Fréchet distance in spatial data quality

Abstract

The purpose of this work is to evaluate the use of Fréchet Distance as a new method of analyzing positional accuracy in linear features. The Fréchet Distance considers the order of the vertices as well as line orientation, graphically demonstrating the behavior between them along the entire path. The graphic resource that makes this analysis possible is entitled free-space diagram, consisting of a system of two-dimensional coordinates that present the interactions throughout ellipses. The discrepancies obtained by the Fréchet Distance were compared with the values found by the Epsilon Band, Hausdorff Distance, Vertex Influence, Buffer, and Buffer Overlap Statistics methods. The experiment is composed of simulated data, which were created to investigate some effects, such as systematic displacements, positional differences in the initial and final vertices of the lines, presence of outliers and scale uncertainties, and also composed of real data. The results portrayed the sensitivity of the Fréchet Distance in relation to the outliers, in addition to proving the variations that occurred in the discrepancies when there was a change in the direction of the lines. At the end of this study, it was possible to propose a new methodology for applying the Fréchet Distance in the analysis of positional accuracy using linear features.