Wang Yunhai, Wang Zeyu, Fu Chi-Wing, Schmauder Hansjorg, Deussen Oliver, Weiskopf Daniel
IEEE Trans Vis Comput Graph. 2018 Aug 20. doi: 10.1109/TVCG.2018.2865266.
Selecting a good aspect ratio is crucial for effective 2D diagrams. There are several aspect ratio selection methods for function plots and line charts, but only few can handle general, discrete diagrams such as 2D scatter plots. However, these methods either lack a perceptual foundation or heavily rely on intermediate isoline representations, which depend on choosing the right isovalues and are time-consuming to compute. This paper introduces a general image-based approach for selecting aspect ratios for a wide variety of 2D diagrams, ranging from scatter plots and density function plots to line charts. Our approach is derived from Federer's co-area formula and a line integral representation that enable us to directly construct image-based versions of existing selection methods using density fields. In contrast to previous methods, our approach bypasses isoline computation, so it is faster to compute, while following the perceptual foundation to select aspect ratios. Furthermore, this approach is complemented by an anisotropic kernel density estimation to construct density fields, allowing us to more faithfully characterize data patterns, such as the subgroups in scatterplots or dense regions in time series. We demonstrate the effectiveness of our approach by quantitatively comparing to previous methods and revisiting a prior user study. Finally, we present extensions for ROI banking, multi-scale banking, and the application to image data.
选择合适的宽高比对于有效的二维图表至关重要。对于函数图和折线图有几种宽高比选择方法，但只有少数方法能处理诸如二维散点图等一般的离散图表。然而，这些方法要么缺乏感知基础，要么严重依赖中间等值线表示，而这取决于选择合适的等值线值且计算耗时。本文介绍了一种基于图像的通用方法，用于为从散点图、密度函数图到折线图等各种二维图表选择宽高比。我们的方法源自费德勒的余面积公式和线积分表示，这使我们能够使用密度场直接构建现有选择方法的基于图像的版本。与先前方法不同，我们的方法绕过了等值线计算，因此计算速度更快，同时遵循感知基础来选择宽高比。此外，该方法通过各向异性核密度估计来构建密度场进行补充，使我们能够更忠实地刻画数据模式，例如散点图中的子群或时间序列中的密集区域。我们通过与先前方法进行定量比较并重新审视之前的用户研究来证明我们方法的有效性。最后，我们介绍了用于感兴趣区域分组、多尺度分组以及应用于图像数据的扩展。
