Abstract

Time-of-flight (ToF) cameras calculate depth maps by reconstructing phase shifts of amplitude-modulated signals. For broad illumination of transparent objects, reflections from multiple scene points can illuminate a given pixel, giving rise to an erroneous depth map. We report here a sparsity-regularized solution that separates K interfering components using multiple modulation frequency measurements. The method maps ToF imaging to the general framework of spectral estimation theory and has applications in improving depth profiles and exploiting multiple scattering.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. M. Cash, T. K. Sinha, W. C. Chapman, H. Terawaki, B. M. Dawant, R. L. Galloway, and M. I. Miga, Med. Phys. 30, 1671 (2003).
    [CrossRef]
  2. P. Breuer, C. Eckes, and S. Müller, Computer Vision/Computer Graphics Collaboration Techniques (Springer, 2007), p. 247.
  3. M. C. Amann, T. Boch, R. Myllyla, M. Rioux, and M. Lescure, Opt. Eng. 40, 10 (2001).
    [CrossRef]
  4. Y. Cui, S. Schoun, D. Chan, S. Thrun, and C. Theobalt, Proceedings of Computer Vision and Pattern Recognition (IEEE, 2010), p. 1173.
  5. J. C. Halimeh and M. Wegener, Opt. Express 20, 63 (2012).
    [CrossRef]
  6. R. Lange and P. Seitz, IEEE J. Quantum Electron. 37, 390 (2001).
    [CrossRef]
  7. S. Foix, G. Alenya, and C. Torras, IEEE Sens. J. 11, 1917 (2011).
    [CrossRef]
  8. A. Kolb, E. Barth, R. Koch, and R. Larsen, Proc. Eurographics (The Eurographics Association, 2009), pp. 119–134.
  9. M. Hansard, S. Lee, O. Choi, and R. Horaud, Time-of-Flight Cameras: Principles, Methods and Applications (Springer, 2013).
  10. M. Frank, M. Plaue, H. Rapp, U. Köthe, B. Jähne, and F. A. Hamprecht, Opt. Eng. 48, 013602 (2009).
    [CrossRef]
  11. J. P. Godbaz, M. J. Cree, and A. A. Dorrington, Remote Sens. 4, 21 (2012).
    [CrossRef]
  12. A. P. P. Jongenelen, D. G. Bailey, A. D. Payne, A. A. Dorrington, and D. A. Carnegie, IEEE Trans. Instrum. Meas. 60, 1861 (2011).
    [CrossRef]
  13. A. Dorrington, J. Godbaz, M. Cree, A. Payne, and L. Streeter, Proc. SPIE 7864, 786404 (2011).
    [CrossRef]
  14. J. Godbaz, M. Cree, and A. Dorrington, Proc. SPIE 8296, 829618 (2012).
    [CrossRef]
  15. J. P. Godbaz, A. A. Dorrington, and M. J. Cree, TOF Range-Imaging Cameras (Springer, 2013), p. 91.
  16. A. Bhandari, A. Kadambi, R. Whyte, L. Streeter, C. Barsi, A. Dorrington, and R. Raskar, “Multifrequency time of flight in the context of transient renderings,” ACM SIGGRAPH Posters, New York, 2013, p. 46.
  17. A. Kadambi, R. Whyte, A. Bhandari, L. Streeter, C. Barsi, A. A. Dorrington, and R. Raskar, ACM Trans. Graph. 32, 1 (2013).
    [CrossRef]
  18. S. K. Nayar, G. Krishman, M. D. Grossberg, and R. Raskar, ACM Trans. Graph. 25, 935 (2006).
    [CrossRef]
  19. S. Y. Chen, Y. F. Li, and J. W. Zhang, IEEE Trans. Image Process. 17, 167 (2008).
    [CrossRef]
  20. S. Y. Chen, Active Sensor Planning for Multiview Vision Tasks (Springer, 2008).
  21. S. Fuchs, Proceedings of Computer Vision and Pattern Recognition (IEEE, 2010), p. 3583.
  22. D. Jimenez, D. Pizarro, M. Mazo, and S. Palazuelos, Proceedings of Computer Vision and Pattern Recognition (IEEE, 2012), p. 893.
  23. P. Stoica and R. L. Moses, Introduction to Spectral Analysis (Prentice Hall, 1997).
  24. T. Yamaguchi and I. Zhang, Opt. Lett. 22, 1268 (1997).
    [CrossRef]
  25. Y. C. Pati, R. Rezaiifar, and P. S. Krishnaprasad, Signals Syst. Comp. 1, 40 (1993).
  26. A. Velten, T. Willwacher, O. Gupta, A. Veeraraghavan, M. G. Bawendi, and R. Raskar, Nat. Commun. 3, 745 (2012).
    [CrossRef]
  27. J. J. Barton, Phys. Rev. Lett. 67, 3106 (1991).
    [CrossRef]

2013

A. Kadambi, R. Whyte, A. Bhandari, L. Streeter, C. Barsi, A. A. Dorrington, and R. Raskar, ACM Trans. Graph. 32, 1 (2013).
[CrossRef]

2012

A. Velten, T. Willwacher, O. Gupta, A. Veeraraghavan, M. G. Bawendi, and R. Raskar, Nat. Commun. 3, 745 (2012).
[CrossRef]

J. Godbaz, M. Cree, and A. Dorrington, Proc. SPIE 8296, 829618 (2012).
[CrossRef]

J. C. Halimeh and M. Wegener, Opt. Express 20, 63 (2012).
[CrossRef]

J. P. Godbaz, M. J. Cree, and A. A. Dorrington, Remote Sens. 4, 21 (2012).
[CrossRef]

2011

A. P. P. Jongenelen, D. G. Bailey, A. D. Payne, A. A. Dorrington, and D. A. Carnegie, IEEE Trans. Instrum. Meas. 60, 1861 (2011).
[CrossRef]

A. Dorrington, J. Godbaz, M. Cree, A. Payne, and L. Streeter, Proc. SPIE 7864, 786404 (2011).
[CrossRef]

S. Foix, G. Alenya, and C. Torras, IEEE Sens. J. 11, 1917 (2011).
[CrossRef]

2009

M. Frank, M. Plaue, H. Rapp, U. Köthe, B. Jähne, and F. A. Hamprecht, Opt. Eng. 48, 013602 (2009).
[CrossRef]

2008

S. Y. Chen, Y. F. Li, and J. W. Zhang, IEEE Trans. Image Process. 17, 167 (2008).
[CrossRef]

2006

S. K. Nayar, G. Krishman, M. D. Grossberg, and R. Raskar, ACM Trans. Graph. 25, 935 (2006).
[CrossRef]

2003

D. M. Cash, T. K. Sinha, W. C. Chapman, H. Terawaki, B. M. Dawant, R. L. Galloway, and M. I. Miga, Med. Phys. 30, 1671 (2003).
[CrossRef]

2001

M. C. Amann, T. Boch, R. Myllyla, M. Rioux, and M. Lescure, Opt. Eng. 40, 10 (2001).
[CrossRef]

R. Lange and P. Seitz, IEEE J. Quantum Electron. 37, 390 (2001).
[CrossRef]

1997

1993

Y. C. Pati, R. Rezaiifar, and P. S. Krishnaprasad, Signals Syst. Comp. 1, 40 (1993).

1991

J. J. Barton, Phys. Rev. Lett. 67, 3106 (1991).
[CrossRef]

Alenya, G.

S. Foix, G. Alenya, and C. Torras, IEEE Sens. J. 11, 1917 (2011).
[CrossRef]

Amann, M. C.

M. C. Amann, T. Boch, R. Myllyla, M. Rioux, and M. Lescure, Opt. Eng. 40, 10 (2001).
[CrossRef]

Bailey, D. G.

A. P. P. Jongenelen, D. G. Bailey, A. D. Payne, A. A. Dorrington, and D. A. Carnegie, IEEE Trans. Instrum. Meas. 60, 1861 (2011).
[CrossRef]

Barsi, C.

A. Kadambi, R. Whyte, A. Bhandari, L. Streeter, C. Barsi, A. A. Dorrington, and R. Raskar, ACM Trans. Graph. 32, 1 (2013).
[CrossRef]

A. Bhandari, A. Kadambi, R. Whyte, L. Streeter, C. Barsi, A. Dorrington, and R. Raskar, “Multifrequency time of flight in the context of transient renderings,” ACM SIGGRAPH Posters, New York, 2013, p. 46.

Barth, E.

A. Kolb, E. Barth, R. Koch, and R. Larsen, Proc. Eurographics (The Eurographics Association, 2009), pp. 119–134.

Barton, J. J.

J. J. Barton, Phys. Rev. Lett. 67, 3106 (1991).
[CrossRef]

Bawendi, M. G.

A. Velten, T. Willwacher, O. Gupta, A. Veeraraghavan, M. G. Bawendi, and R. Raskar, Nat. Commun. 3, 745 (2012).
[CrossRef]

Bhandari, A.

A. Kadambi, R. Whyte, A. Bhandari, L. Streeter, C. Barsi, A. A. Dorrington, and R. Raskar, ACM Trans. Graph. 32, 1 (2013).
[CrossRef]

A. Bhandari, A. Kadambi, R. Whyte, L. Streeter, C. Barsi, A. Dorrington, and R. Raskar, “Multifrequency time of flight in the context of transient renderings,” ACM SIGGRAPH Posters, New York, 2013, p. 46.

Boch, T.

M. C. Amann, T. Boch, R. Myllyla, M. Rioux, and M. Lescure, Opt. Eng. 40, 10 (2001).
[CrossRef]

Breuer, P.

P. Breuer, C. Eckes, and S. Müller, Computer Vision/Computer Graphics Collaboration Techniques (Springer, 2007), p. 247.

Carnegie, D. A.

A. P. P. Jongenelen, D. G. Bailey, A. D. Payne, A. A. Dorrington, and D. A. Carnegie, IEEE Trans. Instrum. Meas. 60, 1861 (2011).
[CrossRef]

Cash, D. M.

D. M. Cash, T. K. Sinha, W. C. Chapman, H. Terawaki, B. M. Dawant, R. L. Galloway, and M. I. Miga, Med. Phys. 30, 1671 (2003).
[CrossRef]

Chan, D.

Y. Cui, S. Schoun, D. Chan, S. Thrun, and C. Theobalt, Proceedings of Computer Vision and Pattern Recognition (IEEE, 2010), p. 1173.

Chapman, W. C.

D. M. Cash, T. K. Sinha, W. C. Chapman, H. Terawaki, B. M. Dawant, R. L. Galloway, and M. I. Miga, Med. Phys. 30, 1671 (2003).
[CrossRef]

Chen, S. Y.

S. Y. Chen, Y. F. Li, and J. W. Zhang, IEEE Trans. Image Process. 17, 167 (2008).
[CrossRef]

S. Y. Chen, Active Sensor Planning for Multiview Vision Tasks (Springer, 2008).

Choi, O.

M. Hansard, S. Lee, O. Choi, and R. Horaud, Time-of-Flight Cameras: Principles, Methods and Applications (Springer, 2013).

Cree, M.

J. Godbaz, M. Cree, and A. Dorrington, Proc. SPIE 8296, 829618 (2012).
[CrossRef]

A. Dorrington, J. Godbaz, M. Cree, A. Payne, and L. Streeter, Proc. SPIE 7864, 786404 (2011).
[CrossRef]

Cree, M. J.

J. P. Godbaz, M. J. Cree, and A. A. Dorrington, Remote Sens. 4, 21 (2012).
[CrossRef]

J. P. Godbaz, A. A. Dorrington, and M. J. Cree, TOF Range-Imaging Cameras (Springer, 2013), p. 91.

Cui, Y.

Y. Cui, S. Schoun, D. Chan, S. Thrun, and C. Theobalt, Proceedings of Computer Vision and Pattern Recognition (IEEE, 2010), p. 1173.

Dawant, B. M.

D. M. Cash, T. K. Sinha, W. C. Chapman, H. Terawaki, B. M. Dawant, R. L. Galloway, and M. I. Miga, Med. Phys. 30, 1671 (2003).
[CrossRef]

Dorrington, A.

J. Godbaz, M. Cree, and A. Dorrington, Proc. SPIE 8296, 829618 (2012).
[CrossRef]

A. Dorrington, J. Godbaz, M. Cree, A. Payne, and L. Streeter, Proc. SPIE 7864, 786404 (2011).
[CrossRef]

A. Bhandari, A. Kadambi, R. Whyte, L. Streeter, C. Barsi, A. Dorrington, and R. Raskar, “Multifrequency time of flight in the context of transient renderings,” ACM SIGGRAPH Posters, New York, 2013, p. 46.

Dorrington, A. A.

A. Kadambi, R. Whyte, A. Bhandari, L. Streeter, C. Barsi, A. A. Dorrington, and R. Raskar, ACM Trans. Graph. 32, 1 (2013).
[CrossRef]

J. P. Godbaz, M. J. Cree, and A. A. Dorrington, Remote Sens. 4, 21 (2012).
[CrossRef]

A. P. P. Jongenelen, D. G. Bailey, A. D. Payne, A. A. Dorrington, and D. A. Carnegie, IEEE Trans. Instrum. Meas. 60, 1861 (2011).
[CrossRef]

J. P. Godbaz, A. A. Dorrington, and M. J. Cree, TOF Range-Imaging Cameras (Springer, 2013), p. 91.

Eckes, C.

P. Breuer, C. Eckes, and S. Müller, Computer Vision/Computer Graphics Collaboration Techniques (Springer, 2007), p. 247.

Foix, S.

S. Foix, G. Alenya, and C. Torras, IEEE Sens. J. 11, 1917 (2011).
[CrossRef]

Frank, M.

M. Frank, M. Plaue, H. Rapp, U. Köthe, B. Jähne, and F. A. Hamprecht, Opt. Eng. 48, 013602 (2009).
[CrossRef]

Fuchs, S.

S. Fuchs, Proceedings of Computer Vision and Pattern Recognition (IEEE, 2010), p. 3583.

Galloway, R. L.

D. M. Cash, T. K. Sinha, W. C. Chapman, H. Terawaki, B. M. Dawant, R. L. Galloway, and M. I. Miga, Med. Phys. 30, 1671 (2003).
[CrossRef]

Godbaz, J.

J. Godbaz, M. Cree, and A. Dorrington, Proc. SPIE 8296, 829618 (2012).
[CrossRef]

A. Dorrington, J. Godbaz, M. Cree, A. Payne, and L. Streeter, Proc. SPIE 7864, 786404 (2011).
[CrossRef]

Godbaz, J. P.

J. P. Godbaz, M. J. Cree, and A. A. Dorrington, Remote Sens. 4, 21 (2012).
[CrossRef]

J. P. Godbaz, A. A. Dorrington, and M. J. Cree, TOF Range-Imaging Cameras (Springer, 2013), p. 91.

Grossberg, M. D.

S. K. Nayar, G. Krishman, M. D. Grossberg, and R. Raskar, ACM Trans. Graph. 25, 935 (2006).
[CrossRef]

Gupta, O.

A. Velten, T. Willwacher, O. Gupta, A. Veeraraghavan, M. G. Bawendi, and R. Raskar, Nat. Commun. 3, 745 (2012).
[CrossRef]

Halimeh, J. C.

Hamprecht, F. A.

M. Frank, M. Plaue, H. Rapp, U. Köthe, B. Jähne, and F. A. Hamprecht, Opt. Eng. 48, 013602 (2009).
[CrossRef]

Hansard, M.

M. Hansard, S. Lee, O. Choi, and R. Horaud, Time-of-Flight Cameras: Principles, Methods and Applications (Springer, 2013).

Horaud, R.

M. Hansard, S. Lee, O. Choi, and R. Horaud, Time-of-Flight Cameras: Principles, Methods and Applications (Springer, 2013).

Jähne, B.

M. Frank, M. Plaue, H. Rapp, U. Köthe, B. Jähne, and F. A. Hamprecht, Opt. Eng. 48, 013602 (2009).
[CrossRef]

Jimenez, D.

D. Jimenez, D. Pizarro, M. Mazo, and S. Palazuelos, Proceedings of Computer Vision and Pattern Recognition (IEEE, 2012), p. 893.

Jongenelen, A. P. P.

A. P. P. Jongenelen, D. G. Bailey, A. D. Payne, A. A. Dorrington, and D. A. Carnegie, IEEE Trans. Instrum. Meas. 60, 1861 (2011).
[CrossRef]

Kadambi, A.

A. Kadambi, R. Whyte, A. Bhandari, L. Streeter, C. Barsi, A. A. Dorrington, and R. Raskar, ACM Trans. Graph. 32, 1 (2013).
[CrossRef]

A. Bhandari, A. Kadambi, R. Whyte, L. Streeter, C. Barsi, A. Dorrington, and R. Raskar, “Multifrequency time of flight in the context of transient renderings,” ACM SIGGRAPH Posters, New York, 2013, p. 46.

Koch, R.

A. Kolb, E. Barth, R. Koch, and R. Larsen, Proc. Eurographics (The Eurographics Association, 2009), pp. 119–134.

Kolb, A.

A. Kolb, E. Barth, R. Koch, and R. Larsen, Proc. Eurographics (The Eurographics Association, 2009), pp. 119–134.

Köthe, U.

M. Frank, M. Plaue, H. Rapp, U. Köthe, B. Jähne, and F. A. Hamprecht, Opt. Eng. 48, 013602 (2009).
[CrossRef]

Krishman, G.

S. K. Nayar, G. Krishman, M. D. Grossberg, and R. Raskar, ACM Trans. Graph. 25, 935 (2006).
[CrossRef]

Krishnaprasad, P. S.

Y. C. Pati, R. Rezaiifar, and P. S. Krishnaprasad, Signals Syst. Comp. 1, 40 (1993).

Lange, R.

R. Lange and P. Seitz, IEEE J. Quantum Electron. 37, 390 (2001).
[CrossRef]

Larsen, R.

A. Kolb, E. Barth, R. Koch, and R. Larsen, Proc. Eurographics (The Eurographics Association, 2009), pp. 119–134.

Lee, S.

M. Hansard, S. Lee, O. Choi, and R. Horaud, Time-of-Flight Cameras: Principles, Methods and Applications (Springer, 2013).

Lescure, M.

M. C. Amann, T. Boch, R. Myllyla, M. Rioux, and M. Lescure, Opt. Eng. 40, 10 (2001).
[CrossRef]

Li, Y. F.

S. Y. Chen, Y. F. Li, and J. W. Zhang, IEEE Trans. Image Process. 17, 167 (2008).
[CrossRef]

Mazo, M.

D. Jimenez, D. Pizarro, M. Mazo, and S. Palazuelos, Proceedings of Computer Vision and Pattern Recognition (IEEE, 2012), p. 893.

Miga, M. I.

D. M. Cash, T. K. Sinha, W. C. Chapman, H. Terawaki, B. M. Dawant, R. L. Galloway, and M. I. Miga, Med. Phys. 30, 1671 (2003).
[CrossRef]

Moses, R. L.

P. Stoica and R. L. Moses, Introduction to Spectral Analysis (Prentice Hall, 1997).

Müller, S.

P. Breuer, C. Eckes, and S. Müller, Computer Vision/Computer Graphics Collaboration Techniques (Springer, 2007), p. 247.

Myllyla, R.

M. C. Amann, T. Boch, R. Myllyla, M. Rioux, and M. Lescure, Opt. Eng. 40, 10 (2001).
[CrossRef]

Nayar, S. K.

S. K. Nayar, G. Krishman, M. D. Grossberg, and R. Raskar, ACM Trans. Graph. 25, 935 (2006).
[CrossRef]

Palazuelos, S.

D. Jimenez, D. Pizarro, M. Mazo, and S. Palazuelos, Proceedings of Computer Vision and Pattern Recognition (IEEE, 2012), p. 893.

Pati, Y. C.

Y. C. Pati, R. Rezaiifar, and P. S. Krishnaprasad, Signals Syst. Comp. 1, 40 (1993).

Payne, A.

A. Dorrington, J. Godbaz, M. Cree, A. Payne, and L. Streeter, Proc. SPIE 7864, 786404 (2011).
[CrossRef]

Payne, A. D.

A. P. P. Jongenelen, D. G. Bailey, A. D. Payne, A. A. Dorrington, and D. A. Carnegie, IEEE Trans. Instrum. Meas. 60, 1861 (2011).
[CrossRef]

Pizarro, D.

D. Jimenez, D. Pizarro, M. Mazo, and S. Palazuelos, Proceedings of Computer Vision and Pattern Recognition (IEEE, 2012), p. 893.

Plaue, M.

M. Frank, M. Plaue, H. Rapp, U. Köthe, B. Jähne, and F. A. Hamprecht, Opt. Eng. 48, 013602 (2009).
[CrossRef]

Rapp, H.

M. Frank, M. Plaue, H. Rapp, U. Köthe, B. Jähne, and F. A. Hamprecht, Opt. Eng. 48, 013602 (2009).
[CrossRef]

Raskar, R.

A. Kadambi, R. Whyte, A. Bhandari, L. Streeter, C. Barsi, A. A. Dorrington, and R. Raskar, ACM Trans. Graph. 32, 1 (2013).
[CrossRef]

A. Velten, T. Willwacher, O. Gupta, A. Veeraraghavan, M. G. Bawendi, and R. Raskar, Nat. Commun. 3, 745 (2012).
[CrossRef]

S. K. Nayar, G. Krishman, M. D. Grossberg, and R. Raskar, ACM Trans. Graph. 25, 935 (2006).
[CrossRef]

A. Bhandari, A. Kadambi, R. Whyte, L. Streeter, C. Barsi, A. Dorrington, and R. Raskar, “Multifrequency time of flight in the context of transient renderings,” ACM SIGGRAPH Posters, New York, 2013, p. 46.

Rezaiifar, R.

Y. C. Pati, R. Rezaiifar, and P. S. Krishnaprasad, Signals Syst. Comp. 1, 40 (1993).

Rioux, M.

M. C. Amann, T. Boch, R. Myllyla, M. Rioux, and M. Lescure, Opt. Eng. 40, 10 (2001).
[CrossRef]

Schoun, S.

Y. Cui, S. Schoun, D. Chan, S. Thrun, and C. Theobalt, Proceedings of Computer Vision and Pattern Recognition (IEEE, 2010), p. 1173.

Seitz, P.

R. Lange and P. Seitz, IEEE J. Quantum Electron. 37, 390 (2001).
[CrossRef]

Sinha, T. K.

D. M. Cash, T. K. Sinha, W. C. Chapman, H. Terawaki, B. M. Dawant, R. L. Galloway, and M. I. Miga, Med. Phys. 30, 1671 (2003).
[CrossRef]

Stoica, P.

P. Stoica and R. L. Moses, Introduction to Spectral Analysis (Prentice Hall, 1997).

Streeter, L.

A. Kadambi, R. Whyte, A. Bhandari, L. Streeter, C. Barsi, A. A. Dorrington, and R. Raskar, ACM Trans. Graph. 32, 1 (2013).
[CrossRef]

A. Dorrington, J. Godbaz, M. Cree, A. Payne, and L. Streeter, Proc. SPIE 7864, 786404 (2011).
[CrossRef]

A. Bhandari, A. Kadambi, R. Whyte, L. Streeter, C. Barsi, A. Dorrington, and R. Raskar, “Multifrequency time of flight in the context of transient renderings,” ACM SIGGRAPH Posters, New York, 2013, p. 46.

Terawaki, H.

D. M. Cash, T. K. Sinha, W. C. Chapman, H. Terawaki, B. M. Dawant, R. L. Galloway, and M. I. Miga, Med. Phys. 30, 1671 (2003).
[CrossRef]

Theobalt, C.

Y. Cui, S. Schoun, D. Chan, S. Thrun, and C. Theobalt, Proceedings of Computer Vision and Pattern Recognition (IEEE, 2010), p. 1173.

Thrun, S.

Y. Cui, S. Schoun, D. Chan, S. Thrun, and C. Theobalt, Proceedings of Computer Vision and Pattern Recognition (IEEE, 2010), p. 1173.

Torras, C.

S. Foix, G. Alenya, and C. Torras, IEEE Sens. J. 11, 1917 (2011).
[CrossRef]

Veeraraghavan, A.

A. Velten, T. Willwacher, O. Gupta, A. Veeraraghavan, M. G. Bawendi, and R. Raskar, Nat. Commun. 3, 745 (2012).
[CrossRef]

Velten, A.

A. Velten, T. Willwacher, O. Gupta, A. Veeraraghavan, M. G. Bawendi, and R. Raskar, Nat. Commun. 3, 745 (2012).
[CrossRef]

Wegener, M.

Whyte, R.

A. Kadambi, R. Whyte, A. Bhandari, L. Streeter, C. Barsi, A. A. Dorrington, and R. Raskar, ACM Trans. Graph. 32, 1 (2013).
[CrossRef]

A. Bhandari, A. Kadambi, R. Whyte, L. Streeter, C. Barsi, A. Dorrington, and R. Raskar, “Multifrequency time of flight in the context of transient renderings,” ACM SIGGRAPH Posters, New York, 2013, p. 46.

Willwacher, T.

A. Velten, T. Willwacher, O. Gupta, A. Veeraraghavan, M. G. Bawendi, and R. Raskar, Nat. Commun. 3, 745 (2012).
[CrossRef]

Yamaguchi, T.

Zhang, I.

Zhang, J. W.

S. Y. Chen, Y. F. Li, and J. W. Zhang, IEEE Trans. Image Process. 17, 167 (2008).
[CrossRef]

ACM Trans. Graph.

A. Kadambi, R. Whyte, A. Bhandari, L. Streeter, C. Barsi, A. A. Dorrington, and R. Raskar, ACM Trans. Graph. 32, 1 (2013).
[CrossRef]

S. K. Nayar, G. Krishman, M. D. Grossberg, and R. Raskar, ACM Trans. Graph. 25, 935 (2006).
[CrossRef]

IEEE J. Quantum Electron.

R. Lange and P. Seitz, IEEE J. Quantum Electron. 37, 390 (2001).
[CrossRef]

IEEE Sens. J.

S. Foix, G. Alenya, and C. Torras, IEEE Sens. J. 11, 1917 (2011).
[CrossRef]

IEEE Trans. Image Process.

S. Y. Chen, Y. F. Li, and J. W. Zhang, IEEE Trans. Image Process. 17, 167 (2008).
[CrossRef]

IEEE Trans. Instrum. Meas.

A. P. P. Jongenelen, D. G. Bailey, A. D. Payne, A. A. Dorrington, and D. A. Carnegie, IEEE Trans. Instrum. Meas. 60, 1861 (2011).
[CrossRef]

Med. Phys.

D. M. Cash, T. K. Sinha, W. C. Chapman, H. Terawaki, B. M. Dawant, R. L. Galloway, and M. I. Miga, Med. Phys. 30, 1671 (2003).
[CrossRef]

Nat. Commun.

A. Velten, T. Willwacher, O. Gupta, A. Veeraraghavan, M. G. Bawendi, and R. Raskar, Nat. Commun. 3, 745 (2012).
[CrossRef]

Opt. Eng.

M. Frank, M. Plaue, H. Rapp, U. Köthe, B. Jähne, and F. A. Hamprecht, Opt. Eng. 48, 013602 (2009).
[CrossRef]

M. C. Amann, T. Boch, R. Myllyla, M. Rioux, and M. Lescure, Opt. Eng. 40, 10 (2001).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

J. J. Barton, Phys. Rev. Lett. 67, 3106 (1991).
[CrossRef]

Proc. SPIE

A. Dorrington, J. Godbaz, M. Cree, A. Payne, and L. Streeter, Proc. SPIE 7864, 786404 (2011).
[CrossRef]

J. Godbaz, M. Cree, and A. Dorrington, Proc. SPIE 8296, 829618 (2012).
[CrossRef]

Remote Sens.

J. P. Godbaz, M. J. Cree, and A. A. Dorrington, Remote Sens. 4, 21 (2012).
[CrossRef]

Signals Syst. Comp.

Y. C. Pati, R. Rezaiifar, and P. S. Krishnaprasad, Signals Syst. Comp. 1, 40 (1993).

Other

J. P. Godbaz, A. A. Dorrington, and M. J. Cree, TOF Range-Imaging Cameras (Springer, 2013), p. 91.

A. Bhandari, A. Kadambi, R. Whyte, L. Streeter, C. Barsi, A. Dorrington, and R. Raskar, “Multifrequency time of flight in the context of transient renderings,” ACM SIGGRAPH Posters, New York, 2013, p. 46.

S. Y. Chen, Active Sensor Planning for Multiview Vision Tasks (Springer, 2008).

S. Fuchs, Proceedings of Computer Vision and Pattern Recognition (IEEE, 2010), p. 3583.

D. Jimenez, D. Pizarro, M. Mazo, and S. Palazuelos, Proceedings of Computer Vision and Pattern Recognition (IEEE, 2012), p. 893.

P. Stoica and R. L. Moses, Introduction to Spectral Analysis (Prentice Hall, 1997).

Y. Cui, S. Schoun, D. Chan, S. Thrun, and C. Theobalt, Proceedings of Computer Vision and Pattern Recognition (IEEE, 2010), p. 1173.

P. Breuer, C. Eckes, and S. Müller, Computer Vision/Computer Graphics Collaboration Techniques (Springer, 2007), p. 247.

A. Kolb, E. Barth, R. Koch, and R. Larsen, Proc. Eurographics (The Eurographics Association, 2009), pp. 119–134.

M. Hansard, S. Lee, O. Choi, and R. Horaud, Time-of-Flight Cameras: Principles, Methods and Applications (Springer, 2013).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

(a) ToF principle: the phase delay of an emitted AMCW wave proportionally encodes the distance of the object. (b) Mirror-like and (c) semi-transparent reflections produce MPI and yield an incorrect phase. (d) A complicated scene with continuous MPI.

Fig. 2.
Fig. 2.

Left: experimental setup. Two transparencies block the left side of the camera (three components), and one transparency blocks the right (two components). Right: measured amplitude and depth at ω=3ω0. Dashed line indicates edge of second transparency.

Fig. 3.
Fig. 3.

Reconstructed amplitudes and depths via sparse regularization. Dashed lines indicate edge of second transparency.

Fig. 4.
Fig. 4.

Depth histogram for reconstructed and measured depth maps. Reconstructed distances cluster around the correct depths, whereas the MPI depth map has a wide variance across the entire range.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

s(t)=1+s0cos(ωt),tR
r(t)=Γ(1+s0cos(ωtϕ)).
Cf,g(τ)=deflimT12TT+Tf*(t+τ)g(t)dt.
mω[q]=defCs,r(τq)=(2)Γ(1+s022cos(ωτq+ϕ)).
Γ˜=(mω[3]mω[1])2+(mω[0]mω[2])2/s02,
tanϕ˜=(mω[3]mω[1]mω[0]mω[2]).
zω=Γ˜ejϕ˜(ω).
r(t)=C0+k=0K1Γkej(ωtϕk(ω)),
mωK[q]=C0+s022ejωτqk=0K1Γkejϕk(ω).
zω(K)=Γ˜(ω)ejϕ˜(ω)=k=0K1Γkejϕk(ω),
z=(zω0(K),z2ω0(K),,zNω0(K))T.
Φ=(ejω0ϕ0ejω0ϕ1ejω0ϕK1ej2ω0ϕ0ej2ω0ϕ1ej2ω0ϕK1ejNω0ϕ0ejNω0ϕ1ejNω0ϕK1),
zΨg22Data-Fidelity<ε0such thatg0=KSparsity,

Metrics