A common dominant scale emerges from images of diverse satellite platforms using the wavelet transform

Abstract

In this article we investigate the scale dependence of spatial heterogeneity in multiresolution and multisensor data using the wavelet transform. The landscape analysed with the wavelets retains the same dominant pattern irrespective of the original pixel size of the image. In agricultural areas, typically characterized by a mosaic of cultivated fields, the wavelet transform quantified consistently a median dominant scale of 512 m in the Orthophoto, Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) and Landsat Enhanced Thematic Mapper Plus (ETM + ). The dominant scale represented the dominant field size of cultivated areas. The shape of the average wavelet energy curves was also similar among the images. In semi-natural areas the wavelet transform quantified consistently a median dominant scale of 128 m in the Orthophoto and ASTER. The median dominant scale of ETM +  was slightly smaller and located at 64 m. We characterized the spatial heterogeneity of agricultural and semi-natural areas in Andalucía (Spain) using multisensor data not time coincident ranging from 1 m (Orthophoto), to 15 m (ASTER) to 28.5 m (ETM + ). The contrast in vegetation cover was measured using Normalized Difference Vegetation Index (NDVI) in ASTER and ETM +  and red band in Orthophoto. We performed a multiresolution analysis using a Haar two-dimension discrete wavelet transform to quantify and compare the intensity (maximum degree of contrast in vegetation cover), the dominant scale (the scale at which the maximum intensity occurs) and the wavelet energy curve (intensity plotted as a function of the scale) of different images at intervals of power of 2 within the scale range from 2 to 4096 m.

Acknowledgements

This research was funded by the International Institute of Geo-Information Science and Earth Observation (ITC), the Netherlands. The authors would like to thank Willem Nieuwenhuis, who wrote a revised version of the IDL script for the wavelet decomposition of large matrices.