Simultaneous Simplification and Aggregation for Interactive Maps

为了在空间分析或地图中使用地理数据集，通常需要粗化其粒度。 在地理信息科学和制图学中，这项任务被称为综合。 项目C1将有助于自动归纳，方法是开发在地理数据集中探测物体组的算法，并为每组计算一个具有代表性的简化物体。 作为两个具体的用例，我们将研究（i）基于地理标记的社交媒体数据划分人类活动区域，以及（ii）从单个建筑物的足迹中导出与建成区，定居点和较大城市群相对应的多边形。 在这两种情况下，我们的目标是交互式地图，允许他们的用户通过不同的比例缩放，并改变地图的时间参考点或时间参考间隔。 例如，通过拖动时间滑块，用户可以及时更改地图的参考点，以获得多年来城市发展的动画。 我们将开发一种方法，将对象组的检测，每个组的聚合到一个多边形，多边形的简化作为一个单一的任务。 我们的中心假设是，这样一个综合的方法比目前占主导地位的方法，首先汇总，然后简化产生更好的解决方案。开发将遵循算法工程过程，包括问题建模，高效算法的设计，数学分析和实验。

To use a geographic data set in a spatial analysis or for a map, one often needs to coarsen its granularity. In geographic information science and cartography, this task is termed generalization. Project C1 will contribute to automated generalization by developing algorithms for detecting groups of objects in a geographic data set and computing a single representative and simplified object for each group. As two concrete use cases we will study (i) the delineation of regions of human activity based on geo-tagged social-media data and (ii) the derivation of polygons corresponding to built-up areas, settlements, and larger urban agglomerations from footprints of individual buildings. In both cases we aim at interactive maps that allow their users to zoom through different scales and to change the map's point of reference in time or its interval of reference in time. For example, by dragging a time slider, a user can change the map's point of reference in time to obtain an animation of urban growth over multiple years. We will develop an approach that treats the detection of groups of objects, the aggregation of each group to a polygon, and the simplification of polygons as a single task. Our central hypothesis is that such an integrated approach yields substantially better solutions than the currently dominating approach of first aggregating and then simplifying. The development will follow an algorithm engineering process including the modelling of problems, the design of efficient algorithms, mathematical analyses, and experiments.