蓝噪声作为格子吉布斯系综
Blue Noise as a Lattice Gibbs Ensemble
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中文总结 AI 辅助
本研究将蓝噪声生成建模为带成对排斥的二元格子吉布斯分布采样，采用带误差界的马尔可夫链采样及瓦片生成，实现低内存的可扩展蓝噪声生成，经实验验证有效。
中文摘要 AI 辅助
蓝噪声采样在计算机图形学中被广泛应用，但现有方法将统计建模与可扩展生成分离开来。优化和传输方法通过将所有样本耦合在一起来生成高质量点集，而程序化和基于瓦片的采样器是局部的，仅隐式定义其输出。我们将蓝噪声生成表述为从具有成对排斥相互作用的二元格子占据的吉布斯分布中采样，密度、排斥强度、相互作用尺度和核硬度是该分布的参数。由于能量是成对求和的，可在对分布产生有界改变的情况下丢弃远距离相互作用，从而得到有界度的马尔可夫随机场。为对其采样，我们采用“向后追踪过去耦合”（Coupling Towards The Past）方法，从期望状态反向追踪马尔可夫链，并在固定深度处截断追踪，这使得成本和每个样本依赖的区域均有界。采用足够 halo（晕）的瓦片独立生成时，其结果与在任意更大域上生成的相同区域完全一致，且瓦片间无需通信。内存由瓦片大小而非输出大小决定，精度通过具有已证明误差界的参数而非切换算法来权衡成本。我们分别验证了模型、采样器及这些保证：该系综可复现标准蓝噪声频谱，并随参数变化在频谱间连续过渡；采样器符合其预测的工作负载和内存；瓦片输出被验证与全域生成完全一致。我们在14K自适应点画（stippling）任务中进行了演示，现有方法需与输出成比例的内存，同时还展示了多类别扩展。
英文摘要
We present an algorithm for generating blue-noise point sets that is simultaneously local and parallel, and whose output is a draw, up to a bounded error, from an explicit probability distribution. Methods that optimize point positions achieve high spectral quality but tend to couple all points globally, while tile-based methods, the main existing local approach, assemble their output from point sets constructed offline rather than generating it from scratch; we show that locality does not require giving that up. Concretely, we model blue noise as a Gibbs distribution over a lattice, with a pairwise penalty whose continuous parameters control repulsion strength, scale, and hardness. To sample this distribution locally, we trace each site's dependencies backward in time and truncate the trace to a bounded region known before sampling begins; tiles can therefore be generated independently in any order, with no communication between them. We stipple a 14557$\times$8418 James Webb Space Telescope image tile by tile, with peak memory under 51 MiB, set by the working window rather than the image dimensions. Spectral quality is competitive with existing methods at matched density, and the construction extends naturally to multi-class outputs.
