Simple and Scalable Surface Reconstruction
Résumé
We present a practical reconstruction algorithm that generates a surface triangulation from an input pointset. In the result, the
input points appear as vertices of the generated triangulation. The algorithm has several interesting properties: it is very simple
to implement, it is time and memory efficient, and it is trivially parallelized. On a standard hardware (core i7, 16Gb) it takes less than 10 seconds to reconstruct a surface from 1 million points, and scales-up to 36 million points (then it takes 350 seconds). On a telephone (ARMV7 Neon, quad core), it takes 55 seconds to reconstruct a surface from 900K points. The algorithm computes the Delaunay triangulation of the input pointset restricted to a "thickening" of the pointset (similarly to several existing methods, like alpha-shapes, crust and co-cone). By considering the problem from the Voronoi point of view (rather than Delaunay), we use a simple observation (radius of security) that makes the problem simpler. The Delaunay triangulation data structure and associated algorithms are replaced by simpler ones (KD-Tree and convex clipping) while the same set of triangles is provably obtained. The restricted Delaunay triangulation can thus be computed by an algorithm that is not longer than 200 lines of code, memory efficient and parallel. The so-computed restricted Delaunay triangulation is finally post-processed to remove the non-manifold triangles that appear in regions where the sampling was not regular/dense enough.
Sensitivity to outliers and noise is not addressed here. Noisy inputs need to be pre-processed with a pointset filtering method. In the presented experimental results, we are using two iterations of projection onto the best approximating plane of the 30 nearest neighbours (more sophisticated ones may be used if the input pointset has many outliers).
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