Characterising local spatial variation in land cover using geostatistical functions and the discrete wavelet transform

Abstract

In this paper, texture in an airborne multispectral image from south eastern England is characterised using the local variance, local semivariance and local variogram range. Local variation in these texture measures is then expressed as images and using the global histogram. The images and histogram are then used to question approaches for defining a single spatial resolution based on the mean of statistics such as the local variance. As a second component of the analysis, the discrete wavelet transform (DWT) is applied to the image and the amount of energy in each sub-image is quantified. Several authors realised in the late 1980s that choice of spatial resolution for remotely sensed imagery should be based on the scale of spatial variation in the property of interest or, more generally, scene of interest. Specifically, Woodcock and Strahler (1987) identified two general classes of interaction between spatial resolution and scale of spatial variation: (i) the L-resolution case in which the variation or objects are not resolved and (ii) the H-resolution case in which the continua or objects are resolved. Depending on the objective (e.g., to produce a thematic map of land cover) and the method of analysis (e.g., hard classification, area proportions prediction) a suitable spatial resolution could be chosen based on the scale(s) of spatial variation in the scene. The average local variance has been used previously to help select a suitable spatial resolution (Woodcock and Strahler 1987; Jupp et al. 1988, 1989)._The average local variance vw 2 may be estimated from a moving (3 by 3) window w applied to an image of L rows by M columns of pixels with support v using: