Journal of Geographical Systems

, Volume 7, Issue 3–4, pp 273–290 | Cite as

Smoothing/filtering LiDAR digital surface models. Experiments with loess regression and discrete wavelets

  • Nicholas J. Tate
  • Chris Brunsdon
  • Martin Charlton
  • A. Stewart Fotheringham
  • Claire H. Jarvis
Original Article


This paper reports on the smoothing/filtering analysis of a digital surface model (DSM) derived from LiDAR altimetry for part of the River Coquet, Northumberland, UK using loess regression and the 2D discrete wavelet transform (DWT) implemented in the S-PLUS and R statistical packages. The chosen method of analysis employs a simple method to generate ‘noise’ which is then added to a smooth sample of LiDAR data; loess regression and wavelet methods are then used to smooth/filter this data and compare with the original ‘smooth’ sample in terms of RMSE. Various combinations of functions and parameters were chosen for both methods. Although wavelet analysis was effective in filtering the noise from the data, loess regression employing a quadratic parametric function produced the lowest RMSE and was the most effective.


Digital surface model LiDAR data 



The LiDAR dataset was kindly supplied by the National Centre for Environmental Data and Surveillance, Environment Agency, Bath. We are grateful to Andrew Large and Malcolm Newson of the University of Newcastle, and Ian Fuller of Massey University New Zealand for collaboration on an earlier stage of this research. Thanks are also extended to Professor Michael Goodchild for permission for the use of his image in Fig. 2, the Cartography Unit at the Department of Geography University of Leicester for preparing Figs. 2 and 3, and the anonymous referees for some useful suggestions that improved the paper.


  1. Abramovich F, Bailey TC, Sapatinas T (2000) Wavelet analysis and its statistical applications. The Statistician 49(1):1–29Google Scholar
  2. Albani M, Klinkenberg B (2003) A spatial filter for the removal of striping artifacts in digital elevation models. Photogram Eng Remote Sens 63:755–766Google Scholar
  3. Argenti F, Alparone L (2002) Speckle removal from SAR images in the undecimated wavelet domain. IEEE Trans Geosci Remote Sens 40(11):2363–2374CrossRefGoogle Scholar
  4. Atkinson PM (2001) Geographical Information Science: Geocomputation and non-stationarity. Prog Phys Geogr 25(1):111–122CrossRefGoogle Scholar
  5. Bjørke JT, Nilsen S (2003) Wavelets applied to simplification of digital terrains. Int J Geogr Inf Sci 17(7):601–621CrossRefGoogle Scholar
  6. Bruce A, Gao H-Y (1995) Applied wavelet analysis with S-PLUS. Springer, Berlin, Heidelberg, New YorkGoogle Scholar
  7. Charlton ME, Large ARG, Fuller IC (2003) Application of airborne LiDAR in river environments: the River Coquet, Northumberland, UK. Earth Sur Land 28:299–306CrossRefGoogle Scholar
  8. Cleveland WS, Loader CL (1996) Smoothing by local regression: principles and methods. In: Haerdle W, Schimek MG (eds) Statistical theory and computational aspects of smoothing. Springer, Berlin Heidelberg, New York, pp 10–49Google Scholar
  9. Cleveland WS, Grosse E, Shyu WM (1992) Local regression models. In: Chambers JM, Hastie TJ (eds) Statistical models in S. Chapman and Hall, New York, pp 309–376Google Scholar
  10. Csillag F, Kabos S (2002) Wavelets, boundaries and the spatial analysis of landscape pattern. Ecoscience 9(2):177–190Google Scholar
  11. Dai M, Peng C, Chan AK, Loguinov D (2004) Bayesian wavelet shrinkage with edge detection for SAR image despeckling. IEEE Trans Geosci Remote Sens 42(8):1642–1648CrossRefGoogle Scholar
  12. Daubechies I (1992) Ten lectures on wavelets. Society for Industrial and Applied Mathematics, PhiladelphiaGoogle Scholar
  13. Davis GM, Nosratinia A (1999) Wavelet-based image coding: an overview. In: Datta BN (ed) Applied and computational control, signals, and circuits vol. 1. Birkhauser, Boston, pp 205–269Google Scholar
  14. Donoho DL, Johnstone IM (1995) Adapting to unknown smoothness via wavelet shrinkage. J Am Stat Assoc 90:1200–1224CrossRefGoogle Scholar
  15. Dubayah R, Knox R, Hofton M, Blair JB, Drake J (2000) Land surface characterization using lidar remote sensing. In: Hill M, Aspinall R (eds) Spatial information for land use management. International Publishers Direct, Singapore, pp 25–38Google Scholar
  16. Fukuda S, Hirosawa H (1998) Suppression of speckle in synthetic aperture radar images using wavelet. Int J Remote Sens 19(3):507–519CrossRefGoogle Scholar
  17. Gallant JC, Hutchinson MF (1997) Scale dependence in terrain analysis. Math Comput Simul 43:313–321CrossRefGoogle Scholar
  18. Graps A (1995) An introduction to wavelets. IEEE Comput Sci Eng 2(2):50–61CrossRefGoogle Scholar
  19. Hubbard BBH (1996) The world according to wavelets: the story of a mathematical technique in the making. Mass: A. Peters, WellesleyGoogle Scholar
  20. Huising EJ, Gomes-Pereira LM (1998) Errors and accuracy estimates of laser data acquired by various laser scanning systems for opographic applications. ISPRS J Photogram Remote Sens 53:245–261CrossRefGoogle Scholar
  21. Jiang XQ, Blunt L, Stout KJ (2000) Development of a lifting wavelet representation for surface characterization. In: Proceedings of the royal society of London A 456:2283–2313Google Scholar
  22. Kumar P, Foufoula-Georgiou E (1997) Wavelet analysis for geophysical applications. Rev Geophys 35(4):385–412CrossRefGoogle Scholar
  23. Lark RM, Webster R (1999) Analysis and elucidation of soil variation using wavelets. Eur J Soil Sci 50:185–206CrossRefGoogle Scholar
  24. Lark RM, Webster R (2004) Analysing soil variation in two dimensions with the discrete wavelet transform. Eur J Soil Sci 55:777–797CrossRefGoogle Scholar
  25. Lillesand TM, Kiefer RW, Chipman JW (2004) Remote sensing and image interpretation. Wiley, New YorkGoogle Scholar
  26. Lòpez C (2002) An experiment on the elevation accuracy improvement of photogrammetrically derived DEM. Int J Geogr Inf Sci 16:361–375CrossRefGoogle Scholar
  27. Mallat SG (1989) A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans Pattern Anal Mach Intell 11:674:693CrossRefGoogle Scholar
  28. McArthur DE, Fuentes RW, Devarajan V (2000) Generation of hierarchical multiresolution terrain databases using wavelet filtering. Photogram Eng Remote Sens 66(3):287–295Google Scholar
  29. Morehart M, Murtagh F, Starck J-L (1999) Spatial representation of economic and financial measures used in agriculture via wavelet analysis. Int J Geogr Inf Sci 13(6):557–576CrossRefGoogle Scholar
  30. Myers DE (1989) To be or not to be... stationary? That is the question. Math Geol 21:347–362CrossRefGoogle Scholar
  31. Newson MD (2005) Environmental capital: strategic and operational guide to the River Coquet Northumberland and additional experiences from the River Wharfe. J Environ Plan Manage (in press)Google Scholar
  32. Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in fortran 77: the art of scientific computing. Cambridge University Press, CambridgeGoogle Scholar
  33. Rosenberg MS (2004) Wavelet analysis for detecting anisotropy in point patterns. J Veg Sci 15:277–284CrossRefGoogle Scholar
  34. Schmidt J, Evans IS, Brinkmann J (2003) Comparison of polynomial models for land surface curvature calculation. Int J Geogr Inf Sci 17(8):797–814CrossRefGoogle Scholar
  35. Stein C (1981) Estimation of the mean of a multivariate normal distribution. Ann Stat 9:1135–1151CrossRefGoogle Scholar
  36. Strang G (1994) Wavelets. Am Sci 82:250–255Google Scholar
  37. Taswell C (2000) The what how and why of wavelet shrinkage denoising. Comput Sci Eng 2(3):12–19CrossRefGoogle Scholar
  38. Taubman DS, Marcellin MW (2001) JPEG200: image compression fundamentals, standards and practice. Kluwer, DordrechtGoogle Scholar
  39. Wahba G (1975) Smoothing noisy data by spline functions. Numer Math 24:383–393CrossRefGoogle Scholar
  40. Wang Z (1998) Applying two-dimensional Kalman filtering techniques to digital elevation models for terrain surface modelling. In: Fritsch D, Englich M, Sester M (eds) ISPRS commission iv symposium on GIS—between visions and applications, International Archives of Photogrammetry and Remote Sensing vol. 32/4 Stuttgart Germany pp 649–656Google Scholar
  41. Wang Z, Trinder J (2002) Wavelet transform based noise removal for terrain surface modelling. The 11th Australasian remote sensing and photogrammetry association conference. Brisbane, Australia, pp 877–884Google Scholar
  42. Wehr A, Lohr U (1999) Airborne laser scanning—an introduction and overview. ISPRS J Photogram Remote Sens 54:68–82CrossRefGoogle Scholar
  43. Whitcher B (2004) Software, Retrieved 12 December 2004 from
  44. Wood JD (1996) The geomorphological characterisation of digital elevation models. Department of Geography, University of Leicester, UKGoogle Scholar
  45. Wood JD (1998) Modelling the continuity of surface form using digital elevation models. In: Poiker T, Chrisman N (eds) Proceedings of the 8th international symposium on spatial data handling. pp 725–36Google Scholar
  46. Zatelli P, Antonello A (2002) New GRASS modules for multiresolution analysis with wavelets. In: Proceedings of the open source GIS-GRASS users conference 2002, Trentino, Italy, 11–13 September 2002 pp 1–27Google Scholar

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  • Nicholas J. Tate
    • 1
  • Chris Brunsdon
    • 2
  • Martin Charlton
    • 3
  • A. Stewart Fotheringham
    • 3
  • Claire H. Jarvis
    • 1
  1. 1.Department of GeographyUniversity of LeicesterLeicesterUK
  2. 2.School of ComputingUniversity of GlamorganPontypriddUK
  3. 3.National Centre for GeocomputationNational University of IrelandMaynoothIreland

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