental Image Reconstruction Plane 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. [1]
    Benton S A (2001) Selected Papers on Three-Dimensional Displays. SPIE Optical Engineering Press, Bellingham, WAGoogle Scholar
  2. [2]
    Javidi B, Okano F (2002) Three Dimensional Television, Video, and Display Technologies. Springer, BerlinGoogle Scholar
  3. [3]
    Okoshi T (1976) Three-Dimensional Imaging Technique. Academic Press, New YorkGoogle Scholar
  4. [4]
    Javidi B, Hong S H, Matoba O (2006) Multi dimensional optical sensors and imaging systems. Appl. Opt. 45:2986–2994ADSCrossRefGoogle Scholar
  5. [5]
    Levoy M (2006) Light fields and computational imaging. IEEE Comput. 39(8):46–55CrossRefGoogle Scholar
  6. [6]
    Lippmann M G (1908) Epreuves reversibles donnant la sensation durelief. J. Phys. 7:821–825Google Scholar
  7. [7]
    Dudnikov Y A (1974) On the design of a scheme for producing integral photographs by a combination method. Sov. J. Opt. Technol. 41:426–429Google Scholar
  8. [8]
    Ives H E (1931) Optical properties of a Lippmann lenticuled sheet. J. Opt. Soc. Am. 21:171–176ADSCrossRefGoogle Scholar
  9. [9]
    Sokolov P (1911) Autostereoscpy and Integral Photography by Professor Lippmann’s Method. Moscow State Univ. Press, Moscow, RussiaGoogle Scholar
  10. [10]
    Okano F, Hoshino H, Arai J et al (1997) Real time pickup method for a three dimensional image based on integral photography. Appl. Opt. 36:1598–1603ADSCrossRefGoogle Scholar
  11. [11]
    Stern A, Javidi B (2006) Three-dimensional image sensing, visualization, and processing using integral imaging. Proc. IEEE 94:591–607CrossRefGoogle Scholar
  12. [12]
    Wilburn B, Joshi N, Vaish V, Barth A et al (2005) High performance imaging using large camera arrays. Proc. ACM 24:765–776CrossRefGoogle Scholar
  13. [13]
    Jang J S, Javidi B (2002) Three-dimensional synthetic aperture integral imaging. Opt. Lett. 27:1144–1146ADSCrossRefGoogle Scholar
  14. [14]
    Burckhardt B (1968) Optimum parameters and resolution limitation of integral photography. J. Opt. Soc. Am. 58:71–76ADSCrossRefGoogle Scholar
  15. [15]
    Hoshino H, Okano F, Isono H et al (1998) Analysis of resolution limitation of integral photography. J. Opt. Soc. Am. A 15:2059–2065ADSCrossRefGoogle Scholar
  16. [16]
    Wilburn B, Joshi N, Vaish V et al (2005) High performance imaging using large camera arrays. ACM Trans. Graph. 24(3): 765–776CrossRefGoogle Scholar
  17. [17]
    Hong S H, Jang J S, Javidi B (2004) Three-dimensional volumetric object reconstruction using computational integral imaging. Opt. Express 12:483–491ADSCrossRefGoogle Scholar
  18. [18]
    Stern A, Javidi B (2003) 3-D computational synthetic aperture integral imaging (COMPSAII). Opt. Express 11:2446–2451ADSCrossRefGoogle Scholar
  19. [19]
    Igarishi Y, Murata H, Ueda M (1978) 3-D display system using a computer-generated integral photograph,. Jpn. J. Appl. Phys. 17:1683–1684ADSCrossRefGoogle Scholar
  20. [20]
    Erdmann L, Gabriel K J (2001) High resolution digital photography by use of a scanning microlens array. Appl. Opt. 40:5592–5599ADSCrossRefGoogle Scholar
  21. [21]
    Kishk S, Javidi B (2003) Improved resolution 3-D object sensing and recognition using time multiplexed computational integral imaging. Opt. Express 11:3528–3541ADSCrossRefGoogle Scholar
  22. [22]
    Martínez-Cuenca R, Saavedra G, Martinez-Corral M et al (2004) Enhanced depth of field integral imaging with sensor resolution constraints. Opt. Express 12:5237–5242ADSCrossRefGoogle Scholar
  23. [23]
    Jang J S, Javidi B (2002) Improved viewing resolution of three-dimensional integral imaging by use of nonstationary micro-optics. Opt. Lett. 27:324–326ADSCrossRefGoogle Scholar
  24. [24]
    Hong J, Park J H, Jung S et al (2004) Depth-enhanced integral imaging by use of optical path control. Opt. Lett. 29:1790–1792.ADSCrossRefGoogle Scholar
  25. [25]
    Min S W, Kim J, Lee B (2004) Wide-viewing projection-type integral imaging system with an embossed screen. Opt. Lett. 29:2420–2422ADSCrossRefGoogle Scholar
  26. [26]
    Martínez-Corral M, Javidi B, Martínez-Cuenca R et al (2004) Integral imaging with improved depth of field by use of amplitude modulated microlens array. Appl. Opt. 43:5806–5813ADSCrossRefGoogle Scholar
  27. [27]
    Hwang Y S, Hong S H, Javidi B (2007) Free view 3-D visualization of occluded objects by using computational synthetic aperture integral imaging. J. Display Technol 3:64–70ADSCrossRefGoogle Scholar
  28. [28]
    Yeom S, Javidi B, Watson E (2005) Photon counting passive 3-D image sensing for automatic target recognition. Opt. Express 13:9310–9330ADSCrossRefGoogle Scholar
  29. [29]
    Frauel Y, Javidi B (2002) Digital three-dimensional image correlation by use of computer-reconstructed integral imaging. Appl. Opt. 41:5488–5496ADSCrossRefGoogle Scholar
  30. [30]
    Tavakoli B, Danesh Panah M, Javidi B et al (2007) Performance of 3-D integral imaging with position uncertainty. Opt. Express 15:11889–11902ADSCrossRefGoogle Scholar
  31. [31]
    Mukhopadhyay N (2000) Probability and Statistical Inference. Marcel Dekker, Inc. New YorkMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Mehdi DaneshPanah
  • Behnoosh Tavakoli
  • Bahram Javidi
    • 1
  • Edward A. Watson
  1. 1.Department of Electrical and Computer EngineeringU-2157 University of ConnecticutStorrsUSA

Personalised recommendations