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 <i>identification vector</i> to each line segment, which reflects the distribution of the rest of line segments with respect to the current one using orientation difference between <i>cells</i>. A new matrix called Orientation Difference Matrix (ODM) has been constructed from the <i>identification vectors</i>. 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.