We present a novel method for the incorporation of shape information into active contour models, and apply it to the extraction of line networks (e.g. road, water) from satellite imagery. The method is based on a new class of contour energies. These energies are quadratic on the space of one-chains in the image, as opposed to classical energies, which are linear. They can be expressed as double integrals on the contour, and thus incorporate non-trivial interactions between different contour points. The new energies describe families of contours that share complex geometric properties, without making reference to any particular shape. Networks fall into such a family, and to model them we make a particular choice of quadratic energy whose minima are reticulated. To optimize the energies, we use a level set approach. The forces derived from the new energies are non-local however, thus necessitating an extension of standard level set methods. Promising experimental results are obtained using real images
