Volume-based similarity of linear features on terrains

Linear features on terrains model the boundaries of ground cover regions, delineate glaciers, or form the boundary of rivers and lakes. When computing the similarity between such linear features, it is important to also take their context into account: the terrain. We hence explore the possibilities of volume-based distance measures for linear features on a terrain. Our measures construct suitable base surfaces between the linear features, which can slice through the input terrain and also hover above. The similarity between two linear features is then captured by the volume of "earth" above the base surface and below the terrain, and possibly also by the volume of "air" below the base surface and above the terrain. We suggest six ways of choosing a suitable base surface. These choices give rise to different measured volumes and can be useful in different application scenarios.