Curvature and torsion feature extraction from freeform 3-D meshes at multiple scales

A novel technique is presented for multi-scale curvature computation on a s moothed 3-D surface. This is achieved by convolving local parameterisations of the surface iteratively with 2-D Gaussian filters. In the technique, ea ch vertex of the mesh becomes a local origin around which semi-geodesic co- ordinates are constructed. A geodesic from the origin is first constructed in an arbitrary direction, typically the direction of one of the incident e dges. The smoothing eliminates surface noise and slowly erodes small surfac e detail, resulting in gradual simplification of the object shape. The surf ace Gaussian and mean curvature values are estimated accurately at multiple scales, together with curvature zero-crossing contours. For better visuali sation, the curvature values are then mapped to colours and displayed direc tly on the surface. Furthermore local maxima of Gaussian and mean curvature s, as well as the torsion maxima of the zero-crossing contours of Gaussian and mean curvatures are also located and displayed on the surface. These fe atures can be utilised by later processes for robust surface matching and o bject recognition. The technique is independent of the underlying triangula tion and is more efficient than volumetric diffusion techniques since 2-D r ather than 3-D convolutions are employed. Another advantage is that it is a pplicable to incomplete surfaces which arise during occlusion or to surface s with holes.