Surface Reconstruction from Point Clouds by Transforming the Medial Scaffold

Abstract

We propose an algorithm for surface reconstruction from unorganized points based on a view of the sampling process as a deformation from the original surface. In the course of this deformation the Medial Scaffold (MS)-a graph representation of the 3D Medial Axis (MA)-of the original surface undergoes abrupt topological changes (transitions) such that the MS of the unorganized point set is significantly different from that of the original surface. The algorithm seeks a sequence of transformations of the MS to invert this process. Specifically, some MS curves (junctions of 3 MA sheets) correspond to triplets of points on the surface and represent candidates for generating a (Delaunay) triangle to mesh that portion of the surface. We devise a greedy algorithm that iteratively transforms the MS by "removing" suitable candidate MS curves (gap transform) from a rank-ordered list sorted by a combination of properties of the MS curve and its neighborhood context. This approach is general and applicable to surfaces which are: non-closed (with boundaries), non-orientable, non-uniformly sampled, non-manifold (with self-intersections), nonsmooth (with sharp features: seams, ridges). In addition, the method is comparable in speed and complexity to current popular Voronoi/Delaunay-based algorithms, and is applicable to very large datasets.

Surface and Curve Skeletonization of Large 3D Models on the GPU

“…The vectors f − x determined by skeleton points and their corresponding feature points are also called spoke vectors [63]. S(Ω) is a set of manifolds with boundaries which meet along a set of Y-intersection curves [13], [18], [37]. S(Ω) can be computed by various methods, as follows.…”

Medialness and the Perception of Visual Art

“…, 2016;Tagliasacchi et al, 2016), as well as the work on shock scaffolds as an extension of earlier work on 2D shock graphs, based on results from (mathematical) singularity theory (Chang et al, 2009;Leymarie, 2003;Leymarie and Kimia, 2007), and (iii) at the junction of 2D and 3D, the work on the recovery of approximate 3D MA information from a plurality of 2D MA obtained from a series of view points taken around a given object of interest (Yasseen et al, 2015(Yasseen et al, , 2017). …”

Improved Part-Based Segmentation of Voxel Shapes by Skeleton Cut Spaces

“…Tierny et al segment shapes hierarchically by topological and geometrical analysis of their Reeb graphs, which are similar to curve skeletons [50]. Chang et al compute shape medial surfaces, separate their manifolds, and back project each manifold on the shape surface to nd a segment [8]. A similar segmentation method, using high-resolution point-cloud skeletons computed on the GPU [17] along the method of Reniers et al [40], is proposed in [22].…”