Cartograms are a technique for visually representing geographically distributed statistical data, where values of a numerical attribute are mapped to the size of geographic regions. Contiguous cartograms preserve the adjacencies of the original regions during the mapping. To be useful, contiguous cartograms also require approximate preservation of shapes and relative positions. Due to these desirable properties, contiguous cartograms are among the most popular ones. Most methods for constructing contiguous cartograms exploit a deformation of the original map. Aiming at the preservation of geographical properties, existing approaches are often algorithmically cumbersome and computationally intensive. We propose a novel deformation technique for computing time-varying contiguous cartograms based on integral images evaluated for a series of discrete density distributions. The density textures represent the given dynamic statistical data. The iterative application of the proposed mapping smoothly transforms the domain to gradually equalize the temporal density, i.e., region areas grow or shrink following their evolutionary statistical data. Global shape preservation at each time step is controlled by a single parameter that can be interactively adjusted by the user. Our efficient GPU implementation of the proposed algorithm is significantly faster than existing state-of-the-art methods while achieving comparable quality for cartographic accuracy, shape preservation, and topological error. We investigate strategies for transitioning between adjacent time steps and discuss the parameter choice. Our approach applies to comparative cartograms' morphing and interactive cartogram exploration.

翻译：面积图是一种用于可视化地理分布统计数据的技术，其中数值属性被映射到地理区域的面积大小。连续面积图在映射过程中保留了原始区域的邻接关系。为了实用，连续面积图还需要近似保持形状和相对位置。由于这些理想特性，连续面积图是最常用的技术之一。大多数构建连续面积图的方法都利用原始地图的变形。为了保持地理属性，现有方法通常在算法上较为复杂且计算量大。我们提出了一种新颖的变形技术，用于计算基于序列离散密度分布积分图像的时变连续面积图。密度纹理表示给定的动态统计数据。通过迭代应用所提出的映射，域逐渐平滑变形以平衡时间密度，即区域面积根据其演化的统计数据而增长或缩小。每个时间步长的全局形状保持由一个可交互调整的参数控制。我们高效的GPU实现显著快于现有最先进方法，同时在制图精度、形状保持和拓扑误差方面达到可比质量。我们研究了相邻时间步长之间的过渡策略，并讨论了参数选择。该方法适用于比较面积图的变形和交互式面积图探索。