Erosion Thickness on Medial Axes of 3D Shapes

摘要

While playing a fundamental role in shape understanding, the medialrnaxis is known to be sensitive to small boundary perturbations.rnMethods for pruning the medial axis are usually guided by somernmeasure of significance. The majority of significance measuresrnover the medial axes of 3D shapes are locally defined and hencernunable to capture the scale of features. We introduce a global significancernmeasure that generalizes in 3D the classical Erosion Thicknessrn(ET) measure over the medial axes of 2D shapes. We givernprecise definition of ET in 3D, analyze its properties, and presentrnan efficient approximation algorithm with bounded error on a piecewisernlinear medial axis. Experiments showed that ET outperformsrnlocal measures in differentiating small boundary noise from prominentrnshape features, and it is significantly faster to compute thanrnexisting global measures. We demonstrate the utility of ET in extractingrnclean, shape-revealing and topology-preserving skeletonsrnof 3D shapes.