Skip to main content
Log in

Depth recovery in time of flight range sensors via compressed sensing algorithm

  • Regular Paper
  • Published:
International Journal of Intelligent Robotics and Applications Aims and scope Submit manuscript

Abstract

Stereo vision, structured light, and time of flight (ToF) are different range imaging techniques that acquire a scene and provide different features such as a depth map and an amplitude image. Compared to other imaging techniques, ToF can measure depth with high speed and good precision according to state of the art. However, it faces multipath interference (MPI) problems that give rise to an error in radiance information. Exploiting the sparsity of the received signal, we solved the multipath interference problem with the help of compressed sensing sparse recovery algorithms with some modification such as applying positivity constraint and proximity constraint. The modification in the algorithm has increased its robustness and proved to be successful in detecting the interference up to two paths successfully. We validated the approach by providing experimental results on synthetic data with ground truth that demonstrated its efficiency and accuracy to give MPI free output. Moreover, we applied a modified sparse recovery algorithm to real data and compared the result with the state-of-the-art methods. It shows better performance in separating the direct path from the multipath component with high accuracy.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Bhandari, A., Feigin, M., Izadi. S., Rhemann, C., Schmidt, M., Raskar, R.: Resolving multipath interference in Kinect: An inverse problem approach. In: SENSORS, 2014 IEEE, pp. 614-617. IEEE (2014a)

  • Bhandari, A., Kadambi, A., Whyte, R., Barsi, C., Feigin, M., Dorrington, A., Raskar, R.: Resolving multipath interference in time-of-flight imaging via modulation frequency diversity and sparse regularization. Opt. Lett. 39(6), 1705–1708 (2014b)

    Article  Google Scholar 

  • Bruckstein, A.M., Elad, M., Zibulevsky, M.: On the uniqueness of nonnegative sparse solutions to underdetermined systems of equations. Inf. Theory IEEE Trans. 54(11), 4813–4820 (2008)

    Article  MathSciNet  Google Scholar 

  • Candes, E.J., Tao, T.: Decoding by linear programming. IEEE Trans. Inf. Theory 51(12), 4203–4215 (2005). (12)

    Article  MathSciNet  Google Scholar 

  • Candes, E.J., Romberg, J.K., Tao, T.: Stable signal recovery from incomplete and inaccurate measurements. Commun. Pure Appl. Math. 59(8), 1207–1223 (2006). (13)

    Article  MathSciNet  Google Scholar 

  • Donoho, D.L.: Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006)

    Article  MathSciNet  Google Scholar 

  • Dorrington, A.A., Godbaz, J.P., Cree, M.J., Payne, A.D, Streeter, L.V.: Separating true range measurements from multi-path and scattering interference in commercial range cameras. In: Three-Dimensional Imaging, Interaction, and Measurement, vol. 7864, p. 786404. International Society for Optics and Photonics (2011)

  • Eldar, Y.C., Kutyniok, G. (eds.): Compressed Sensing: Theory and Applications. Cambridge University Press, Cambridge (2012)

    Google Scholar 

  • Falie, D., Buzuloiu, V.: Further investigations on ToF cameras distance errors and their corrections. In Circuits and Systems for Communications, 2008. ECCSC 2008. 4th European Conference on, pp. 197–200. IEEE (2008)

  • Foix, S., Alenya, G., Torras, C.: Lock-in time-of-flight (ToF) cameras: a survey. IEEE Sens. J. 11, 1917–1926 (2011)

    Article  Google Scholar 

  • Foucart, S., Rauhut, H.: A Mathematical Introduction to Compressive Sensing, vol. 1. Birkhäuser, Basel (2013). (no. 3)

    Book  Google Scholar 

  • Freedman, D., Smolin, Y., Krupka, E., Leichter, I., Schmidt, M.: SRA: fast removal of general multipath for ToF sensors. In: European Conference on Computer Vision, pp. 234–249. Springer, Cham (2014)

  • Fuchs, S.: Multipath interference compensation in time-of-flight camera images. In: Proceedings of the 2010 20th International Conference on Pattern Recognition, ICPR, IEEE Computer Society, Washington, DC, USA, pp. 3583–3586 (2010)

  • Fuchs, S., Suppa, M., Hellwich, O.: Compensation for multipath in tof camera measurements supported by photometric calibration and environment integration. In: Computer Vision Systems, pp. 31–41. Springer (2013)

  • Godbaz, J.P., Cree, M.J., Dorrington, A.A.: Undue influence: Mitigating range-intensity coupling in AMCW ‘flash’ lidar using scene texture. In: Image and Vision Computing New Zealand, 2009. IVCNZ’09. 24th International Conference, pp. 304-309. IEEE (2009)

  • Godbaz, J.P., Cree, M.J., Dorrington, A.A.: Undue Closed-form inverses for the mixed pixel/multipath interference problem in amcw lidar. In: Computational Imaging X, vol. 8296, p. 829618. International Society for Optics and Photonics (2012)

  • Jimenez, D., Pizarro, D., Mazo, M., Palazuelos, S.: Modeling and correction of multipath interference in time of flight cameras. Elsevier J. Image aVis. Comput. 32(1), 1–13 (2014)

    Article  Google Scholar 

  • Kirmani, A., Benedetti, A.,. Chou, P.A.: Spumic Simultaneous phase unwrapping and multipath interference cancellation in time-of-flight cameras using spectral methods. In: Multimedia and Expo (ICME), 2013 IEEE International Conference on, pp. 1–6. IEEE, 2013

  • Mure-Dubois, J., Hügli, H.: Real-time scattering compensation for time-of-flight camera. In: Proceedings of the ICVS Workshop on Camera Calibration Methods for Computer Vision Systems (2007a)

  • Mure-Dubois, J., Hügli, H.: Optimized scattering compensation for time-of-flight camera. In: Optics East 2007. International Society for Optics and Photonics, pp. 67620H–67620H (2007b)

  • Patil, S.S., Inamdar, V.S.: Multipath mitigation in Time of Flight 3D sensor based on direct and global separation technique. In: Computing, Analytics and Security Trends (CAST), International Conference on, pp. 632-636. IEEE 2016

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Swati S. Patil.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Patil, S.S., Bhade, P.M. & Inamdar, V.S. Depth recovery in time of flight range sensors via compressed sensing algorithm. Int J Intell Robot Appl 4, 243–251 (2020). https://doi.org/10.1007/s41315-020-00130-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41315-020-00130-7

Keywords

Navigation