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We explore how to improve the quality of the height map recovered from faces using shape-from-shading. One of the problems with reliable face surface reconstruction using shape-from-shading is that local errors in the needle map can cause implosion of facial features, and in particular the nose. To overcome this problem in this paper we develop a method for ensuring surface convexity. This is done by modifying the gradient orientations in accordance with critical points on the surface. We utilize a local shape indicator as a criteria to decide which surface normals are to be modified. Experiments show that altering the directions of a surface normal field of a face leads to a considerable improvement in its integrated height map.