An algorithm for automatically computing the horizontal shift between homologous contours from DTMs
The algorithm we present here is useful for measuring the planimetric discrepancy between two models which can be represented by contours. In cartography the paradigm of such models is represented by digital terrain models (DTMs). The measure we propose is based on an area enclosed between homologous contours (two level contours, each belonging to two different models). Our measure is similar to another used previously, although, in the previous studies, the area enclosed between homologous contours was computed manually or it was restricted to particular conditions. The innovation of our approach consists of the automation of the entire process and in the constraint elimination. The main problem to solve before computing the horizontal shift measure is how to determine the area enclosed between homologous contours. This is a problem because there is no bijective correspondence between homologous contours, and therefore the identification of the homologous contours is not a trivial task. Our approach overcomes this difficulty by closing following the limit of the DTM the open contours (the contours which cut the limit of the DTM) and classifying them by the external level. We achieve the automation assisted by the Boolean polygon operations, specifically using the symmetric difference operation. Our algorithm facilitates the computation of accuracy of a DTM by comparison with another and it is applicable in such fields as hydrology (precision estimation of the hydrological features), cartographic generalization, and civil engineering. Finally we use our measure for estimating the planimetric discrepancy between the same streams derived from different DEMs (different sources and precisions).
homologous contours non-bijective correspondence