Fairing of Polygon Meshes Via Bayesian Discriminant Analysis

Design of an anisotropic diffusion-based filter that performs Bayesian classification for automatic selection of a proper weight for fairing polygon meshes is proposed. The data analysis based on Bayesian classification is adopted to determine the decision boundary for separating potential edge and non-edge vertices in the curvature space. The adaptive diffusion filter is governed by a double-degenerate anisotropic equation that determines how each polygon vertex is moved along its normal direction in the curvature space iteratively until a steady state is reached. The determination of how much a polygon vertex should be moved depends on whether it is a potential edge or a non-edge vertex. At each fairing step, conceptually, a bi-directional curvature map whose boundary line while couched by the weight value can be plotted to understand the type of a vertex. Experimental results show that the proposed diffusion-based approach could effectively smooth out noises while retaining useful data to a very good degree.