Direct blue noise resampling of meshes of arbitrary topology

Abstract

We propose in this paper a novel sampling method and an improvement of a spectral analysis tool that both handle complex shapes and sharp features. Starting from an arbitrary triangular mesh, our algorithm generates a new sampling pattern that exhibits blue noise properties. The fidelity to the original surface being essential, our algorithm preserves sharp features. Our sampling is based on a discrete dart throwing applied directly on the surface to get good blue noise sampling patterns. It is also driven by a feature detection tool to avoid geometric aliasing. Experimental results prove that our sampling scheme is faster than techniques based on brute-force dart throwing, and produces sampling patterns with blue noise properties even for complex surfaces of arbitrary topology. In parallel, we also propose an improvement of a tool initially developed for the spectral analysis of nonuniform sampling patterns, that may generate biased results with complex shapes. The proposed improvement overcomes this problem.

A Survey of Blue-Noise Sampling and Its Applications

“…Euclidean distance is used in these approaches. Besides the Euclidean metric, the geodesic metric is also used for Poisson-disk sampling [38][39][40][41] . Surface sampling techniques can be also used for surface remeshing by computing the restricted Delaunay triangulation [42] .…”

Blue noise Sampling of surfaces from stereoscopic images

“…There are several prior works about the blue noise (re)sampling of surfaces. Two kinds of approaches exist: directly on the surfaces [11,4], or on a 2D parametric domain of the surfaces [12]. As expected, the first approaches are efficient in term of sampling quality but are time-consuming, because of the computation of geodesics over the surface (to estimate the distances between samples).…”

“…the position, in the 3D space, of the pixels belonging to the POI region, by triangulation [14]. 4. Sampling This step distributes the 3D samples on the scanned surface.…”

“…Our method is inspired by the Dart Throwing for surfaces proposed in [4]. This method is considered as a direct 3D sam- pling method, because the sampling domain Ω is the triangular mesh associated to the surface sampled (no parameterization).…”

“…To overcome this problem, many methods of mesh simplification [1], remeshing [2,3], resampling [4], etc. have been developed during the last two decades, to reduce the size of geometrical data and to make their process easier, or just... possible.…”