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

Abstract

A novel technique is presented for multi-scale curvature computation on a smoothed 3-D surface. This is achieved by convolving local parameterisations of the surface iteratively with 2-D Gaussian filters. In the technique, each 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 edges. The smoothing eliminates surface noise and slowly erodes small surface detail, resulting in gradual simplification of the object shape. The surface Gaussian and mean curvature values are estimated accurately at multiple scales, together with curvature zero-crossing contours. For better visualisation, the curvature values are then mapped to colours and displayed directly on the surface. Furthermore local maxima of Gaussian and mean curvatures, 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 features can be utilised by later processes for robust surface matching and object recognition. The technique is independent of the underlying triangulation and is more efficient than volumetric diffusion techniques since 2-D rather than 3-D convolutions are employed. Another advantage is that it is applicable to incomplete surfaces which arise during occlusion or to surfaces with holes.