Approximate topological matching of quad meshes
In this paper, we study the problem of approximate topological matching for quadrilateral meshes, that is, the problem of finding as large a set as possible of matching portions of two quadrilateral meshes. This study is motivated by applications in graphics that involve the modeling of different shapes that have results needing to be merged in order to produce a final unified representation of an object. We show that the problem of producing a maximum approximate topological match of two quad meshes is NP-hard and that its decision version is NP-complete. Given these results, which make an exact solution extremely unlikely, we show that the natural greedy algorithm derived from polynomial-time graph isomorphism can produce poor results, even when it is possible to find matches with only a few nonmatching quads. Nevertheless, we provide a "lazy-greedy" algorithm that is guaranteed to find good matches when mismatching portions of mesh are localized. Finally, we provide empirical evidence that this approach produces good matches between similar quad meshes.
topological matching quad mesh np-hard isomorphism np-complete lazy-greedy heuristic