We describe in this paper a new global approach to characterize the geometry of the root system area from black-and-white silhouettes. We introduce a covering polygon composed of two superimposed quadrangles to evaluate geometry features or to classify the growth strategy of root systems: the convex hull of the root system is progressively reduced to a double-quadrangle-shaped polygon by iterative suppression of least significant vertices to only keep the major geometry features. The root system density is addressed by the analysis of the hole distribution. The root system porosity is estimated from the decomposition of background regions in circular elements. An automated repartition of circular elements by 2-means clustering is introduced for a best appreciation of macro- and micro-holes, respectively associated to the anchorage and nutrient recovery potentials. The global parameters of the root system are evaluated from the geometry and density properties of the double-quadrangle-shaped polygon. The experimental studies address the sensitivity of the double-quadrangle-shaped polygon, especially the evaluation of the geometrical stability of the polygon according to slight variations of the root system segmentation. Several experiments, performed using a representative set composed of 100 root system silhouettes of several species - arabidopsis, chick pea, palm tree, rice, sorghum, and wheat - at different stages of growth, underline the robustness of the shape parameters, especially the upper and lower penetration angles.