Assessment of Displacements of Linestrings Based on Homologous Vertexes

Antonio Mozas-Calvache,Francisco Ariza-López

doi:10.3390/ijgi7120473

Antonio Mozas-Calvache, Francisco Ariza-López

Open Access

https://doi.org/10.3390/ijgi7120473

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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.

Highlights

One of the most important types of data of the vector geographical databases is linestrings
We propose an adaptation of the Vertex Influence Method (VIM) method where the displacement vectors that were obtained are not determined to the closest point of the XL line, but are referred to a homologous vertex previously determined on the XL line
For a general case, this approach proposes that the displacement vectors may be obtained between the vertexes of the QL and the homologous vertexes of an auxiliary line AL, which may be determined from XL when taking into account the distribution of vertexes of QL and the shape of both lines (Figure 4)

Summary

Introduction

One of the most important types of data of the vector geographical databases is linestrings. In addition the use of mobile devices is generating a great amount of georeferenced data, which are usually considered as lines, such as the Global Navigation Satellite System (GNSS) tracks of routes These lines can be shared on the Internet as Volunteered Geographical Information (VGI) [1] while using several applications (e.g., Wikiloc: https://www.wikiloc.com) or they can even be used for the generation of cooperative maps (e.g., OpenStreetMap: https://www.openstreetmap.org). We can definitely highlight the extensive use of lines for representing the linear features of GI, including that of non-expert users, and the increasing interest both of producers and users in the quality, and in the positional accuracy of data and of linestring data. The comparison between two polygons is derived from a distance function between the turning functions of both elements

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