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

M. Kalbermatten1, D. Van De Ville2, S. Joost1, M. Unser2 , F. Golay1
1 Ecole Polytechnique Fédérale de Lausanne (EPFL), GIS laboratory, Station 18, 1015 Lausanne, Switzerland
Telephone (+41) 21 693 57 83
Fax: (+41) 21 693 57 90
Email: {michael.kalbermatten, stephane.joost, francois.golay}
2 Ecole Polytechnique Fédérale de Lausanne (EPFL), Biomedical Imaging Group, Station 17, 1015 Lausanne, Switzerland
Telephone: (+41) 21 693 51 42
Fax: (+41) 21 693 37 01
Email: {dimitri.vandeville, michael.unser}

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.

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