Shape simplification through graph sparsification

In this paper, we draw on Spielman and Srivastava's method for graph sparsification in order to simplify shape representations. The underlying principle of graph sparsification is to retain only the edges which are key to the preservation of desired properties. In this regard, sparsification by edge resistance allows us to preserve (to some extent) links between protrusions and the remainder of the shape (e.g. parts of a shape) while removing in-part edges. Applying this idea to alpha shapes (abstract representations which have a huge number of edges) opens up a way of introducing a hierarchy of the edge strength, thus being relevant for shape analysis and interpretation.