# Hierarchical additive poisson disk sampling

## Abstract

Generating samples of point clouds and meshes with blue noise characteristics is desirable for many applications in rendering and geometry processing. Working with laser-scanned or lidar point clouds, we usually find region with artifacts called scan- lines and scan-edges. These regions are problematic for geometry processing applications, since it is not clear how many points should be selected to define a proper neighborhood. We present a method to construct a hierarchical additive poisson disk sampling from densely sampled point sets, which yield better point neighborhoods. It can be easily implemented using an octree data structure where each octree node contains a grid, called Modifiable Nested Octree [Sch14]. The generation of the sampling amounts to distributing the points over a hierarchy (octree) of resolution levels (grids) in a greedy manner. Propagating the distance constraint r through the hierarchy while drawing samples from the point set leads to a hierarchy of well distributed, random samplings. This ensures that in a disk with radius r, around a point, no other point upwards in the hierarchy is found. The sampling is additive in the sense that the union of points sets up to a certain hierarchy depth D is a poisson disk sampling. This makes it easy to select a resolution where the scan-artifacts have a lower impact on the processing result. The generated sampling can be made sensitive to surface features by a simple preprocessing step, yielding high quality low resolution poisson samplings of point clouds.

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## Bibtex

@INPROCEEDINGS{DieckmannSampling, author = {Dieckmann, Alexander and Klein, Reinhard}, title = {{Hierarchical additive poisson disk sampling}}, booktitle = {Vision, Modeling and Visualization}, year = {2018}, publisher = {The Eurographics Association}, abstract = {Generating samples of point clouds and meshes with blue noise characteristics is desirable for many applications in rendering and geometry processing. Working with laser-scanned or lidar point clouds, we usually find region with artifacts called scan- lines and scan-edges. These regions are problematic for geometry processing applications, since it is not clear how many points should be selected to define a proper neighborhood. We present a method to construct a hierarchical additive poisson disk sampling from densely sampled point sets, which yield better point neighborhoods. It can be easily implemented using an octree data structure where each octree node contains a grid, called Modifiable Nested Octree [Sch14]. The generation of the sampling amounts to distributing the points over a hierarchy (octree) of resolution levels (grids) in a greedy manner. Propagating the distance constraint r through the hierarchy while drawing samples from the point set leads to a hierarchy of well distributed, random samplings. This ensures that in a disk with radius r, around a point, no other point upwards in the hierarchy is found. The sampling is additive in the sense that the union of points sets up to a certain hierarchy depth D is a poisson disk sampling. This makes it easy to select a resolution where the scan-artifacts have a lower impact on the processing result. The generated sampling can be made sensitive to surface features by a simple preprocessing step, yielding high quality low resolution poisson samplings of point clouds.} }