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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 22 — Oct. 24, 2011
  • pp: 21485–21507

Exploiting sparsity in time-of-flight range acquisition using a single time-resolved sensor

Ahmed Kirmani, Andrea Colaço, Franco N. C. Wong, and Vivek K. Goyal  »View Author Affiliations

Optics Express, Vol. 19, Issue 22, pp. 21485-21507 (2011)

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Range acquisition systems such as light detection and ranging (LIDAR) and time-of-flight (TOF) cameras operate by measuring the time difference of arrival between a transmitted pulse and the scene reflection. We introduce the design of a range acquisition system for acquiring depth maps of piecewise-planar scenes with high spatial resolution using a single, omnidirectional, time-resolved photodetector and no scanning components. In our experiment, we reconstructed 64 × 64-pixel depth maps of scenes comprising two to four planar shapes using only 205 spatially-patterned, femtosecond illuminations of the scene. The reconstruction uses parametric signal modeling to recover a set of depths present in the scene. Then, a convex optimization that exploits sparsity of the Laplacian of the depth map of a typical scene determines correspondences between spatial positions and depths. In contrast with 2D laser scanning used in LIDAR systems and low-resolution 2D sensor arrays used in TOF cameras, our experiment demonstrates that it is possible to build a non-scanning range acquisition system with high spatial resolution using only a standard, low-cost photodetector and a spatial light modulator.

© 2011 OSA

OCIS Codes
(110.6880) Imaging systems : Three-dimensional image acquisition
(110.1758) Imaging systems : Computational imaging

ToC Category:
Imaging Systems

Original Manuscript: August 19, 2011
Revised Manuscript: October 2, 2011
Manuscript Accepted: October 3, 2011
Published: October 17, 2011

Ahmed Kirmani, Andrea Colaço, Franco N. C. Wong, and Vivek K. Goyal, "Exploiting sparsity in time-of-flight range acquisition using a single time-resolved sensor," Opt. Express 19, 21485-21507 (2011)

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  1. K. Carlsson, P. E. Danielsson, R. Lenz, A. Liljeborg, L. Majlöf, and N. Åslund, “Three-dimensional microscopy using a confocal laser scanning microscope,” Opt. Lett. 10, 53–55 (1985). [CrossRef] [PubMed]
  2. J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3d microscopy and gene expression studies,” Science 296, 541–545 (2002). [CrossRef] [PubMed]
  3. A. Wehr and U. Lohr, “Airborne laser scanning—an introduction and overview,” ISPRS J. Photogramm. Remote Sens. 54, 68–82 (1999). [CrossRef]
  4. D. A. Forsyth and J. Ponce, Computer Vision: A Modern Approach (Prentice-Hall, 2002).
  5. S. M. Seitz, B. Curless, J. Diebel, D. Scharstein, and R. Szeliski, “A comparison and evaluation of multi-view stereo reconstruction algorithms,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, (2006), pp. 519–528.
  6. S. Hussmann, T. Ringbeck, and B. Hagebeuker, “A performance review of 3D TOF vision systems in comparison to stereo vision systems,” in Stereo Vision, A. Bhatti, ed. (InTech, 2008), pp. 103–120.
  7. E. Stoykova, A. A. Alatan, P. Benzie, N. Grammalidis, S. Malassiotis, J. Ostermann, S. Piekh, V. Sainov, C. Theobalt, T. Thevar, and X. Zabulis, “3-D time-varying scene capture technologies—A survey,” IEEE Trans. Circ. Syst. Video Tech. 17, 1568–1586 (2007). [CrossRef]
  8. D. Scharstein and R. Szeliski, “A taxonomy and evaluation of dense two-frame stereo correspondence algorithms,” Int. J. Comput. Vis. 47, 7–42 (2002). [CrossRef]
  9. B. Schwarz, “LIDAR: mapping the world in 3D,” Nat. Photonics 4, 429–430 (2010). [CrossRef]
  10. S. B. Gokturk, H. Yalcin, and C. Bamji, “A time-of-flight depth sensor — system description, issues and solutions,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition Workshops, (2004), p. 35.
  11. S. Foix, G. Alenyà, and C. Torras, “Lock-in time-of-flight (ToF) cameras: a survey,” IEEE Sens. J.11, 1917–1926 (2011). [CrossRef]
  12. A. P. Cracknell and L. W. B. Hayes, Introduction to Remote Sensing (Taylor & Francis, 1991).
  13. F. Blais, “Review of 20 years of range sensor development,” J. Electron. Imaging 13, 231–240 (2004). [CrossRef]
  14. R. Lamb and G. Buller, “Single-pixel imaging using 3d scanning time-of-flight photon counting,” SPIE News-room (2010). . [CrossRef]
  15. A. Medina, F. Gayá, and F. del Pozo, “Compact laser radar and three-dimensional camera,” J. Opt. Soc. Am. A 23, 800–805 (2006). [CrossRef]
  16. S. Schuon, C. Theobalt, J. Davis, and S. Thrun, “High-quality scanning using time-of-flight depth superresolution,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition Workshops, (2008). [CrossRef]
  17. M. Vetterli, P. Marziliano, and T. Blu, “Sampling signals with finite rate of innovation,” IEEE Trans. Signal Process. 50, 1417–1428 (2002). [CrossRef]
  18. T. Blu, P.-L. Dragotti, M. Vetterli, P. Marziliano, and L. Coulot, “Sparse sampling of signal innovations,” IEEE Signal Process. Mag. 25, 31–40 (2008). [CrossRef]
  19. M. Sarkis and K. Diepold, “Depth map compression via compressed sensing,” in Proceedings of IEEE International Conference on Image Processing, (2009), pp. 737–740.
  20. I. Tošić, B. A. Olshausen, and B. J. Culpepper, “Learning sparse representations of depth,” IEEE J. Sel. Top. Signal Process. 5, 941–952 (2011). [CrossRef]
  21. E. J. Candès and T. Tao, “Near-optimal signal recovery from random projections: Universal encoding strategies?” IEEE Trans. Inf. Theory 52, 5406–5425 (2006). [CrossRef]
  22. D. L. Donoho, “Compressed sensing,” IEEE Trans. Inform. Theory52, 1289–1306 (2006). [CrossRef]
  23. M. B. Wakin, J. N. Laska, M. F. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. F. Kelly, and R. G. Baraniuk, “An architecture for compressive imaging,” in Proceedings of IEEE International Conference on Image Processing, (2006), pp. 1273–1276.
  24. M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag.25, 83–91 (2008). [CrossRef]
  25. M. Elad, Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing (Springer, 2010). [PubMed]
  26. G. Howland, P. Zerom, R. W. Boyd, and J. C. Howell, “Compressive sensing LIDAR for 3D imaging,” in CLEO:2011 - Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CMG3.
  27. P. L. Dragotti, M. Vetterli, and T. Blu, “Sampling moments and reconstructing signals of finite rate of innovation: Shannon meets Strang-Fix,” IEEE Trans. Signal Process.55, 1741–1757 (2007). [CrossRef]
  28. A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing, 3rd ed. (Prentice-Hall, 2009).
  29. M. Grant and S. Boyd, “CVX: Matlab software for disciplined convex programming, version 1.21,” http://cvxr.com/cvx .
  30. M. Grant and S. Boyd, “Graph implementations for nonsmooth convex programs,” in Recent Advances in Learning and Control, V. Blondel, S. Boyd, and H. Kimura, eds. (Springer-Verlag Limited, 2008), pp. 95–110. [CrossRef]
  31. G. C. M. R. de Prony, “Essai éxperimental et analytique: Sur les lois de la dilatabilité de fluides élastique et sur celles de la force expansive de la vapeur de l’alkool, à différentes températures,” J. de l’ École Polytechnique 1, 24–76 (1795).

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