A Survey on Shape Representations

Abstract

Geometric structures have an important role in shape analysis. The reconstruction problem is an active and challenging problem due to its ill-posed nature. It has various applications in the fields of computational geometry, computer vision, computer graphics, image processing, medical fields, and pattern recognition. There exist a few challenges in approximating the shape of a point set. First, it is unclear that which geometric shape approximates the optimal shape due to mathematical inconvenience. Second, the point set shapes are highly subjective and often depend on a specific application context or other human cognitive factors. As a consequence, the shapes perceived by humans for a majority of point sets vary and reaching a conclusion on the optimum shape is an extremely difficult task. The rich variety of shapes available in nature and the heterogeneity of point sets further weaken a well-defined formulation of the shape approximation problem.