Approximate topological matching of quadrilateral meshes

We study approximate topological matching of 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 shape modeling whose results need 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 in NP-hard. Given this result, which makes 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 non-matching quads. Nevertheless, we provide a "lazy-greedy" algorithm that is guaranteed to find good matches when mis-matching portions of mesh are localized. Finally, we provide empirical evidence that this approach produces good matches between similar quad meshes.