Influence of the density of vertices on the Hausdorff Distance and Vertex Influence methods
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Abstract
Using linear features for cartographic quality control is advantageous because they represent the majority of the data in a cartographic base and are spatially well distributed over it. However, the application of some linear feature methods from the calculation of positional discrepancies between homologous lines may not translate the true geometry of these lines, mainly the methods that are based on the distances between the vertices of homologous lines. This work aims at evaluating the discrepancies obtained from the Hausdorff Distance and Vertex Influence methods using densified linear features of numerical hydrography and watershed lines, extracted from two Digital Surface Models. For this analysis, vertices were added along the extracted linear features (vertex densification) and the results were compared with the original features. For the Hausdorff Distance method, the discrepancies using densified linear features were relatively lower than the discrepancies obtained using unaltered features: the average and the RMS of the sample using features were 19.9 m and 20.7 m and, for the densified features, were 18.6 m and 19.5 m respectively. In the other hand, for the Vertex Influence method, the discrepancies showed minimal differences: the average and the RMS of the sample using unaltered features were 16.8 m and 17.8 m and, for the densified features, were 16.7 m and 17.7 m respectively. This result is directly related to the mathematical development of the methods themselves. Finally, the densification of linear features is recommended when applying the Hausdorff Distance and Vertex Influence methods to classify a cartographic product.
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