Abstract

In-camera light scattering is a systematic error of Time-of-Flight depth cameras that significantly reduces the accuracy of the systems. A completely new model is presented, based on raw data calibration and only one additional intrinsic camera parameter. It is shown that the approach effectively removes the errors of in-camera light scattering.

© 2014 Optical Society of America

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References

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  1. W. Karel, S. Ghuffar, and N. Pfeifer, “Modelling and compensating internal light scattering in time of flight range cameras,” The Photogrammetric Record 27, 155–174 (2012).
    [Crossref]
  2. M. Hansard, S. Lee, O. Choi, and R. Horaud, Time-of-Flight Cameras (Springer, 2013).
    [Crossref]
  3. D. Lefloch, R. Nair, F. Lenzen, H. Schäfer, L. Streeter, M. J. Cree, R. Koch, and A. Kolb, “Technical foundation and calibration methods for time-of-flight cameras,” in “Time-of-Flight and Depth Imaging: Sensors, Algorithms, and Applications,”, vol. 8200 of LNCS (Springer, 2013), pp. 3–24.
  4. M. Schmidt, “Analysis, modeling and dynamic optimization of 3d time-of-flight imaging systems,” Dissertation, IWR, Fakultät für Physik und Astronomie, Univ. Heidelberg (2011).
  5. M. Frank, M. Plaue, K. Rapp, U. Köthe, B. Jähne, and F. Hamprecht, “Theoretical and experimental error analysis of continuous-wave time-of-flight range cameras,” Optical Engineering 48, 13602 (2009).
    [Crossref]
  6. F. Lenzen, K. I. Kim, H. Schäfer, R. Nair, S. Meister, F. Becker, C. S. Garbe, and C. Theobalt, “Denoising strategies for time-of-flight data,” in “Time-of-Flight and Depth Imaging: Sensors, Algorithms, and Applications,”, vol. 8200 of LNCS (Springer, 2013), pp. 25–45.
  7. T. Kahlmann, F. Remondino, and H. Ingensand, “Calibration for increased accuracy of the range imaging camera swissranger:,” in “Proceedings of the ISPRS Commission V Symposium ’Image Engineering and Vision Metrology’,” (ISPRS, 2006), pp. 136–141.
  8. M. Lindner and A. Kolb, “Calibration of the intensity-related distance error of the PMD ToF-camera,” in “Optics East,” (International Society for Optics and Photonics, 2007).
  9. M. Lindner, I. Schiller, A. Kolb, and R. Koch, “Time-of-flight sensor calibration for accurate range sensing,” Comput. Vis. Image Underst. 114, 1318–1328 (2010).
    [Crossref]
  10. J. Godbaz, M. Cree, and A. Dorrington, “Understanding and ameliorating non-linear phase and amplitude responses in AMCW Lidar,” Remote Sensing 4, 21–42 (2012).
    [Crossref]
  11. J. Mure-Dubois and H. Hügli, “Real-time scattering compensation for time-of-flight camera,” in “Proceedings of the ICVS Workshop on Camera Calibration Methods for Computer Vision Systems - CCMVS2007,” (2007), pp. 117–122.
  12. T. Kavli, T. Kirkhus, J. T. Thielemann, and B. Jagielski, “Modelling and compensating measurement errors caused by scattering in time-of-flight cameras,” in “Two- and Three-Dimensional Methods for Inspection and Metrology VI,” (2008), 706604.
    [Crossref]
  13. S. Jamtsho and D. D. Lichti, “Modelling scattering distortion in 3D range camera,” International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences 38, 299–304 (2010).
  14. D. D. Lichti, X. Qi, and T. Ahmed, “Range camera self-calibration with scattering compensation,” ISPRS Journal of Photogrammetry and Remote Sensing 74, 101–109 (2012).
    [Crossref]
  15. D. D. Lichti, J. C. Chow, E. Mitishita, J. A. S. Centeno, F. M. M. d. Silva, R. A. Barrios, and I. Contreras, “New models for scattering bias compensation in time-of-flight range camera self-calibration,” Journal of Surveying Engineering 140, 04014003 (2014).
    [Crossref]

2014 (1)

D. D. Lichti, J. C. Chow, E. Mitishita, J. A. S. Centeno, F. M. M. d. Silva, R. A. Barrios, and I. Contreras, “New models for scattering bias compensation in time-of-flight range camera self-calibration,” Journal of Surveying Engineering 140, 04014003 (2014).
[Crossref]

2012 (3)

D. D. Lichti, X. Qi, and T. Ahmed, “Range camera self-calibration with scattering compensation,” ISPRS Journal of Photogrammetry and Remote Sensing 74, 101–109 (2012).
[Crossref]

W. Karel, S. Ghuffar, and N. Pfeifer, “Modelling and compensating internal light scattering in time of flight range cameras,” The Photogrammetric Record 27, 155–174 (2012).
[Crossref]

J. Godbaz, M. Cree, and A. Dorrington, “Understanding and ameliorating non-linear phase and amplitude responses in AMCW Lidar,” Remote Sensing 4, 21–42 (2012).
[Crossref]

2010 (2)

S. Jamtsho and D. D. Lichti, “Modelling scattering distortion in 3D range camera,” International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences 38, 299–304 (2010).

M. Lindner, I. Schiller, A. Kolb, and R. Koch, “Time-of-flight sensor calibration for accurate range sensing,” Comput. Vis. Image Underst. 114, 1318–1328 (2010).
[Crossref]

2009 (1)

M. Frank, M. Plaue, K. Rapp, U. Köthe, B. Jähne, and F. Hamprecht, “Theoretical and experimental error analysis of continuous-wave time-of-flight range cameras,” Optical Engineering 48, 13602 (2009).
[Crossref]

Ahmed, T.

D. D. Lichti, X. Qi, and T. Ahmed, “Range camera self-calibration with scattering compensation,” ISPRS Journal of Photogrammetry and Remote Sensing 74, 101–109 (2012).
[Crossref]

Barrios, R. A.

D. D. Lichti, J. C. Chow, E. Mitishita, J. A. S. Centeno, F. M. M. d. Silva, R. A. Barrios, and I. Contreras, “New models for scattering bias compensation in time-of-flight range camera self-calibration,” Journal of Surveying Engineering 140, 04014003 (2014).
[Crossref]

Becker, F.

F. Lenzen, K. I. Kim, H. Schäfer, R. Nair, S. Meister, F. Becker, C. S. Garbe, and C. Theobalt, “Denoising strategies for time-of-flight data,” in “Time-of-Flight and Depth Imaging: Sensors, Algorithms, and Applications,”, vol. 8200 of LNCS (Springer, 2013), pp. 25–45.

Centeno, J. A. S.

D. D. Lichti, J. C. Chow, E. Mitishita, J. A. S. Centeno, F. M. M. d. Silva, R. A. Barrios, and I. Contreras, “New models for scattering bias compensation in time-of-flight range camera self-calibration,” Journal of Surveying Engineering 140, 04014003 (2014).
[Crossref]

Choi, O.

M. Hansard, S. Lee, O. Choi, and R. Horaud, Time-of-Flight Cameras (Springer, 2013).
[Crossref]

Chow, J. C.

D. D. Lichti, J. C. Chow, E. Mitishita, J. A. S. Centeno, F. M. M. d. Silva, R. A. Barrios, and I. Contreras, “New models for scattering bias compensation in time-of-flight range camera self-calibration,” Journal of Surveying Engineering 140, 04014003 (2014).
[Crossref]

Contreras, I.

D. D. Lichti, J. C. Chow, E. Mitishita, J. A. S. Centeno, F. M. M. d. Silva, R. A. Barrios, and I. Contreras, “New models for scattering bias compensation in time-of-flight range camera self-calibration,” Journal of Surveying Engineering 140, 04014003 (2014).
[Crossref]

Cree, M.

J. Godbaz, M. Cree, and A. Dorrington, “Understanding and ameliorating non-linear phase and amplitude responses in AMCW Lidar,” Remote Sensing 4, 21–42 (2012).
[Crossref]

Cree, M. J.

D. Lefloch, R. Nair, F. Lenzen, H. Schäfer, L. Streeter, M. J. Cree, R. Koch, and A. Kolb, “Technical foundation and calibration methods for time-of-flight cameras,” in “Time-of-Flight and Depth Imaging: Sensors, Algorithms, and Applications,”, vol. 8200 of LNCS (Springer, 2013), pp. 3–24.

Dorrington, A.

J. Godbaz, M. Cree, and A. Dorrington, “Understanding and ameliorating non-linear phase and amplitude responses in AMCW Lidar,” Remote Sensing 4, 21–42 (2012).
[Crossref]

Frank, M.

M. Frank, M. Plaue, K. Rapp, U. Köthe, B. Jähne, and F. Hamprecht, “Theoretical and experimental error analysis of continuous-wave time-of-flight range cameras,” Optical Engineering 48, 13602 (2009).
[Crossref]

Garbe, C. S.

F. Lenzen, K. I. Kim, H. Schäfer, R. Nair, S. Meister, F. Becker, C. S. Garbe, and C. Theobalt, “Denoising strategies for time-of-flight data,” in “Time-of-Flight and Depth Imaging: Sensors, Algorithms, and Applications,”, vol. 8200 of LNCS (Springer, 2013), pp. 25–45.

Ghuffar, S.

W. Karel, S. Ghuffar, and N. Pfeifer, “Modelling and compensating internal light scattering in time of flight range cameras,” The Photogrammetric Record 27, 155–174 (2012).
[Crossref]

Godbaz, J.

J. Godbaz, M. Cree, and A. Dorrington, “Understanding and ameliorating non-linear phase and amplitude responses in AMCW Lidar,” Remote Sensing 4, 21–42 (2012).
[Crossref]

Hamprecht, F.

M. Frank, M. Plaue, K. Rapp, U. Köthe, B. Jähne, and F. Hamprecht, “Theoretical and experimental error analysis of continuous-wave time-of-flight range cameras,” Optical Engineering 48, 13602 (2009).
[Crossref]

Hansard, M.

M. Hansard, S. Lee, O. Choi, and R. Horaud, Time-of-Flight Cameras (Springer, 2013).
[Crossref]

Horaud, R.

M. Hansard, S. Lee, O. Choi, and R. Horaud, Time-of-Flight Cameras (Springer, 2013).
[Crossref]

Hügli, H.

J. Mure-Dubois and H. Hügli, “Real-time scattering compensation for time-of-flight camera,” in “Proceedings of the ICVS Workshop on Camera Calibration Methods for Computer Vision Systems - CCMVS2007,” (2007), pp. 117–122.

Ingensand, H.

T. Kahlmann, F. Remondino, and H. Ingensand, “Calibration for increased accuracy of the range imaging camera swissranger:,” in “Proceedings of the ISPRS Commission V Symposium ’Image Engineering and Vision Metrology’,” (ISPRS, 2006), pp. 136–141.

Jagielski, B.

T. Kavli, T. Kirkhus, J. T. Thielemann, and B. Jagielski, “Modelling and compensating measurement errors caused by scattering in time-of-flight cameras,” in “Two- and Three-Dimensional Methods for Inspection and Metrology VI,” (2008), 706604.
[Crossref]

Jähne, B.

M. Frank, M. Plaue, K. Rapp, U. Köthe, B. Jähne, and F. Hamprecht, “Theoretical and experimental error analysis of continuous-wave time-of-flight range cameras,” Optical Engineering 48, 13602 (2009).
[Crossref]

Jamtsho, S.

S. Jamtsho and D. D. Lichti, “Modelling scattering distortion in 3D range camera,” International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences 38, 299–304 (2010).

Kahlmann, T.

T. Kahlmann, F. Remondino, and H. Ingensand, “Calibration for increased accuracy of the range imaging camera swissranger:,” in “Proceedings of the ISPRS Commission V Symposium ’Image Engineering and Vision Metrology’,” (ISPRS, 2006), pp. 136–141.

Karel, W.

W. Karel, S. Ghuffar, and N. Pfeifer, “Modelling and compensating internal light scattering in time of flight range cameras,” The Photogrammetric Record 27, 155–174 (2012).
[Crossref]

Kavli, T.

T. Kavli, T. Kirkhus, J. T. Thielemann, and B. Jagielski, “Modelling and compensating measurement errors caused by scattering in time-of-flight cameras,” in “Two- and Three-Dimensional Methods for Inspection and Metrology VI,” (2008), 706604.
[Crossref]

Kim, K. I.

F. Lenzen, K. I. Kim, H. Schäfer, R. Nair, S. Meister, F. Becker, C. S. Garbe, and C. Theobalt, “Denoising strategies for time-of-flight data,” in “Time-of-Flight and Depth Imaging: Sensors, Algorithms, and Applications,”, vol. 8200 of LNCS (Springer, 2013), pp. 25–45.

Kirkhus, T.

T. Kavli, T. Kirkhus, J. T. Thielemann, and B. Jagielski, “Modelling and compensating measurement errors caused by scattering in time-of-flight cameras,” in “Two- and Three-Dimensional Methods for Inspection and Metrology VI,” (2008), 706604.
[Crossref]

Koch, R.

M. Lindner, I. Schiller, A. Kolb, and R. Koch, “Time-of-flight sensor calibration for accurate range sensing,” Comput. Vis. Image Underst. 114, 1318–1328 (2010).
[Crossref]

D. Lefloch, R. Nair, F. Lenzen, H. Schäfer, L. Streeter, M. J. Cree, R. Koch, and A. Kolb, “Technical foundation and calibration methods for time-of-flight cameras,” in “Time-of-Flight and Depth Imaging: Sensors, Algorithms, and Applications,”, vol. 8200 of LNCS (Springer, 2013), pp. 3–24.

Kolb, A.

M. Lindner, I. Schiller, A. Kolb, and R. Koch, “Time-of-flight sensor calibration for accurate range sensing,” Comput. Vis. Image Underst. 114, 1318–1328 (2010).
[Crossref]

D. Lefloch, R. Nair, F. Lenzen, H. Schäfer, L. Streeter, M. J. Cree, R. Koch, and A. Kolb, “Technical foundation and calibration methods for time-of-flight cameras,” in “Time-of-Flight and Depth Imaging: Sensors, Algorithms, and Applications,”, vol. 8200 of LNCS (Springer, 2013), pp. 3–24.

M. Lindner and A. Kolb, “Calibration of the intensity-related distance error of the PMD ToF-camera,” in “Optics East,” (International Society for Optics and Photonics, 2007).

Köthe, U.

M. Frank, M. Plaue, K. Rapp, U. Köthe, B. Jähne, and F. Hamprecht, “Theoretical and experimental error analysis of continuous-wave time-of-flight range cameras,” Optical Engineering 48, 13602 (2009).
[Crossref]

Lee, S.

M. Hansard, S. Lee, O. Choi, and R. Horaud, Time-of-Flight Cameras (Springer, 2013).
[Crossref]

Lefloch, D.

D. Lefloch, R. Nair, F. Lenzen, H. Schäfer, L. Streeter, M. J. Cree, R. Koch, and A. Kolb, “Technical foundation and calibration methods for time-of-flight cameras,” in “Time-of-Flight and Depth Imaging: Sensors, Algorithms, and Applications,”, vol. 8200 of LNCS (Springer, 2013), pp. 3–24.

Lenzen, F.

D. Lefloch, R. Nair, F. Lenzen, H. Schäfer, L. Streeter, M. J. Cree, R. Koch, and A. Kolb, “Technical foundation and calibration methods for time-of-flight cameras,” in “Time-of-Flight and Depth Imaging: Sensors, Algorithms, and Applications,”, vol. 8200 of LNCS (Springer, 2013), pp. 3–24.

F. Lenzen, K. I. Kim, H. Schäfer, R. Nair, S. Meister, F. Becker, C. S. Garbe, and C. Theobalt, “Denoising strategies for time-of-flight data,” in “Time-of-Flight and Depth Imaging: Sensors, Algorithms, and Applications,”, vol. 8200 of LNCS (Springer, 2013), pp. 25–45.

Lichti, D. D.

D. D. Lichti, J. C. Chow, E. Mitishita, J. A. S. Centeno, F. M. M. d. Silva, R. A. Barrios, and I. Contreras, “New models for scattering bias compensation in time-of-flight range camera self-calibration,” Journal of Surveying Engineering 140, 04014003 (2014).
[Crossref]

D. D. Lichti, X. Qi, and T. Ahmed, “Range camera self-calibration with scattering compensation,” ISPRS Journal of Photogrammetry and Remote Sensing 74, 101–109 (2012).
[Crossref]

S. Jamtsho and D. D. Lichti, “Modelling scattering distortion in 3D range camera,” International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences 38, 299–304 (2010).

Lindner, M.

M. Lindner, I. Schiller, A. Kolb, and R. Koch, “Time-of-flight sensor calibration for accurate range sensing,” Comput. Vis. Image Underst. 114, 1318–1328 (2010).
[Crossref]

M. Lindner and A. Kolb, “Calibration of the intensity-related distance error of the PMD ToF-camera,” in “Optics East,” (International Society for Optics and Photonics, 2007).

Meister, S.

F. Lenzen, K. I. Kim, H. Schäfer, R. Nair, S. Meister, F. Becker, C. S. Garbe, and C. Theobalt, “Denoising strategies for time-of-flight data,” in “Time-of-Flight and Depth Imaging: Sensors, Algorithms, and Applications,”, vol. 8200 of LNCS (Springer, 2013), pp. 25–45.

Mitishita, E.

D. D. Lichti, J. C. Chow, E. Mitishita, J. A. S. Centeno, F. M. M. d. Silva, R. A. Barrios, and I. Contreras, “New models for scattering bias compensation in time-of-flight range camera self-calibration,” Journal of Surveying Engineering 140, 04014003 (2014).
[Crossref]

Mure-Dubois, J.

J. Mure-Dubois and H. Hügli, “Real-time scattering compensation for time-of-flight camera,” in “Proceedings of the ICVS Workshop on Camera Calibration Methods for Computer Vision Systems - CCMVS2007,” (2007), pp. 117–122.

Nair, R.

F. Lenzen, K. I. Kim, H. Schäfer, R. Nair, S. Meister, F. Becker, C. S. Garbe, and C. Theobalt, “Denoising strategies for time-of-flight data,” in “Time-of-Flight and Depth Imaging: Sensors, Algorithms, and Applications,”, vol. 8200 of LNCS (Springer, 2013), pp. 25–45.

D. Lefloch, R. Nair, F. Lenzen, H. Schäfer, L. Streeter, M. J. Cree, R. Koch, and A. Kolb, “Technical foundation and calibration methods for time-of-flight cameras,” in “Time-of-Flight and Depth Imaging: Sensors, Algorithms, and Applications,”, vol. 8200 of LNCS (Springer, 2013), pp. 3–24.

Pfeifer, N.

W. Karel, S. Ghuffar, and N. Pfeifer, “Modelling and compensating internal light scattering in time of flight range cameras,” The Photogrammetric Record 27, 155–174 (2012).
[Crossref]

Plaue, M.

M. Frank, M. Plaue, K. Rapp, U. Köthe, B. Jähne, and F. Hamprecht, “Theoretical and experimental error analysis of continuous-wave time-of-flight range cameras,” Optical Engineering 48, 13602 (2009).
[Crossref]

Qi, X.

D. D. Lichti, X. Qi, and T. Ahmed, “Range camera self-calibration with scattering compensation,” ISPRS Journal of Photogrammetry and Remote Sensing 74, 101–109 (2012).
[Crossref]

Rapp, K.

M. Frank, M. Plaue, K. Rapp, U. Köthe, B. Jähne, and F. Hamprecht, “Theoretical and experimental error analysis of continuous-wave time-of-flight range cameras,” Optical Engineering 48, 13602 (2009).
[Crossref]

Remondino, F.

T. Kahlmann, F. Remondino, and H. Ingensand, “Calibration for increased accuracy of the range imaging camera swissranger:,” in “Proceedings of the ISPRS Commission V Symposium ’Image Engineering and Vision Metrology’,” (ISPRS, 2006), pp. 136–141.

Schäfer, H.

F. Lenzen, K. I. Kim, H. Schäfer, R. Nair, S. Meister, F. Becker, C. S. Garbe, and C. Theobalt, “Denoising strategies for time-of-flight data,” in “Time-of-Flight and Depth Imaging: Sensors, Algorithms, and Applications,”, vol. 8200 of LNCS (Springer, 2013), pp. 25–45.

D. Lefloch, R. Nair, F. Lenzen, H. Schäfer, L. Streeter, M. J. Cree, R. Koch, and A. Kolb, “Technical foundation and calibration methods for time-of-flight cameras,” in “Time-of-Flight and Depth Imaging: Sensors, Algorithms, and Applications,”, vol. 8200 of LNCS (Springer, 2013), pp. 3–24.

Schiller, I.

M. Lindner, I. Schiller, A. Kolb, and R. Koch, “Time-of-flight sensor calibration for accurate range sensing,” Comput. Vis. Image Underst. 114, 1318–1328 (2010).
[Crossref]

Schmidt, M.

M. Schmidt, “Analysis, modeling and dynamic optimization of 3d time-of-flight imaging systems,” Dissertation, IWR, Fakultät für Physik und Astronomie, Univ. Heidelberg (2011).

Silva, F. M. M. d.

D. D. Lichti, J. C. Chow, E. Mitishita, J. A. S. Centeno, F. M. M. d. Silva, R. A. Barrios, and I. Contreras, “New models for scattering bias compensation in time-of-flight range camera self-calibration,” Journal of Surveying Engineering 140, 04014003 (2014).
[Crossref]

Streeter, L.

D. Lefloch, R. Nair, F. Lenzen, H. Schäfer, L. Streeter, M. J. Cree, R. Koch, and A. Kolb, “Technical foundation and calibration methods for time-of-flight cameras,” in “Time-of-Flight and Depth Imaging: Sensors, Algorithms, and Applications,”, vol. 8200 of LNCS (Springer, 2013), pp. 3–24.

Theobalt, C.

F. Lenzen, K. I. Kim, H. Schäfer, R. Nair, S. Meister, F. Becker, C. S. Garbe, and C. Theobalt, “Denoising strategies for time-of-flight data,” in “Time-of-Flight and Depth Imaging: Sensors, Algorithms, and Applications,”, vol. 8200 of LNCS (Springer, 2013), pp. 25–45.

Thielemann, J. T.

T. Kavli, T. Kirkhus, J. T. Thielemann, and B. Jagielski, “Modelling and compensating measurement errors caused by scattering in time-of-flight cameras,” in “Two- and Three-Dimensional Methods for Inspection and Metrology VI,” (2008), 706604.
[Crossref]

Comput. Vis. Image Underst. (1)

M. Lindner, I. Schiller, A. Kolb, and R. Koch, “Time-of-flight sensor calibration for accurate range sensing,” Comput. Vis. Image Underst. 114, 1318–1328 (2010).
[Crossref]

International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences (1)

S. Jamtsho and D. D. Lichti, “Modelling scattering distortion in 3D range camera,” International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences 38, 299–304 (2010).

ISPRS Journal of Photogrammetry and Remote Sensing (1)

D. D. Lichti, X. Qi, and T. Ahmed, “Range camera self-calibration with scattering compensation,” ISPRS Journal of Photogrammetry and Remote Sensing 74, 101–109 (2012).
[Crossref]

Journal of Surveying Engineering (1)

D. D. Lichti, J. C. Chow, E. Mitishita, J. A. S. Centeno, F. M. M. d. Silva, R. A. Barrios, and I. Contreras, “New models for scattering bias compensation in time-of-flight range camera self-calibration,” Journal of Surveying Engineering 140, 04014003 (2014).
[Crossref]

Optical Engineering (1)

M. Frank, M. Plaue, K. Rapp, U. Köthe, B. Jähne, and F. Hamprecht, “Theoretical and experimental error analysis of continuous-wave time-of-flight range cameras,” Optical Engineering 48, 13602 (2009).
[Crossref]

Remote Sensing (1)

J. Godbaz, M. Cree, and A. Dorrington, “Understanding and ameliorating non-linear phase and amplitude responses in AMCW Lidar,” Remote Sensing 4, 21–42 (2012).
[Crossref]

The Photogrammetric Record (1)

W. Karel, S. Ghuffar, and N. Pfeifer, “Modelling and compensating internal light scattering in time of flight range cameras,” The Photogrammetric Record 27, 155–174 (2012).
[Crossref]

Other (8)

M. Hansard, S. Lee, O. Choi, and R. Horaud, Time-of-Flight Cameras (Springer, 2013).
[Crossref]

D. Lefloch, R. Nair, F. Lenzen, H. Schäfer, L. Streeter, M. J. Cree, R. Koch, and A. Kolb, “Technical foundation and calibration methods for time-of-flight cameras,” in “Time-of-Flight and Depth Imaging: Sensors, Algorithms, and Applications,”, vol. 8200 of LNCS (Springer, 2013), pp. 3–24.

M. Schmidt, “Analysis, modeling and dynamic optimization of 3d time-of-flight imaging systems,” Dissertation, IWR, Fakultät für Physik und Astronomie, Univ. Heidelberg (2011).

F. Lenzen, K. I. Kim, H. Schäfer, R. Nair, S. Meister, F. Becker, C. S. Garbe, and C. Theobalt, “Denoising strategies for time-of-flight data,” in “Time-of-Flight and Depth Imaging: Sensors, Algorithms, and Applications,”, vol. 8200 of LNCS (Springer, 2013), pp. 25–45.

T. Kahlmann, F. Remondino, and H. Ingensand, “Calibration for increased accuracy of the range imaging camera swissranger:,” in “Proceedings of the ISPRS Commission V Symposium ’Image Engineering and Vision Metrology’,” (ISPRS, 2006), pp. 136–141.

M. Lindner and A. Kolb, “Calibration of the intensity-related distance error of the PMD ToF-camera,” in “Optics East,” (International Society for Optics and Photonics, 2007).

J. Mure-Dubois and H. Hügli, “Real-time scattering compensation for time-of-flight camera,” in “Proceedings of the ICVS Workshop on Camera Calibration Methods for Computer Vision Systems - CCMVS2007,” (2007), pp. 117–122.

T. Kavli, T. Kirkhus, J. T. Thielemann, and B. Jagielski, “Modelling and compensating measurement errors caused by scattering in time-of-flight cameras,” in “Two- and Three-Dimensional Methods for Inspection and Metrology VI,” (2008), 706604.
[Crossref]

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Figures (7)

Fig. 1
Fig. 1

Left: Mean dark signal of a single pixel, averaged over 100 frames at two different camera temperatures. The fitted function is according to Eq. (3). The different temperatures are set by warming up the camera at a constant integration time but different frame rates. For recording the data points at varying integration times but constant camera temperatures, the integration time increase is compensated by an appropriately reduced frame rate. Center/Right: Mean dark signal sub-frame difference and error of a single pixel, compared to the first sub-frame, averaged over 100 frames for different frame rates (10 and 20fps) and different integration times (200 and 2000 μs). Camera temperature is in steady state at every measurement. The time on the x-axis gives the time since the last frame was recorded. The difference increases with lower frame rates and lower integration times.

Fig. 2
Fig. 2

Scattering effect. Incident light is scattered diffusely and spread over the whole sensor area.

Fig. 3
Fig. 3

Raw data of the scene to measure the scattering parameter s. The scattering surface is positioned at an angle to avoid direct reflections of the light sources. In the left part (measurement area), the unscattered incident light I li i is considered equal (cf. Eq. (9)). The two crops on the right show the difference of the two raw intensities in the measurement area on the left and the scattering parameter s for each pixel. The scattering parameter shows a slight scene dependency but is mostly dominated by noise. (Brightness and contrast adjusted.)

Fig. 4
Fig. 4

3D surface plots: depth data from the previous scene. Left column: without white cylinder present. Right column: with white cylinder present. Surface maps from top to bottom: depth from uncalibrated raw, depth from calibrated raw, depth from calibrated raw with scattering correction. It is apparent, that the calibration process reduces the noise in the data, while it does not affect the intensity related distance error. The scattering compensation effectively removes the influence of the bright white cylinder in the foreground. The results of the depth measurement are then qualitatively indistinguishable from the scene without the cylinder. Furthermore, the scattering correction does not compromise measurements without strong scattering sources. This means it can safely be applied to any measurement without prior knowledge of the scene.

Fig. 5
Fig. 5

Color maps of phase shift and differences. a and b: calibrated data. c: difference of b and a. d and e: scattering corrected data. f: difference of e and d. g: difference of d and a. h: difference of e and b. i: difference of e and a. The average phase values of the outlined areas can be found in Tab. 2. The images show clearly that the scattering effect is much stronger in the dark parts of the frame. The depth differences here are greatly reduced with the proposed scattering correction.

Fig. 6
Fig. 6

Color maps of intensities and phase shift of a different scene. The top row shows the intensities of the raw data (left) after calibration (center) and scattering correction (right). The intensity data after the calibration is very noisy because the pixels are not calibrated against each other but only linearized. The bottom row shows the phase data after calibration (left), after scattering correction (center) and the difference of both (right). The average phase values of the outlined areas can be found in Tab. 3. The scattering effect is much weaker here because of the smaller scattering object and the smaller depth difference. But the effect becomes apparent again in the dark spots and also in the background.

Fig. 7
Fig. 7

Example for scattering in a different camera (Bluetechnix Argos3D). Left: recorded without scattering object in the foreground. Right: recorded with scattering object in the foreground.

Tables (3)

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Table 1 Mean depth of the different depth data from the crops in Fig. 4 in the same order.

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Table 2 Mean phase shift of the different measurements from the areas highlighted in Fig. 5. There is a slight overcompensation in area C of the cylinder scene, probably due to in-scene scattering.

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Table 3 Mean phase shift of the different measurements from the areas highlighted in Fig. 6. The scattering is much weaker here and hard to evaluate quantitatively. Except for the unreliable background data of area A, the mean values of the corrected data both with and without scattering converge nicely.

Equations (14)

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a ( x , y ) = 1 2 ( I 4 ( x , y ) I 2 ( x , y ) ) 2 + ( I 1 ( x , y ) I 3 ( x , y ) ) 2 ,
φ ( x , y ) = arctan ( I 4 ( x , y ) I 2 ( x , y ) I 1 ( x , y ) I 3 ( x , y ) ) ,
I dark i = I off i + ( I dc i ) γ = I off i + ( i dc i t int ) γ .
I i = I off i + ( I dc i + I lc i ) γ = I off i + ( i dc i t int + i lc i t int ) γ .
I lc i : = I li i + s I ¯ li i .
I i = I off i + ( I dc i + I li i + s I ¯ li i ) γ ,
I li i = ( I i I off i ) 1 / γ I dc i s I ¯ li i .
I ¯ li i = 1 1 + s I ¯ lc i = 1 1 + s ( ( I i I off i ) 1 / γ ¯ I ¯ dc i ) ,
I li , 1 i = ! I li , 2 i ( in measurement area )
I lc , 1 i s I ¯ li , 1 i = I lc , 2 i s I ¯ li , 2 i
s = I lc , 1 i I lc , 2 i I ¯ li , 1 i I ¯ li , 2 i .
s = I ˜ lc , 1 i I ˜ lc , 2 i 1 1 + s ( I ¯ lc , 1 i I ¯ lc , 2 i )
s = I ˜ lc , 1 i I ˜ lc , 2 i ( I ¯ lc , 1 i I ¯ lc , 2 i ) ( I ˜ lc , 1 i I ˜ lc , 2 i ) .
I li i = I lc i s 1 + s I ¯ lc i .

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