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.

Positional quality assessment based on linear elements

“…The results show several maximum and average displacements by zones of up to 3,44 m. The determination of displacement vectors allowed them to obtain the main direction of the displacement of the terrain surface of the landslide. • Mozas-Calvache & Ariza-López (2018) tested the adaptation of the VIM method, described previously as VIM-V, based on the determination of homologous vertexes on both databases. They applied this method to five datasets of lines of about 190 km.…”

“…This method was derived from the previous one. In this case, Mozas-Calvache & Ariza-López (2018) suggested the application of the VIM method to calculating the distances and components between the vertexes of the QL line and their homologous vertexes of the XL line. The main goal was the determination of biases because lines can hide these type of displacements when the direction is coincident to the direction of the line.…”

As distâncias de Manhattan e Chebyshev na avaliação da acurácia posicional com feições lineares em produtos cartográficos

“…A Equação 9 representa como é calculada esta métrica de distância. Já Oliveira (2017) realizou um estudo do processo de soldagem para investigar a integridade da solda no tubo de aço, visando a localização e dimensionamento do defeito em um intervalo de milímetros, que é utilizado para aprovar ou rejeitar os tubos.…”

“…Xavier et al (2017) elaboraram um conjunto de dados com o objetivo de auxiliar na avaliação de métodos geoespaciais utilizando dados vetoriais, incluindo a análise da qualidade posicional. Tal conjunto foi construído a partir de dados de mapeamento produzidos por agências cartográficas espanholas (Figura 10).…”

“…O conjunto de dados utilizado foi escolhido devido ao fato de serem dados sintéticos que podem simular dados reais. Este conjunto contém 10 pares de linhas elaboradas por Xavier et al (2017), sendo escolhido dois pares para cada grupo de sinuosidade, além de variar o comprimento. A Figura 31 apresenta o conjunto de linhas escolhidos.…”