In this paper we propose a framework of constructing and using a shape prior in estimation problems. The key novelty of our technique is a new way to use high level, global shape knowledge to derive a local driving force in a curve evolution context. We capture information about shape in the form of a family of shape distributions (cumulative distribution functions) of features related to the shape. We design a prior objective function that penalizes the differences between model shape distributions and those of an estimate. We incorporate this prior in a curve evolution formulation for function minimization. Shape distribution-based representations are shown to satisfy several desired properties, such as robustness and invariance. They also have good discriminative and generalizing properties. To our knowledge, shape distribution-based representations have only been used for shape classification. Our work represents the development of a tractable framework for their incorporation in estimation problems. We apply our framework to three applications: shape morphing, average shape calculation, and image segmentation.