A new Voronoi-based surface reconstruction algorithm

Abstract

We describe our experience with a new algorithm for the reconstruction of surfaces from unorganized sample points in ¢ £ ¥ ¤. The algorithm is the first for this problem with provable guarantees. Given a "good sample" from a smooth surface, the output is guaranteed to be topologically correct and convergent to the original surface as the sampling density increases. The definition of a good sample is itself interesting: the required sampling density varies locally, rigorously capturing the intuitive notion that featureless areas can be reconstructed from fewer samples. The output mesh interpolates, rather than approximates, the input points.Our algorithm is based on the three-dimensional Voronoi diagram. Given a good program for this fundamental subroutine, the algorithm is quite easy to implement.

Graph Cut Based Point-Cloud Segmentation for Polygonal Reconstruction

“…There exist processes mainly based on marching cubes [20] or voronoi diagrams [21,22]. Those approaches try to represent 3D point-cloud as a solid 3D polygonal object.…”

Curve reconstruction from unorganized points

“…Note that the α-shape of Edelsbrunner et al [5] is another subset of DT which can represent the appropriate connectivity of the point elements though the parameter α is usually chosen interactively [1,8]. Now, in the local regression for P * , we use the EMST to collect the neighboring points.…”

“…Many approaches have been suggested for the reconstruction of surfaces from unorganized point sets [1,2,9,10,18]. For curve reconstruction, there are many solutions for cases where the ordering of points is known.…”

A fast and efficient projection-based approach for surface reconstruction

“…al. [2,1] use a Voronoi filtering approach based on three-dimensional Voronoi diagram and Delaunay triangulation to construct the crust of the sample points. They provide theoretical guarantees on the topology of their reconstructed mesh given "good" sampling.…”

“…However, sufficiency conditions like sampling theorems are fairly difficult to formulate and as a result, most of the existing reconstruction algorithms ignore this aspect of the problem. Exceptions include the works of [3,7,2].…”