Quantitative Estimation of Local Distortions in Historical Maps by Moving Least Squares Technique

Abstract

This paper proposes a method to quantitatively estimate the local-distortion characteristics in historical maps. First, the Euclidean regression technique is applied to a given historical map to fit its size, direction and location to those of a present map. Next, the moving least squares technique is used to formulate the relationship between the present map and the fitted historical map as a localized similarity-transformation function. The coefficients of the obtained function quantitatively and separately give the amounts of two main local-distortion processes at each local area: rotation heuristics and implicit scaling. The experimental results show the effectiveness of the proposed method.