In this paper, we introduce a really 3-D deformable model, which evolves in true 3-D images, un der the action of internaI forces (describing some elasticity properties of the surface), and external forces attracting the surface toward some detected edgels. Our formalism leads to the minimization of an energy which is expressed as a functional. We use a variational approach and a finite element method to actually express the surface in a discrete basis of continuous functions. This leads to a reduced computational complexity and a better numerical stability. The power of the approach to segment 3-D images is demonstrated by a set of experimental results on various complex medical 3-D images. Another contribution of this approach is the possibility to infer easily the differential structure of the segmented surface. As we end-up with an analytical description of class Coo of the surface almost everywhere, t.his allows to compute for instance its first and second fundamcntal forms. From this, one can ext.ract a curvature primaI sketch of the surface, including sorne intrinsic features like parabolic lines, extrema of curvatures, umbilic points etc ... , which can be uscd as landmarks for 3-D image interpretation.