Extracting geometric models through constraint minimization

The authors propose a methodology that will extract a topologically closed geometric model from a two-dimensional image. This is accomplished by starting with a simple model that is already topologically closed and deforming the model, based on a set of constraints, so that the model grows (shrinks) to fit the feature within the image while maintaining its closed and locally simple nature. The initial model is a non-self-intersecting polygon that is either embedded in the feature or surrounds the feature. There is a cost function associated with every vertex that quantifies its deformation, the properties of simple polygons, and the relationship between noise and feature. The constraints embody local properties of simple polygons and the nature of the relationship between noise and the features in the image