This paper explores a geometrical and computationally simple operator, named Ds, for local isotropy assessment on SAR images. It is assumed that isotropic intensity distributions in natural areas, either textured or nontextured, correspond to a single cover class. Ds is used to measure isotropy in processing neighborhoods and decide if they can be considered as belonging to a unique cover class. The speckle statistical properties are used to determine suitable Ds thresholds for discriminating heterogeneous targets from isotropic cover types at different window sizes. An assessment of Ds as an edge detector showed sensitivities similar to those of the ratio edge operator for straight, sharp boundaries, centered in the processing window, but significantly better sensitivity for detecting heterogeneities during the window expansion in multiresolution filtering. Furthermore, Ds presents the advantage versus the ratio edge coefficient of being rotationally invariant, and its computation indicates the direction of the main intensity gradient in the processing window. The Ds operator is used in a multiresolution fashion for filtering ASAR scenes of the Doñana wetland. The intensities in isotropic areas are averaged in order to flatten fluctuations within cover types and facilitate a subsequent land cover classification. The results show high degree of smoothing within textured cover classes, plus effective spatial adaptation to gradients and irregular boundaries, substantiating the usefulness of this operator for filtering SAR data of natural areas with the purpose of classification.