We here present a new approach to characterize similar areas of two 2D point clouds, which is a major issue in Pattern Recognition and Image Analysis. To do so, we define a similarity measure that takes into account several criteria such as invariance by rotation, outlier elimination, and one-dimensional structure enhancement. We use this similarity measure to associate locations from one cloud to the other, to use this result in the frame of a registration process between these two point clouds. Our main contributions are the integration of various one-dimensional structure representations into a unified formalism, and the design of a robust estimator to evaluate the common information related to these structures. Finally, we show how to use this approach to register images of different modalities.