The 2D Anisotropic Wavelet Transform (2DAWT) is an image analysis tool which is able to decipher signals where information obtained from different scales are intermixed. Extended from the Optimised Anisotropic Wavelet Coefficient method (OAWC) of Ouillon et al. [1995>, we present a method which discriminates the objects and groups of objects depending on their area, shape ratio, orientation and position. Illustrated in a synthetic example, we show that this method allows one to distinguish between different sub-populations of objects within a single phase, and quantify the anisotropies of shape, orientation and spatial distribution at different scales (objects, clusters of objects, alignments of objects or clusters). Applied to a natural rock sample (Sidobre granite, Montagne Noire, France), the 2DAWT has permitted us to detect and accurately characterise the different levels of mineral organisation, and thus, to contribute to the understanding of the physical processes, such as crystallisation, fluid migration, deformation, etc… responsible for such organisations.¿ 1997 American Geophysical Union