Abstract : We address the problem of quasi-automatic extraction of directed networks, which have characteristic geometric features, from images. To include the necessary prior knowledge about these geometric features, we use a phase field higher-order active contour model of directed networks. The model has a large number of unphysical parameters (weights of energy terms), and can favour different geometric structures for different parameter values. To overcome this problem, we perform a stability analysis of a long, straight bar in order to find parameter ranges that favour networks. The resulting constraints necessary to produce stable networks eliminate some parameters, replace others by physical parameters such as network branch width, and place lower and upper bounds on the values of the rest.We validate the theoretical analysis via numerical experiments, and then apply the model to the problem of hydrographic network extraction from multi-spectral VHR satellite images.