Advertisement

Journal of the Indian Society of Remote Sensing

, Volume 47, Issue 1, pp 165–175 | Cite as

Rational Polynomial Coefficients Modeling and Bias Correction by Using Iterative Polynomial Augmentation

  • Bhaskar DubeyEmail author
  • B. Kartikeyan
  • Manthira Moorthi Subbiah
Research Article
  • 32 Downloads

Abstract

In this article, we establish an update procedure for rapid positioning coefficients or rational polynomial coefficients (RPCs) via iterative refinements using polynomial augmentation and reference images. RPCs are widely popular in establishing a ground-to-image relationship without using physical sensor model. However, the accuracies of RPCs are degraded due to unavoidable errors in physical sensor model based on colinearity conditions. These inaccuracies essentially arise due to undulating terrain, residual errors in attitude parameters, viz. roll, pitch and yaw, inexact modeling of drift and micro-vibration, orbit error, etc. In the paper, first an initial estimate of RPCs is obtained by using \(L^2\)-regularized least square estimation. Subsequently, the RPCs are refined by using iterative affine augmentation. The RPC accuracy is further improved by a second-order polynomial augmentation. The results show that with the improved RPCs the average scan and pixel errors are within 0.5 pixel. The results of the paper are employed and validated on Resourcesat-2 imagery.

Keywords

Rational function model Bias compensation RPC refinement Ground control points (GCPs) 

Notes

Acknowledgements

The authors would like to thank Director Space Applications Centre, Ahmedabad, for his support and encouragement toward this work. Authors further thank Group Director, Signal and Image Processing Group, Space Applications Centre, Ahmedabad, for unabated support and keen interest in the study. Support from IAQD and ODPD team members is thankfully acknowledged. We sincerely express our gratitude to anonymous reviewers for their valuable comments that resulted in the current form of the paper.

References

  1. Di, K., Ma, R., & Li, R. (2003). Rational functions and potential for rigorous sensor model recovery. Photogrammetric Engineering and Remote Sensing, 69, 33–41.CrossRefGoogle Scholar
  2. Diala, G., & Grodecki, J. (2005). RPC replacement camera models. The International Archives of Photogrammetry, Remote Sensing, and Spacial Information Science, 34, 1–9.Google Scholar
  3. Dowman, I., & Dolloff, J. (2000). An evaluation of rational functions for photogrammetric restitution. International Archives of Photogrammetric Engineering and Remote Sensing, 33(B3), 254–266.Google Scholar
  4. Dowman, I., & Tao, V. (2002). An update on the use of rational functions for photogrammetric restitution. ISPRS Highlights, 7(3), 22–29.Google Scholar
  5. Dubey, B., & Kartikeyan, B., (2018). A novel approach for estimation of residual attitude of a remote-sensing satellite. International Journal of Remote Sensing.  https://doi.org/10.1080/01431161.2018.1483086.
  6. Eftekhari, A., Saadatseresht, M., & Motagh, M. (2013). A study on rational functional model generation. Sensors, 13(9), 12030–12043.CrossRefGoogle Scholar
  7. Fraser, C., Dial, G., & Grodecki, J. (2006). Sensor orientation via RPCS. ISPRS Journal of Photogrammetry and Remote Sensing, 60(3), 182–194.CrossRefGoogle Scholar
  8. Fraser, C., & Hanley, H. (2003). Bias compensation in rational functions for IKONOS satellite imagery. Photogrammetric Engineering and Remote Sensing, 69(1), 53–57.CrossRefGoogle Scholar
  9. Fraser, C., & Hanley, H. (2005). Bias-compensated RPCS for sensor orientation of high-resolution satellite imagery. Photogrammetric Engineering and Remote Sensing, 71(8), 909–915.CrossRefGoogle Scholar
  10. Grodecki, J., & Gene, D. (2003). Block adjustment of high-resolution satellite images described by rational polynomials. Photogrammetric Engineering and Remote Sensing, 69(1), 59–68.CrossRefGoogle Scholar
  11. Hoffman, K., & Kunze, R. (1961). Linear algebra. Upper Saddle River: Prentice-Hall.Google Scholar
  12. Koh, K., Kim, S., & Boyd, S. (2007). An interior-point method for large scale regularized logistic regression. Journal of Machine Learning Research, 8, 1519–1555.Google Scholar
  13. Long, T., Jiao, W., & He, G. (2015). RPC estimation via \(l_{1}\)-norm-regularized least squares. IEEE Transaction on Geoscience and Remote Sensing, 53(8), 4554–4566.CrossRefGoogle Scholar
  14. Maras, E. (2015). Improved non-parametric geometric corrections for satellite imagery through co-variance constraints. Journal of Indian Society of Remote Sensing, 43(1), 19–26.CrossRefGoogle Scholar
  15. Sekhar, K., Kumar, A. S., & Dadhwal, V. K. (2014). Geocoding RISAT-1 MRS images using bias-compensated RPC models. International Journal of Remote Sensing, 35(20), 7303–7315.CrossRefGoogle Scholar
  16. Shen, X., Li, Q., Wu, G., & Zhu, J. (2017a). Bias compensation for rational polynomial coefficients of high resolution satellite imagery by local polynomial modeling. Remote Sensing.  https://doi.org/10.3390/rs9030200.
  17. Shen, X., Liu, B., & Li, Q. (2017b). Correcting bias in the rational polynomial coefficients of satellite imagery using thin-plate smoothing splines. ISPRS Journal of Photogrammetry and Remote Sensing, 125(137), 125–131.CrossRefGoogle Scholar
  18. Singh, M., Gupta, R., Snehmani, B. A., & Ganju, A. (2016). Effect of sensor modelling methods on computation of 3-d coordinates from cartosat-1 stereo data. Geocarto International, 31(5), 506–526.CrossRefGoogle Scholar
  19. Singh, S., Naidu, S., Srinivasan, T., Krishna, B., & Srivastava, P., (2008). Rational polynomial modelling for cartosat-1 data. In International archives of the photogram. Remote sensing and spacial information science. ISPRS, Beiging, part B1.Google Scholar
  20. Tao, C. (2001). A comprehensive study of the rational function model for photogrammetric processing. Photogrammetric Engineering and Remote Sensing, 67(12), 1347–1357.Google Scholar
  21. Xiong, Z., & Zhang, Y. (2009). A generic method for RPC refinement using ground control information. Photogrammetric Engineering and Remote Sensing, 75(9), 1083–1092.CrossRefGoogle Scholar

Copyright information

© Indian Society of Remote Sensing 2018

Authors and Affiliations

  • Bhaskar Dubey
    • 1
    Email author
  • B. Kartikeyan
    • 1
  • Manthira Moorthi Subbiah
    • 2
  1. 1.Image Analysis and Quality Evaluation Division, Space Applications CentreIndian Space Research OrganizationAhmedabadIndia
  2. 2.Optical Data Processing Division, Space Applications CentreIndian Space Research OrganizationAhmedabadIndia

Personalised recommendations