We show how to integrate the normal field of a surface in the presence of discontinuities by three different ways. We obtain very satisfactory 3D-reconstructions, from the point of view of the accuracy of the reconstructions. As an important consequence, no prior segmentation of the scene into parts without discontinuity is required anymore. Finally, we test the three proposed methods of integration in the framework of photometric stereo, a technique which aims at computing the normal field of a scene surface from several images of this scene lighted under different directions.