  The $\mathcal{G}_I^0$ distribution is able to characterize different regions
in monopolarized SAR imagery. It is indexed by three parameters: the number of
looks (which can be estimated in the whole image), a scale parameter and a
texture parameter. This paper presents a new proposal for feature extraction
and region discrimination in SAR imagery, using the geodesic distance as a
measure of dissimilarity between $\mathcal{G}_I^0$ models. We derive geodesic
distances between models that describe several practical situations, assuming
the number of looks known, for same and different texture and for same and
different scale. We then apply this new tool to the problems of (i)~identifying
edges between regions with different texture, and (ii)~quantify the
dissimilarity between pairs of samples in actual SAR data. We analyze the
advantages of using the geodesic distance when compared to stochastic
distances.
