Several difficulties are met when detecting roads in satellite images. They are due to the poor quality of existing information and may be solved by using global information. Dynamic programming is popular in line detection, but deals awkwardly with global information due to its constraints on the decision process and to the local nature of the cost. \newline There are various ways to integrate global information in this framework. The most widely used consists in computing as a pre-processing some global characteristics of a feature, and attributing these characteristics to each state belonging to the feature. A second solution is to use a hierarchic approach, from coarse to fine. Thirdly, the states may be defined in an elaborated way as a set of several successive pixels. We have developed a new algorithm of roads detection, which takes into account local curvature by defining the cost on three successive points. We present in our work a new solution : auxiliary functions. They store temporary information about the current shortest path to take into account global information in the potential. They are updated in a recursive way each time a new shortest path is found. Optimality is lost, but the constraint is properly imposed to the solution as we show in integrating global direction, global curvature, and in minimizing the average of the potential. The constraint may be modulated, and the complexity of the problem is not changed. \newline Besides shape information, we present a new method to define automatically the cost from the grey-levels in windows around the extremities of the roads. The respective influence of contrast and grey level is weighted by using conditional probabilities. \newline We finally compare the speeds of computation with various scannings of the states : by eliminating part of the states and ordering them, at initialization or during integration, and by stopping the integration before convergence. The gains are often above 50~%.