论文标题
一种离散的概率方法来可视化
A Discrete Probabilistic Approach to Dense Flow Visualization
论文作者
论文摘要
密集的流量可视化是一种流行的可视化范式。传统上，该领域的各种模型和方法都采用连续的配方，这取决于功能分析的坚实基础。在这项工作中，我们检查了密集流动可视化的离散公式。从概率理论中，我们得出了一个相似性矩阵，该矩阵可以测量流域中不同点之间的相似性，从而发现了一个全新的可视化模型。使用此矩阵，我们提出了一种新型的可视化方法，该方法由光谱嵌入的计算，即由粒子混合物概率定义的特征域图。这些嵌入是标量场，可深入了解不同尺度上流的混合过程。光谱嵌入的方法已经在图像分割中进行了很好的研究，并且我们看到光谱嵌入与傅立叶膨胀和频率相连。我们使用不同的2D和3D流量展示了方法的实用性。
Dense flow visualization is a popular visualization paradigm. Traditionally, the various models and methods in this area use a continuous formulation, resting upon the solid foundation of functional analysis. In this work, we examine a discrete formulation of dense flow visualization. From probability theory, we derive a similarity matrix that measures the similarity between different points in the flow domain, leading to the discovery of a whole new class of visualization models. Using this matrix, we propose a novel visualization approach consisting of the computation of spectral embeddings, i.e., characteristic domain maps, defined by particle mixture probabilities. These embeddings are scalar fields that give insight into the mixing processes of the flow on different scales. The approach of spectral embeddings is already well studied in image segmentation, and we see that spectral embeddings are connected to Fourier expansions and frequencies. We showcase the utility of our method using different 2D and 3D flows.
