Semantically correct 2.5D GIS data — The integration of a DTM and topographic vector data

Abstract

The most commonly used topographic vector data, the reference data of national geographic information systems (GIS) are currently two-dimensional. The topography is modelled by different objects which are represented by single points, lines and areas with additional attributes containing information, for instance on the function and size of the object. In contrast, a digital terrain model (DTM) in most cases is a 2.5D representation of the earth's surface. The integration of the two data sets leads to an augmentation of the dimension of the topographic objects. However, due to inconsistencies between the data the integration process may lead to semantically incorrect results. This paper presents a new approach for the integration of a DTM and 2D GIS vector data including the re-establishment of the semantic correctness of the integrated data set. The algorithm consists of two steps. In the first step the DTM and the topographic objects are integrated without considering the semantics of the objects. This geometric integration is based on a DTM TIN (triangular irregular network) computed using a constrained Delaunay triangulation. In the second step those objects which contain implicit height information are further utilized: object representations are formulated and the semantics of the objects are considered within an optimization process using equality and inequality constraints. The algorithm is based on an inequality constrained least squares adjustment formulated as the linear complementary problem (LCP). The algorithm results in an integrated semantically correct 2.5D GIS data set. Results are presented using simulated and real data. Lakes represented by horizontal planes with increasing terrain outside the lake and roads which are composed of several tilted planes were investigated. The algorithm shows satisfying results: the constraints are fulfilled and the visualization of the integrated data set corresponds to the human view of the topography.