Entropy-Based Models for Positional Uncertainty of Line Segments in GIS

Abstract This paper presents an error model based on the theory of information entropy for describing positional uncertainty of line segments in Geographical Information System. The model is independent of confident level. In this model, an error entropy band is established by using information entropy of marginal probability distribution of errors along the direction perpendicular to the line segment. Based on that, an average error entropy band is drawn by using average information entropy of marginal probability distribution of the whole line segment. Further, a generic error entropy band is extended from the entropy error ellipse, which is derived from the error entropy band. These three error entropy bands provide a more complete and objective measure for the errors of line segments, since the entropy-based error bands are determined according to different entropy criteria. Practical examples in this paper show that these three error bands are suitable measurement indices for positional uncertainty of line segments.