Active vector graph for regularized tesselation

A discretized parametric curve can be seen as a sparse graph of vectors where each vertex is linked to two other vertices. Following this observation, we propose to generalize parametric active contours to a larger framework we call active vector graphs. This can be achieved by allowing each vertex of a graph of vectors to be linked to more than two vertices. An active graph does not need to be parameterized and the computation of its energy can be achieved by integrating over all its vertices. The optimization scheme pushes the graph toward the edges and in the direction of the normal which we show can be defined for all vertices. This offers a regularized model which addresses in an elegant and very fast way a certain set of problems such as the segmentation of connected regions. The method is described along with an example.