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.

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