Geometric Correction of Historical Maps Based on Vector Field Analysis

Abstract

It is well known that the following two conditions should be satisfied in the control-point based geometric correction of historical maps: (a) Conversion from a historical map into a present map is a homeomorphism and (b) The straightness of designated specific line segments is maintained. In this paper, a new method for the control-point based geometric correction of historical maps, which simultaneously satisfies both the above conditions, is proposed. The correction process is modeled as a phenomenon in a three-dimensional vector field. Each point in a historical map is connected with the corresponding point in a present map by a streamline of the field. Since a unique streamline passes through any point in the vector field having no zero-vector point, the above connection relationship becomes a homeomorphism. As a result, Condition (a) is satisfied. On the other hand, the straightness of designated line segments is maintained because streamlines intersecting with the line segments in the historical map are formed so as to necessarily intersect with the corresponding line segments in the present map. Consequently, Condition (b) is satisfied. The experimental results demonstrate the effectiveness of the proposed method.