Identifying the characteristic scale of scene variation in fine spatial resolution imagery with wavelet transform-based sub-image statistics

Understanding the spatial structure of fine spatial resolution images is instrumental for either pixel- or object-based image analysis. In this Letter, the characteristic scale of scene variation in images is evaluated using statistics of sub-images produced by a wavelet transform. Six statistics, namely mean, variance, standard deviation (SD), coefficient of variation, skewness and kurtosis, were calculated for three directional sub-images and their derivative energy signature image at a sequence of wavelet decomposition levels. A simulated image, an aerial AUSIMAGE™ image (spatial resolution 0.2 m) and a recent Système Probatoire de l'Observation de la Terre (SPOT)-5 High Resolution Geometric (HRG) panchromatic image (spatial resolution 2.5 m) were analysed. It was found that with energy signature images, the change rate of SD over spatial resolution ranges between two successive decomposition levels ( ( SD/ ( R) suggested a synoptic and approximate description for the characteristic scale of scene variation. However, by comparing the result with the ranges of geostatistical variograms, it is suggested that the geostatistical method can correctly identify the characteristic scales of scene variation; semivariances can be calculated at any lag and orientation, while standard wavelet transforms are decomposed at only limited spatial resolution and orientation levels.