Multi-scale 3-d surface description: open and closed surfaces

A novel technique for multi-scale smoothing of a free-form 3-D surface is presented. Complete tri-angulated models of 3-D objects are constructed automatically and using a local parametrization technique, are then smoothed using a 2-D Gaus-sian filter. Our method for local parametrization makes use of semigeodesic coordinates as a natu-ral and efficient way of sampling the local surface shape. The smoothing eliminates the surface noise together with high curvature regions such as sharp edges, therefore, sharp corners become rounded as the object is smoothed iteratively. Our technique for free-form 3-D multi-scale surface smoothing is independent of the underlying triangulation. It is also argued that the proposed technique is pre-ferrable to volumetric smoothing or level set meth-ods since it is applicable to incomplete surface data which occurs during occlusion. Our technique was applied to closed as well as open 3-D surfaces and the results are presented here.