A representation of line images by an algebraic expression is proposed and image registration between two maps by use of matching of the line segments is discussed using this expression. In this method, input map images are transformed into line images in which line segments are expressed by piecewise linear lines using unit vectors. Next, the structure of the line images is represented by image graphs. The matching process makes use of a degree of the structural similarity between nodes using the image graphs. The results of the computer simulations show that the approach is insensitive to scaling, rotation and grey level modification of the map image and effective to the matching of the real map images.