Shape-extraction for curves using geometry-driven diffusion and functional optimization

In this paper we show how both geometry-driven diffusion and optimization of the Mumford-Shah functional can be used to develop a type of curve-evolution that is able to preserve salient features of closed curves (such as corners and straight line segments), while simultaneously suppressing noise and irrelevant details. The idea is to characterize the curve by means of its angle-function (i.e. the angle between the tangent and a fixed axis) and to apply the appropriate dynamics to this one-dimensional representation. We show how constrained evolution equations can be used to keep the corresponding curve closed at all times