Standard deviation of line objects in geographic information science

Abstract

Standard deviation of points is regarded as an effective precision indicator and has been used widely for over 100 years. However, to date, no standard deviation for line objects exists, despite lines being the most fundamental geometric objects in geographic information science. This paper proposes a new theory: the measurement of random line precision using standard deviation. The new theory involves: (1) standard deviation presented graphically, in a band-shape: termed the standard deviation band; (2) the rigorous derivation of analytical equations for the standard deviation band; (3) the probability that a line falls within the standard deviation band. The main contributions of this research include: (1) the derivation of an analytical equation of the standard deviation band; (2) a method to estimate the probability of a line falling within a standard deviation band. These contributions form a foundation for the proposition of further control measures for spatial data quality.

Probabilistic analysis and evaluation of classical line error band models of ε-band, G-band, and standard deviation band

“…The line segment is regarded as the whole when calculating probability in the statistically simulated error band, the probability that the endpoints of line segment fall into its error ellipse was discussed [4] . The probability of line segment falling into the standard deviation band has also been estimated by using the upper and lower probability [5] .…”

“…And the proposed statistically simulated error band was the projection of the four-dimensional error ellipsoid of the two endpoints on the two-dimensional plane. Shi defined the standard deviation of two endpoints of a line segment as the standard deviation of the line segment, and the proposed standard deviation band was the envelope of line segments with equal probability densities [5] . Although the two models determine the line segment's position in different ways, generally the boundaries of the two error bands are consistent with each other.…”