A Compact Representation for Topological Decompositions of Non-manifold Shapes

Simplicial complexes are extensively used for discretizing digital shapes in several applications. A structural description of a non-manifold shape can be obtained by decomposing the input shape into a collection of meaningful components with a simpler topology. Here, we consider a unique and dimension-independent decomposition of a non-manifold shape into nearly manifold components, known as the Manifold-Connected (MC-) decomposition. We present the Compact Manifold-Connected (MC-) graph, an efficient graph-based representation for the MC-decomposition, which can be combined with any topological data structure for encoding the underlying components. We present the main properties of this representation as well as algorithms for its generation. We also show that this representation is more compact than several topological data structures, which do not explicitly describe the non-manifold structure of a shape.