Systems Science and Informatics Unit, Indian Statistical Institute-Bangalore Centre, 8th Mile, Mysore Road, RVCE PO, Bangalore 560059, India.
IEEE Trans Pattern Anal Mach Intell. 2010 Feb;32(2):378-84. doi: 10.1109/TPAMI.2009.163.
Spatial interpolation is one of the demanding techniques in Geographic Information Science (GISci) to generate interpolated maps in a continuous manner by using two discrete spatial and/or temporal data sets. Noise-free data (thematic layers) depicting a specific theme at varied spatial or temporal resolutions consist of connected components either in aggregated or in disaggregated forms. This short paper provides a simple framework: 1) to categorize the connected components of layered sets of two different time instants through their spatial relationships and the Hausdorff distances between the companion-connected components and 2) to generate sequential maps (interpolations) between the discrete thematic maps. Development of the median set, using Hausdorff erosion and dilation distances to interpolate between temporal frames, is demonstrated on lake geometries mapped at two different times and also on the bubonic plague epidemic spread data available for 11 consecutive years. We documented the significantly fair quality of the median sets generated for epidemic data between alternative years by visually comparing the interpolated maps with actual maps. They can be used to visualize (animate) the spatiotemporal behavior of a specific theme in a continuous sequence.
空间插值是地理信息科学（GISci）中一项要求很高的技术，它通过使用两个离散的空间和/或时间数据集以连续的方式生成插值地图。无噪声数据（主题层）以不同的空间或时间分辨率描绘特定主题，由聚合或离散形式的连接组件组成。本文提供了一个简单的框架：1）通过空间关系和伴侣连接组件之间的 Hausdorff 距离，对两个不同时间点的分层数据集的连接组件进行分类，以及 2）在离散主题地图之间生成顺序地图（插值）。使用 Hausdorff 侵蚀和膨胀距离在时间帧之间进行插值来开发中位数集，展示了在两个不同时间点绘制的湖泊几何形状以及可用于 11 年连续的腺鼠疫流行传播数据。我们通过将插值地图与实际地图进行视觉比较，记录了替代年份之间为流行数据生成的中位数集的明显良好质量。它们可用于以连续序列可视化（动画）特定主题的时空行为。
