Abstract

Images play many vital roles today: satellite images in environmental and climate studies; MRI imagery in medicine; microscope images in cell biology. Increasing data volume means that the automatic extraction of information from these images is essential if the potential of the data is to be realized. Many of the key problems involve shape, for example `segmentation’: the delineation of a specified entity in the image. Shape modelling is thus a crucial ingredient of automatic inference methods.

For the most part, work has focused on families of shapes consisting of perturbations of a given reference shape with a simple topology. There are applications, however, where the family of shapes involved does not have such a constrained behaviour. Cases where the number of individual objects is unknown a priori, or where the topology of the shape may be otherwise complex (for example network shapes), require new techniques.

I will begin by describing the ‘higher-order active contour’ (HOAC) framework. By introducing explicit long-range interactions between shape boundary points, HOA Cs can model families of shapes sharing geometric properties without overly constraining topology. The representation of complex shapes by their boundaries is, however, often inconvenient, despite its intuitive nature. The alternative, ‘phase field’ representation offers a number of advantages without loss of expressive power. In particular, phase field equivalents of HOA Cs can be constructed. Phase fields also facilitate the translation of models to a third useful representation, binary Markov random fields, simplifying sampling and annealing.

I will present several models developed within this framework, in particular models of network shapes and of a ‘gas of near-circles’, and will describe applications to the segmentation of road networks and tree crowns from satellite and aerial images, and cells from microscopic images.