A Geometric Perspective on Structured Light Coding

  • Mohit GuptaEmail author
  • Nikhil Nakhate
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11220)


We present a mathematical framework for analysis and design of high-performance structured light (SL) coding schemes. Using this framework, we design Hamiltonian SL coding, a novel family of SL coding schemes that can recover 3D shape with high precision, with only a small number (as few as three) of images. We establish structural similarity between popular discrete (binary) SL coding methods, and Hamiltonian coding, which is a continuous coding approach. Based on this similarity, and by leveraging design principles from several different SL coding families, we propose a general recipe for designing Hamiltonian coding patterns with specific desirable properties, such as patterns with high spatial frequencies for dealing with global illumination. We perform several experiments to evaluate the proposed approach, and demonstrate that Hamiltonian coding based SL approaches outperform existing methods in challenging scenarios, including scenes with dark albedos, strong ambient light, and interreflections.



This research was supported in parts by the ONR grant number N00014-16-1-2995, and the DARPA REVEAL program.

Supplementary material

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Supplementary material 1 (pdf 4047 KB)


  1. 1.
    Boyer, K.L., Kak, A.C.: Color-encoded structured light for rapid active ranging. IEEE Trans. Pattern Anal. Mach. Intell. PAMI-9(1), 14–28 (1987)CrossRefGoogle Scholar
  2. 2.
    Carrihill, B., Hummel, R.: Experiments with the intensity ratio depth sensor. Comput. Vis. Gr. Image Process. 32(3), 337–358 (1985)CrossRefGoogle Scholar
  3. 3.
    Caspi, D., Kiryati, N., Shamir, J.: Range imaging with adaptive color structured light. IEEE Trans. Pattern Anal. Mach. Intell. 20(5), 470–480 (1998)CrossRefGoogle Scholar
  4. 4.
    Chang, G.J., Eu, S.P., Yeh, C.H.: On the (n, t)-Antipodal Gray Codes. Theoretical Comput. Sci. 374(1–3) (2007)Google Scholar
  5. 5.
    Chazan, G., Kiryati, N.: Pyramidal intensity ratio depth sensor. Technical Report No. 121, Department of Electrical Engineering, Technion, Haifa (1995)Google Scholar
  6. 6.
    Chen, T., Seidel, H.P., Lensch, H.: Modulated phase-shifting for 3D scanning. In: Proceedings of IEEE CVPR (2008)Google Scholar
  7. 7.
    Chen, T., Lensch, H.P.A., Fuchs, C., Peter Seidel, H.: Polarization and phase-shifting for 3D scanning of translucent objects. In: IEEE Proceedings of CVPR (2007)Google Scholar
  8. 8.
    Couture, V., Martin, N., Roy, S.: Unstructured light scanning to overcome interreflections. In: Proceedings of IEEE ICCV (2011)Google Scholar
  9. 9.
    Curless, B., Levoy, M.: Better optical triangulation through spacetime analysis. In: Proceedings of IEEE International Conference on Computer Vision (1995)Google Scholar
  10. 10.
    Gotsman, C., Lindenbaum, M.: On the metric properties of discrete space-filling curves. IEEE TIP 5(5) (1996)CrossRefGoogle Scholar
  11. 11.
    Gray, F.: Pulse code communication. US Patent 2,632,058 (1953)Google Scholar
  12. 12.
    Gupta, M., Yin, Q., Nayar, S.K.: Structured light in sunlight. In: IEEE International Conference on Computer Vision (2013)Google Scholar
  13. 13.
    Gupta, M., Agrawal, A., Veeraraghavan, A., Narasimhan, S.G.: A practical approach to 3d scanning in the presence of interreflections, subsurface scattering and defocus. Int. J. Comput. Vis. 102(1), 33–55 (2013)CrossRefGoogle Scholar
  14. 14.
    Gupta, M., Nayar, S.K.: Micro phase shifting. In: Proceedings of IEEE CVPR (2012)Google Scholar
  15. 15.
    Gupta, M., Velten, A., Nayar, S., Breitbach, E.: What are optimal coding functions for time-of-flight imaging? ACM Trans. Gr. 37(2) (2018)CrossRefGoogle Scholar
  16. 16.
    Gushov, V.I., Solodkin, Y.N.: Automatic processing of fringe patterns in integer interferometers. Op. Lasers Eng. 14, 311–324 (1991)CrossRefGoogle Scholar
  17. 17.
    Hasinoff, S.W., Durand, F., Freeman, W.T.: Noise-optimal capture for high dynamic range photography. In: Proceedings of IEEE CVPR (2010)Google Scholar
  18. 18.
    Horn, E., Kiryati, N.: Toward optimal structured light patterns. In: International Conference on Recent Advances in 3D Digital Imaging and Modeling (1997)Google Scholar
  19. 19.
    Huang, P.S., Zhang, S., Chiang, F.P.: Trapezoidal phase-shifting method for threedimensional shape measurement. Op. Eng. 44(12), 123601 (2005)CrossRefGoogle Scholar
  20. 20.
    Inokuchi, S., Sato, K., Matsuda, F.: Range imaging system for 3-d object recognition. In: International Conference Pattern Recognition, pp. 806–808 (1984)Google Scholar
  21. 21.
    Kilian, C.E., Savage, C.D.: Antipodal Gray Codes. Discret. Math. 281(1–3), 221–236 (2004)Google Scholar
  22. 22.
    Kim, D., Ryu, M., Lee, S.: Antipodal gray codes for structured light. In: IEEE Internal Conference on Robotics and Automation (ICRA) (2008)Google Scholar
  23. 23.
    Koninckx, T., Van Gool, L.: Real-time range acquisition by adaptive structured light. IEEE Trans. Pattern Anal. Mach. Intell. 28(3), 432–445 (2006)CrossRefGoogle Scholar
  24. 24.
    Mirdehghan, P., Chen, W., Kutulakos, K.N.: Optimal structured light la carte. In: Proceedings of CVPR (2018)Google Scholar
  25. 25.
    Moreno, D., Son, K., Taubin, G.: Embedded phase shifting: Robust phase shifting with embedded signals. In: Proceedings of IEEE CVPR (2015)Google Scholar
  26. 26.
    Nayar, S.K., Krishnan, G., Grossberg, M.D., Raskar, R.: Fast separation of direct and global components of a scene using high frequency illumination. ACM Trans. Gr. 25(3), 935–944 (2006)CrossRefGoogle Scholar
  27. 27.
    O’Toole, M., Mather, J., Kutulakos, K.N.: 3d shape and indirect appearance by structured light transport. In: Proceedings of IEEE CVPR (2014)Google Scholar
  28. 28.
    Posdamer, J.L., Altschuler, M.D.: Surface measurement by space-encoded projected beam systems. Comput. Gr. Image Process. 18(1), 1–17 (1982)CrossRefGoogle Scholar
  29. 29.
    Proesmans, M., Van Gool, L.J., Oosterlinck, A.J.: Active acquisition of 3d shape for moving objects. In: Proceedings of the International Conference on Image Processing, vol. 3, pp. 647–650 (1996)Google Scholar
  30. 30.
    Proesmans, M., Van Gool, L.J., Oosterlinck, A.J.: One-shot active 3d shape acquisition. In: Proceedings of the International Conference on Pattern Recognition, vol. 3, pp. 336–340 (1996)Google Scholar
  31. 31.
    Ragland, E.A., Harry B. Schultheis, J.: Direction-sensitive binary code position control system. US Patent 2,823,345 (1953)Google Scholar
  32. 32.
    Rosman, G., Rus, D., Fisher, J.W.: Information-driven adaptive structured-light scanners. In: IEEE Conference on Computer Vision and Pattern Recognition (2016)Google Scholar
  33. 33.
    Sagawa, R., Ota, Y., Yagi, Y., Furukawa, R., Asada, N., Kawasaki, H.: Dense 3d reconstruction method using a single pattern for fast moving object. In: Proceedings of IEEE ICCV, pp. 1779–1786 (2009)Google Scholar
  34. 34.
    Salvi, J., Fernandez, S., Pribanic, T., Llado, X.: A state of the art in structured light patterns for surface profilometry. Pattern Recognit. 43(8), 2666–2680 (2010)CrossRefGoogle Scholar
  35. 35.
    Srinivasan, V., Liu, H.C., Halioua, M.: Automated phase-measuring profilometry: a phase mapping approach. Appl. Opt. 24(2), 185–188 (1985)CrossRefGoogle Scholar
  36. 36.
    Towers, C.E., Towers, D.P., Jones, J.D.C.: Absolute fringe order calculation using optimised multi-frequency selection in full-field profilometry. Opt. Lasers Eng. 43(7), 788–800 (2005)CrossRefGoogle Scholar
  37. 37.
    Ulusoy, A.O., Calakli, F., Taubin, G.: One-shot scanning using de bruijn spaced grids. In: IEEE ICCV Workshops, pp. 1786–1792 (2009)Google Scholar
  38. 38.
    Wang, Y., Liu, K., Lau, D.L., Hao, Q., Hassebrook, L.G.: Maximum snr pattern strategy for phase shifting methods in structured light illumination. J. Opt. Soc. Am. A 27(9), 1962–71 (2010)CrossRefGoogle Scholar
  39. 39.
    Xu, Y., Aliaga, D.: An adaptive correspondence algorithm for modeling scenes with strong interreflections. IEEE Trans. Vis. Comput. Gr. 15, 465–480 (2009)Google Scholar

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Authors and Affiliations

  1. 1.Department of Computer SciencesUniversity of Wisconsin-MadisonMadisonUSA

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