Differential domain analysis for non-uniform sampling
Differential domain analysis for non-uniform sampling
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DOI：
10.1145/1964921.1964945
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发表时间：
2011-07
期刊：
影响因子：
--
通讯作者：
Li-Yi Wei;Rui Wang
中科院分区：
文献类型：
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作者：
Li-Yi Wei;Rui Wang
采样是许多图形应用程序的核心组件，包括渲染、成像、动画和几何处理。这些应用程序的功效通常很大程度上取决于基础样本的分布质量。虽然可以使用现有的空间和光谱方法来分析均匀采样，但这些方法不能轻易扩展到一般的非均匀设置，例如自适应、各向异性或非欧几里德域。我们提出了分析非均匀样本分布的新方法。我们的主要见解是，取决于样本空间位置的标准傅立叶分析可以重新表述为仅取决于其位置差异分布的等效形式。我们称之为微分域分析。这种重新表述的主要好处是它弥合了样本的空间统计数据与其光谱特性之间的基本联系。此外，它允许我们用不同的计算内核和差分测量来推广我们的方法。使用这种分析，我们可以定量测量各种非均匀样本分布的空间和光谱特性，包括自适应域、各向异性域和非欧几里得域。
Sampling is a core component for many graphics applications including rendering, imaging, animation, and geometry processing. The efficacy of these applications often crucially depends upon the distribution quality of the underlying samples. While uniform sampling can be analyzed by using existing spatial and spectral methods, these cannot be easily extended to general non-uniform settings, such as adaptive, anisotropic, or non-Euclidean domains. We present new methods for analyzing non-uniform sample distributions. Our key insight is that standard Fourier analysis, which depends on samples' spatial locations, can be reformulated into an equivalent form that depends only on the distribution of their location differentials. We call this differential domain analysis. The main benefit of this reformulation is that it bridges the fundamental connection between the samples' spatial statistics and their spectral properties. In addition, it allows us to generalize our method with different computation kernels and differential measurements. Using this analysis, we can quantitatively measure the spatial and spectral properties of various non-uniform sample distributions, including adaptive, anisotropic, and non-Euclidean domains.