Extended phase field higher-order active contour models for networks

Abstract. This paper addresses the segmentation from an image of entities that have the form of a ‘network’, i.e. the region in the image corresponding to the entity is composed of branches joining together at junctions, e.g. road or vascu-lar networks. We present a new phase field higher-order active contour (HOAC) prior model for network regions, and apply it to the segmentation of road net-works from very high resolution satellite images. This is a hard problem for two reasons. First, the images are complex, with much ‘noise ’ in the road region due to cars, road markings, etc., while the background is very varied, contain-ing many features that are locally similar to roads. Second, network regions are complex to model, because they may have arbitrary topology. In particular, we address a severe limitation of a previous model in which network branch width was constrained to be similar to maximum network branch radius of curvature, thereby providing a poor model of networks with straight narrow branches or highly curved, wide branches. To solve this problem, we propose a new HOAC prior energy term, and reformulate it as a nonlocal phase field energy. We anal-yse the stability of the new model, and find that in addition to solving the above problem by separating the interactions between points on the same and opposite sides of a network branch, the new model permits the modelling of two widths simultaneously. The analysis also fixes some of the model parameters in terms of network width(s). After adding a likelihood energy, we use the model to ex-tract the road network quasi-automatically from pieces of a QuickBird image, and compare the results to other models in the literature. The results demonstrate the superiority of the new model, the importance of strong prior knowledge in general, and of the new term in particular.