For the most part, shape modelling has focused on modelling families of regions consisting of deviations around a given reference shape with a simple topology. There are applications; however, where the family of regions involved does not show such constrained behaviour. Cases where the number of objects is unknown a priori, or where the topology of the region may be otherwise complex (for example network shapes), require new techniques. 'Higher-order active contours' (HOACs) represent one approach to modelling such families of regions. By introducing explicit long-range interactions between region boundary points, HOACs can model families of regions sharing geometric properties without overly constraining region topology. Representing regions by their boundaries is often inconvenient, however, both analytically and numerically, especially for complex topologies. An alternative is the approach known as 'phase field' modelling. The phase field representation and modelling framework offers a number of advantages, both for the simplest region models and for HOACs. By way of illustration, the use of HOAC and HOAC phase field models to estimate the regions corresponding to road networks and tree crowns in satellite and aerial images will be described.