Curvature Estimation on Smoothed 3-D Meshes

A novel technique for multi-scale curvature computation on a smoothed 3D surface is presented. In our technique, semigeodesic coordinates are constructed at each vertex of the mesh which becomes the local origin. A geodesic from the origin is first constructed in an arbitrary direction such as the direction of one of the incident edges. The surface Gaussian and mean curvatures are then estimated. Next, the curvature zero-crossing contours were recovered. Curvature features such as zero-crossing contours and maxima recovered at multiple scales are useful for surface matching and object recognition algorithms, as well as registration of 3-D medical data. The performance of our technique when selecting different directions as an arbitrary direction for the geodesic at each vertex is also evaluated. Our experiments demonstrate that estimation of smoothed surface curvatures are very accurate and not affected by the arbitrary direction of the first geodesic line when constructing semigeodesic coordinates. Our technique is independent of the underlying triangulation and is also more efficient than volumetric diffusion techniques since 2-D rather than 3-D convolutions are employed.