Modelling error propagation in vector-based overlay analysis

This paper proposes two methods for analyzing error propagation in overlay analysis of vector polygons, an analytical and simulation method. First, for the analytical method, the error is derived based on the error propagation law in statistics. In the second method, error propagation of overlay is simulated based on the positional error of the original polygon vertices, assuming a given error distribution of the vertices. For both methods, several geometrical error measures for the derived polygons are defined: (i) error measures for the perimeter, area and center of gravity of a polygon, and (ii) the error intervals for the polygon vertices. A test is performed to compare the differences between the two methods and their applicability. The results indicate that there is no significant difference in estimating the propagated error between the two methods. However, these two methods are suitable for different cases. The analytical method is applicable when the error ellipse of any intersection point of the original polygons does not intersect with error ellipses of all the vertices of the original polygons, if the intersection point exists; or, in case of disjoint polygon boundaries, the error ellipse of any point on the boundary of one original polygon does not intersect with the error ellipse of any point on the boundary of the other original polygons. On the other hand, the simulation method is more generic, but more time consuming.