Connect the dots: The reconstruction of region boundaries from contour sampling points

Abstract

Twodimensional contour reconstruction from a set of points is a very common problem not only in computer vision. I.e. in graph theory one may ask for the minimal spanning tree or the shortest Hamiltonian graph. In psychology the question arises under which circumstances people are able to recognize certain contours given only a few points. In the context of discrete geometry, there exist a lot of algorithms for 2D contour reconstruction from sampling points. Here a commonly addressed problem is to define an algorithm for which it can be proved that the reconstuction result resembles the original contour if this has been sampled according to certain density criteria. Most of these algorithms can not properly deal with background noise like humans can do. This paper gives an overview of the most important algorithms for contour reconstruction and shows that a relatively new algorithm, called 'cleaned refinement reduction' is the most robust one with regard to significant background noise and even shows a reconstruction ability being similar to the one of a child at the age of 4. © 2012 Springer-Verlag.