Non local point set surfaces

We introduce a non local point set surface model for mesh less geometry processing. Compared to previous approaches, our model better preserves features by exploiting self-similarities present in natural and man-made 3D shapes. The basic idea is to decompose 3D samples into scalar displacements over a coarse smooth domain. Then, considering the displacement field stemming from the local neighboring set of a given point, we collect similar functions over the entire model and define a specific displacement value for the point by the mean of similarity-based weighted combination of them. The underlying scale-space decomposition allows for a wide range of similarity metrics, while scalar displacements simplify rotation-invariant registration of the local sample sets. Our contribution is a non local extension of all previous point set surface models, which (i) improves feature preservation by exploiting self-similarities, iif present, and (ii) boils down to the underlying (local) point set surface model, when self-similarities are not strong enough. We evaluate our approach against state-of-the-art point set surface models and demonstrate its ability to better preserve details in the presence of noise and highly varying sampling rates. We apply it to several data sets, in the context of typical point-based applications.