Higher-order active contour energies for gap closure

One of the main difficulties in extracting line networks from images, and in particular road networks from remote sensing images, is the existence of interruptions in the data caused, for example, by occlusions. These can lead to gaps in the extracted network that do not correspond to gaps in the real network. In this paper, we describe a higher-order active contour energy that in addition to favouring network-like regions, includes a prior term penalizing networks containing 'nearby opposing extremities', thereby making gaps in the extracted network less likely. The new energy term causes such extremities to attract one another during gradient descent. They thus move towards one another and join, closing the gap. To minimize the energy, we develop specific techniques to handle the high-order derivatives that appear in the gradient descent equation. We present the results of automatic extraction of networks from real remote-sensing images, showing the ability of the model to overcome interruptions.