Abstract
The optimal location of the representative point is discussed in relation to the estimation accuracy of the point-in-polygon interpolation method. The point-in-polygon interpolation is an areal interpola-tion method that is most frequently used in geography and GIS. This method implicitly assumes that all points are located on the representative points, and thus it yields an estimation error if the assump-tion does not hold. The accuracy of estimated data depends heavily on the location of the representa-tive point. Hence this paper analyzes the relationship between estimation accuracy and the location of the representative point, and discusses the optimal location of the representative point which mini-mizes the estimation error of the point-in-polygon method. The point distribution and the surface were investigated and it was found in both cases that the geometrical (spatial) median of the distribu-tion is the optimal location of the representative point. A numerical examination was performed on the basis of the analytical study. The results showed that the estimation accuracy given by the geomet-rical median is significantly higher than that given by the centroid when the surface distribution has a strongly concentrated form. On the other hand, these two locations yield similar accuracy of estima-tion if the surface distribution is rather smooth. These results and the fact that the geometrical me-dian cannot be easily computed suggest that in practice the geometrical median and the centroid should be chosen based on the surface distribution.
