Detecting undersampling in surface reconstruction

Current surface reconstruction algorithms perform satisfactorily on we ll-sampled, smooth surfaces without boundaries. However, these algorithms face difficulty with undersampling. Cases of undersampling are prevalent in real data since often they sample a part of the boundary of an object, or are derived from a surface with high curvature or nonsmoothness. In this paper we present an algorithm to detect the boundaries where dense sampling stops and undersampling begins. This information can be used to reconstruct surfaces with boundaries, and also to localize small and sharp features where usually undersampling happens. We report the effectiveness of the algorithm with a number of experimental results. Theoretically, we justify the algorithm with some mild assumptions that are valid for most practical data.