This paper deals with the characterization of the anisotropy of textured images. It is well known that either the dominant direction or the texture anisotropy strongly depends on the scale used for the observation. In this paper we propose a new operator for the estimation of the dominant direction, the Directional Mean Vector (DMV), which can be computed at any observation scale. Then, we present a new indicator for the estimation of the DMV field anisotropy. This indicator, called Iso, is computed at a given observation scale. Iso is based on the computation of the DMV field local differences. It is shown that the evolution of Iso versus the observation scale gives a curve which simultaneously characterizes the anisotropy of the texture and the size of the textural patterns. In order to establish this property, we build a specific texture model which allows to assess an analytical expression for Iso. Finally, Iso is applied to the characterization of various images including synthetic textures, Brodatz textures and composite material images.