HLO: Halfkernel Laplacian operator for surface smoothing Abstract   This paper presents a simple yet effective and efficientw method for featurepreserving surface smoothing. Through analyzing the differential property of surfaces, we show that the conventional discrete Laplacian operator with uniform weights is not applicable to feature points at which the surface is nondifferentiable and the second order derivatives do not exist. To overcome this difficulty, we propose a Halfkernel Laplacian Operator (HLO) as an alternative to the conventional Laplacian. Given a vertex    v   , HLO first finds all pairs of its neighboring vertices and divides each pair into two subsets (called half windows); then computes the uniform Laplacians of all such subsets and subsequently projects the computed Laplacians to the fullwindow uniform Laplacian to alleviate flipping and degeneration. The half window with least regularization energy is then chosen for    v   . We develop an iterative approach to apply HLO for surface denoising. Our method is conceptually simple and easy to use because it has a single parameter, i.e., the number of iterations for updating vertices. We show that our method can preserve features better than the popular uniform Laplacianbased denoising and it significantly alleviates the shrinkage artifact. Extensive experimental results demonstrate that HLO is better than or comparable to stateoftheart techniques both qualitatively and quantitatively and that it is particularly good at handling meshes with high noise. Also, it outperforms all other compared methods in terms of computational time. We make our executable program publicly available.

Gaussianproduct subdivision surfaces Probabilistic distribution models like Gaussian mixtures have shown great potential for improving both the quality and speed of several geometric operators. This is largely due to their ability to model large fuzzy data using only a reduced set of atomic distributions, allowing for large compression rates at minimal information loss. We introduce a new surface model that utilizes these qualities of Gaussian mixtures for the definition and control of a parametric smooth surface. Our approach is based on an enriched mesh data structure, which describes the probability distribution of spatial surface locations around each vertex via a Gaussian covariance matrix. By incorporating this additional covariance information, we show how to define a smooth surface via a nonlinear probabilistic subdivision operator based on products of Gaussians, which is able to capture rich details at fixed control mesh resolution. This entails new applications in surface reconstruction, modeling, and geometric compression.