Extended Phase Field Higher-Order Active Contour Models for Networks
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The representation and modelling of regions is an important topic in computer vision. In this paper, we represent a region via a level set of a 驴phase field驴 function. The function is not constrained, e.g. to be a distance function; nevertheless, phase field energies equivalent to classical active contour energies can be defined. They represent an advantageous alternative to other methods: a linear representation space; ease of implementation (a PDE with no reinitialization); neutral initialization; greater topological freedom. We extend the basic phase field model with terms that reproduce 驴higher-order active contour驴 energies, a powerful way of including prior geometric knowledge in the active contour framework via nonlocal interactions between contour points. In addition to the above advantages, the phase field greatly simplifies the analysis and implementation of the higher-order terms. We define a phase field model that favours regions composed of thin arms meeting at junctions, combine this with image terms, and apply the model to the extraction of line networks from remote sensing images.