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A Discrete Probabilistic Approach to Dense Flow Visualization.
IEEE Transactions on Visualization and Computer Graphics ( IF 5.2 ) Pub Date : 2021-10-27 , DOI: 10.1109/tvcg.2020.3006995
Daniel Preuss , Tino Weinkauf , Jens Harald Kruger

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.

中文翻译:

密集流可视化的离散概率方法。

密集流可视化是一种流行的可视化范例。传统上,该领域的各种模型和方法使用连续公式,建立在泛函分析的坚实基础之上。在这项工作中,我们检查了密集流可视化的离散公式。从概率论中,我们推导出一个相似度矩阵来衡量流域中不同点之间的相似度,从而发现了一类全新的可视化模型。使用这个矩阵,我们提出了一种新的可视化方法,包括计算谱嵌入,即由粒子混合概率定义的特征域图。这些嵌入是标量场,可以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得到很好的研究,我们看到光谱嵌入与傅里叶展开和频率有关。我们使用不同的 2D 和 3D 流程展示了我们方法的实用性。
更新日期:2020-07-13
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