Assessment of Displacements of Linestrings Based on Homologous Vertexes

Abstract

This study describes a new method that was developed in order to assess the displacements between two linestrings that represent the same element in two datasets based on their shape. Until now, all existing line-based methods have been focused on the calculation of distances or buffer inclusions between the two linestrings. However, these approaches assess a spatial difference between two linestrings, but they can hide the displacements that were suffered because of the geometry of the linestrings themselves. In our approach, the shapes of the linestrings are taken into account in order to identify homologous vertexes and estimate real displacements. Between two lines a pair of homologous vertices are defined as those that represent in reality the same characteristic feature of the line. Homologous vertexes can be detected by means of any appropriate algorithm. In order to test this method, we developed a design of experiment that was based on its application to a large dataset of lines classified into five sinuosity classes. These datasets were obtained from an external source that contains perturbed linestrings with several known random and systematic disturbances. 496 linestrings and 59 configurations were used in this experiment. The results have demonstrated the viability of the proposed method in estimating the real displacement of the lines, and consequently assessing their positional accuracy.