Topographic maps are a common support for geographical information because they have the particularity to portray the relief through a set of contour lines. This topographic 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 layers 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 affected 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 orientation flow to fill the gaps with a smooth curve that respects the tangents at the en-points.