A framework for the visual representation of three-dimensional free-form curved surfaces based on a special class of surface curves, herein called the surface structure curves, is in progress. By analyzing their properties, we attempt to construct a basis for describing the topographical structures of curved surfaces which give a global description of the surface geometry. Surface structure curves are a set of surface curves defined by using viewpoint-invariant features-surface curvatures (and their gradients and asymptotes) from differential geometry. From these surface structure curves, surface sketches by means of the topographical structure of ridge lines, valley lines and the enclosing boundaries of bumps and dents can be inferred. This paper proposes a view-point invariant representation scheme which provides a smooth surface sketch",--a natural parameterization of free-form curved surfaces. We define three types of surface structure points and five types of surface structure curves in terms of zero-crossings, asymptotes and gradients of the Gaussian and mean curvatures. We discuss their properties and usefulness in edge based segmentation and description of free-form curved surfaces. Some examples of surface sketches using the surface structure curves are shown.

Surface reconstruction and visualization from sparse and incomplete surface data is a fundamental problem and has received growing attention in both computer vision and graphics. This paper presents a computational scheme for realistic visualization of free-formed surfaces from 3D range images. The novelty of this scheme is that by integrating computer vision and computer graphics techniques, we dynamically construct a mesh representation of the arbitrary view of the surfaces, from a view-invariant shape description obtained from 3D range images. We outline the principle of this scheme and describle the frame work of a graphical reconstruction model, we call arbitrarily oriented meshes', which is developed based on differential geometry. The experimental results on real range data of human faces are shown.