The detection of roads in satellite images has drawn a lot of attention in the last ten years. Problems of resolution, noise and image understanding are involved and one of the best method developed so far is the F* algorithm of Fischler, which is based on dynamic programming. We present herein a mathematical formalization of the F* an extension to cliques of higher order to deal with the contrast an extension to neighborhoods of higher order to take into account the curvature and a physical dynamic model to use the curvature information in a more natural and global way.