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Laplace-Gradient Wavelet Pyramid and Multiscale Tensor Structures Applied on High-Resolution DEMs

M. Kalbermatten, D. Van De Ville, S. Joost, M. Unser, F. Golay

Proceedings of Geomorphometry 2009 (G'09), Zürich ZH, Swiss Confederation, August 31-September 2, 2009, pp. 124-132.

Wavelet decompositions are a powerful tool for multiscale image analysis. Their use in DEMs (Digital Elevation Models) analysis is still limited. Nevertheless, some researchers (de Boer 1992, Wilson & Gallant 2000) demonstrated that scale and structure play an important role to determine the elementary shape of landscape features. Wavelets are ideally localized functions fulfilling that condition (Mahler 2001, Gallant & Hutchinson 1996).

Wavelet analysis of high-resolution (1-meter) DEMs is highly complementary to morphometric indicators (Wood 1996); e.g., applications include multiscale filtering and enhancement. Here, we introduce various methods using wavelets and structure tensors in order to show the multiscale nesting of landscape features. The method was applied on a DEM including a well-known landslide, and the results were compared to an ordinary geomorphological analysis. The aim is to show the potential of this method and to give hints for further development of such tools in terrain analysis systems.


  1. D.H. de Boer, "Hierarchies and Spatial Scale in Process Geomorphology: A Review," Geomorphology, vol. 4, no. 5, pp. 303-318, March 1992.

  2. J.P. Wilson, J.C. Galant, Terrain Analysis: Principles and Applications, John Wiley & Sons, 479 p., 2000.

  3. E. Mahler, "Scale-Dependent Filtering of High Resolution Digital Terrain Models in the Wavelet Domain," MSc. Thesis, Department of Geography, University of Zürich, Switzerland, 2001.

  4. J.C. Gallant, M.F. Hutchinson, "Towards an Understanding of Landscape Scale and Structure," Third International Conference/Workshop on Integrating GIS and Environmental Modeling, Santa Fe CA, USA, January 21-25, 1996.

  5. J. Wood, "The Geomorphological Characterisation of Digital Elevation," PhD. Thesis, City University London, UK, 1996.

AUTHOR="Kalbermatten, M. and Van De Ville, D. and Joost, S. and Unser,
        M. and Golay, F.",
TITLE="Laplace-Gradient Wavelet Pyramid and Multiscale Tensor Structures
        Applied on High-Resolution DEMs",
BOOKTITLE="Proceedings of Geomorphometry 2009 ({G'09})",
address="Z{\"{u}}rich ZH, Swiss Confederation",
month="August 31-September 2,",

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