Topographic maps are a common support for geograph- ical information because they have the particularity to por- tray the relief through a set of contour lines. This to- pographic feature can be very useful in many context but the automatic extraction of this information is not an easy task, especially because the map contains many other lay- ers which overlay the contours. In this paper we propose an automatic approach to reconstruct gaps in contour lines. Our novel parameterless reconstruction scheme is based on the extrapolation of the gradient orientation field from the available pieces of thinned contours. A weight is then af- fected to each pair of end-points according the force needed by its potential reconstructed curve to cross the field. The computation of the optimal global solution is obtained by solving a perfect matching problem. We finally use the ori- entation flow to fill the gaps with a smooth curve that re- spects the tangents at the en-points.