In this paper, we consider the geometrical analysis of oriented digital surfaces, which form the boundary of connected voxel sets. We present a method for the detection and reconstruction of its convex and concave parts. The proposed method composes two tools: the first one is a probing approach for the extraction of locally extremal points, the second one, based on the notion of visibility, joins some pairs of points whenever the straight segment between them stays sufficiently close to the input surface without crossing it. Finally, outer and inner candidate segments are assembled separately into facets, thus building polyhedral approximations of the local convex and concave zones.