document: 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 iteratively , the error is further reduced . The results also show that the estimation error of Gaussian curvature is less than that of mean curvature . 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 . Finally , the method presented here is a generalisation of the Curvature Scale Space method for 2-D contours . The CSS method has outperformed comparable techniques within the MPEG-7 evaluation framework . As a result , it has been selected for inclusion in the MPEG-7 package of standards
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