On a recent afternoon in Maracaibo, Venezuela, Alexander Marinez, who has short-cropped black hair and three-to-four-day stubble, sat in front of his computer tracking herbiboars in the mushroom forests on Fossil Island. He pressed down on his glowing mouse, the newest addition to his otherwise timeworn gaming setup. The pixelated character on his computer screen followed the tracks of a hedgehoglike creature with triangular tusks and herbs growing out of its back. Outside Marinez's one-story house, the sun bore down on the dirt road. His home lies about six miles away from the strait that connects the Caribbean Sea with Lake Maracaibo, one of the world's richest sources of oil. The character inspected a tunnel. Suddenly, the herbiboar appeared, and the character attacked, stunning it.

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.