Measurement Indices of Positional Uncertainty for Plane Line Segments Based on the σ ε Model

Guoqin Zhang 1 and Changqing Zhu 2 
1 Information Engineering University, Zhengzhou 450052, China 
2 Ministry of Education Key Laboratory of VGE, Nanjing 210046, China

Abstract. Firstly, eight cases of the random line segments are discussed. Secondly, to the eight existing cases of line segment, the analytic  expressions of the error band for the σ ε  uncertainty  model  of  line segment are deduced, the parameter equations of the error band boundary are gotten, and it is proved that the boundary of the error band is continuous. Thirdly, the average error band width and the algebraic expressions of the uncertainty region area bounded by error band are calculated. Finally, the visual graphics of the error band are drawn with analytic expression of the error  band by examples. Thus, three indexes are given to measure the precision of the line uncertainty: the average error band width, the uncertainty region area and the visual graphics. 

Keywords: plane line, uncertainty, σ ε  model, error band

In: Wan, Y. et al. (eds) Proceeding of the 8th international symposium on spatial accuracy assessment in natural resources and environmental sciences, World Academic Union (Press). 

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