Hierarchical Structure Recovery of Point-Sampled Surfaces

We focus on the class of 'regular' models defined by Varady et al. for reverse engineering purposes. Given a 3D surface M represented through a dense set of points, we present a novel algorithm that converts M to a hierarchical representation HM. In HM, the surface is encoded through patches of various shape and size, which form a hierarchical atlas. If M belongs to the class of regular models, then HM captures the most significant features of M at all the levels of detail. In this case, we show that HM can be exploited to interactively select regions of interest onMand intuitively re-design the model. Furthermore, HM intrinsically encodes a hierarchy of useful 'segmentations' of M. We present a simple though efficient approach to extract and optimize such segmentations, and we show how they can be used to approximate the input point sets through idealized manifold meshes.