An adaptive point sampler on a regular lattice

Abstract

(a) (b) Tiled multi-class sets can be used to partition a tiled blue noise set into separate blue-noise sets. The two bottom lines show the filling order of our recursive tile in (a). First, sample points are filled in that are shared by one of the respective child tiles. The parent tile then visits the remaining children (in an optimized order) and instructs them to add their samples. For each subsequent 16 (number of children) samples, control is passed recursively to the childrenin the same order -to add more samples.We present a framework to distribute point samples with controlled spectral properties using a regular lattice of tiles with a single sample per tile. We employ a word-based identification scheme to identify individual tiles in the lattice. Our scheme is recursive, permitting tiles to be subdivided into smaller tiles that use the same set of IDs. The corresponding framework offers a very simple setup for optimization towards different spectral properties. Small lookup tables are sufficient to store all the information needed to produce different point sets. For blue noise with varying densities, we employ the bit-reversal principle to recursively traverse sub-tiles. Our framework is also capable of delivering multi-class blue noise samples. It is well-suitedWe thank the anonymous reviewers for their detailed feedback to improve the paper. Thanks to Cengiz Öztireli for sharing the grid test scene. Thanks to Carla Avolio for the voice over of the supporting video clip.

Blue-noise sampling for human retinal cone spatial distribution modeling

“…A large variety of optimization-based approaches has been proposed since then. Two main optimization-based approaches have been developed and presented in numerous papers: (1) on-line optimization [20, 27, 24, (2) off-line optimization [44][45][46][47][48][49], where the near-optimal solution is prepared in form of lookup tables, used in runtime. The present work uses the approach developed by de Goes et al [39], called Blue Noise Through Optimal Transport (BNOT), as reference.…”

“…Wachtel et al [47] propose a tile-based method that incorporates spectral control over sample distributions. More recently, Ahmed et al [49] proposed a 2-D square tile-based sampling method with one sample per tile and controllable Fourier spectra. However, all precalculated structures used in this family of approaches rely on the offline generation of high-quality blue noise.…”

Visibility‐Aware Progressive Farthest Point Sampling on the GPU

“…This allows for a very fast generation of lower quality Poisson‐disk patterns. Another category of tile‐based sampling techniques uses a recursive subdivision of the sampling domain into self‐similar tiles, like Polyominos [Ost07], Polyhexes [WPC∗ 14], or Adaptive Regular Tiles [ANHD17], where each tile is associated with a single sample. These sampling techniques are also inherently progressive.…”

Progressive Multi‐Jittered Sample Sequences

“…Recently, work has been done to combine blue noise and stratification. Ahmed et al [ANHD17] introduced adaptive regular tiling (ART), an elegant and flexible tiling method to generate blue‐noise sequences that also have some stratification (they are jittered due to the generation on a regular lattice, but not multi‐jittered). The stratification reduces the unevenness and reduces sampling error, making their error comparable to most randomized quasi‐random sequences.…”