Estimation of Error in Curvature Computation on Multi-Scale Free-Form Surfaces

A novel technique for multi-scale curvature computation on a free-form 3-D surface is presented. This is achieved by convolving local parametrisations of the surface with 2-D Gaussian filters iteratively. In our technique, semigeodesic coordinates are constructed at each vertex of the mesh. Smoothing results are shown for 3-D surfaces with different shapes indicating that surface noise is eliminated and surface details are removed gradually. A number of evolution properties of 3-D surfaces are described. Next, the surface Gaussian and mean curvature values are estimated accurately at multiple scales which are then mapped to colours and displayed directly on the surface. The performance of the technique when selecting different directions as an arbitrary direction for the geodesic at each vertex are also presented. The results indicate that the error observed for the estimation of Gaussian and mean curvatures is quite low after only one iteration. Furthermore, as the surface is smoothed...

• Type: Journal
• Year: 2002
• Where: IJCV
• Authors: Farzin Mokhtarian, Nasser Khalili, Peter Yuen
• Keywords: 3-d Surfaces, Free-form 3-D Surface, IJCV 2002, Mean Curvature