We present an approach for extracting extremal feature lines of scalar indicators on surface meshes, based on discrete Morse Theory. By computing initial Morse‐Smale complexes of the scalar indicators of the mesh, we obtain a candidate set of extremal feature lines of the surface. A hierarchy of Morse‐Smale complexes is computed by prioritizing feature lines according to a novel criterion and applying a cancellation procedure that allows us to select the most significant lines. Given the scalar indicators on the vertices of the mesh, the presented feature line extraction scheme is interpolation free and needs no derivative estimates. The technique is insensitive to noise and depends only on one parameter: the feature significance. We use the technique to extract surface features yielding impressive, non photorealistic images.