We address here two important problems when reconstructing the three-dimensional surface of a biological structure from a stack of section contours. The correspondence problem, which aims at associating contours on adjacent sections, is solved using connection constraints and a contour association cost function to build a correspondence graph. The branching problem, which aims to reconstruct the surface between one contour and several ones on the adjacent section, is decomposed as a cascade of bifurcations at linearly interpolated contour locations between sections. Our method restores connections even for distant contours and produces anatomically relevant branching reconstructions. The validity of this approach is illustrated on two neuroanatomical datasets.