Evaluating Isosurfaces with Level‐set‐based Information Maps
Evaluating Isosurfaces with Level‐set‐based Information Maps
复制标题
使用基于水平集的信息图评估等值面
DOI：
10.1111/cgf.12087
复制
发表时间：
2013
影响因子：
2.5
通讯作者：
Han
中科院分区：
文献类型：
--
作者：
Tzu;Teng;Han
虽然等值面已广泛用于标量数据可视化，但通常很难确定所选择的等值面是否足以表示整个标量场。在本文中，我们提出了一种评价给定等值面的代表性的信息理论方法。我们的基本思想是，给定两个等值面来包围子体，如果子体中的中间等值面可以通过从一个等值面平滑地变形到另一个等值面来生成，则不需要额外的等值面，因为子体内真正等值面的几何形状可以很容易地推断出来。为了实现这个想法，给定一对等值面，为了确定在封闭区域内是否满足这样的光滑条件，我们使用水平集方法来生成中间曲面。在每个中间曲面上，我们从标量场中抽取值并检验其分布。如果分布的熵较低，则该中间面与标量场中的真正等值面很好地对齐。对于由边界等值面的水平集方法生成的中间曲面，水平集曲面的标量值分布形成二维分布，称为等值面的信息映射。该信息图可以用作子区域数据的边界等值面的代表性的指示器，允许对输入等值面的可表示信息进行定量测量。基于这种信息理论方法，本文提出了一种等值面选择算法，该算法可以自动选择等值面，从而更有效地实现标量场的可视化。
While isosurfaces have been widely used for scalar data visualization, it is often difficult to determine if the selected isosurfaces for visualization are sufficient to represent the entire scalar field. In this paper, we present an information‐theoretic approach to evaluate the representativeness of a given isosurface set. Our basic idea is that given two isosurfaces that enclose a subvolume, if the intermediate isosurfaces in the subvolume can be generated by smoothly morphing from one isosurface to the other, no additional isosurfaces are needed since the geometry of the true isosurfaces within the subvolume can be easily inferred. To realize this idea, given a pair of isosurfaces, to determine if such a smooth condition in the enclosed region is satisfied, we use a level‐set approach to generate the intermediate surfaces. On each intermediate surface, we sample the values from the scalar field and exam the distribution. If the entropy of the distribution is low, this intermediate surface is aligned well with a true isosurface in the scalar field. For the intermediate surfaces generated by the level‐set method from the boundary isosurfaces, the distributions of scalar values from the level‐set surfaces form a 2D distribution, called isosurface information map. This information map can be used as an indicator of the representativeness of the boundary isosurfaces for the data in the subregion, allowing a quantitative measurement of information representable by the input isosurfaces. Based on this information‐theoretic approach, this paper presents an isosurface selection algorithm that can automatically select isosurfaces for more effective visualization of scalar fields.