The paper proposes an approach for stable extraction of the skeleton of a polygonal surface and detection of surface features, ridges and ravines, corresponding to skeletal edges. The approach adapts the three-dimensional Voronoi diagram technique for skeleton extraction, explores the singularity theory for ridge and ravine detection, and combines several filtering methods for skeleton denoising and for selecting perceptually salient ridges and ravines.Rather than extract the skeleton as a CW-complex, we approximate it by a two-sided surface. It allows us to use standard mesh editing tools for skeleton denoising and achieve stably extract the ridges and ravines.