This paper deals with the registration of images which are subject to translation, rotation, scaling and other geometric transformations. The problem is tackled with a contour-based registration technique. We present a novel approach for finding a representation of planar curves and matching such two representations in this paper. In our framework, the matching of curves is proceeded by (1) using connected equi-length line segments (CELLS) to represent curves, (2) attaching an identification vector to each line segment, which reflects the distribution of the rest of line segments with respect to the current one using orientation difference between cells. A new matrix called Orientation Difference Matrix (ODM) has been constructed from the identification vectors. This approach uniquely specifies a curve and the representation for matching is invariant under rotation, scaling and translation of the curve. A practical use of the proposed approach is demonstrated by registering a SAR image of a certain area to a map.