HLO: Half-kernel Laplacian operator for surface smoothing. (April 2020) - Pan, Wei; Lu, Xuequan; Gong, Yuanhao; Tang, Wenming; Liu, Jun; He, Ying; Qiu, Guoping
Abstract: This paper presents a simple yet effective and efficient method for feature-preserving 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 non-differentiable and the second order derivatives do not exist. To overcome this difficulty, we propose a Half-kernel 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 full-window 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 Laplacian-based denoising and it significantly alleviates the shrinkage artifact. Extensive experimental results demonstrate that HLO is better than or comparable to state-of-the-art 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. Graphical abstract: Highlights: Mathematical analysis of the differential property at feature points. A half-window algorithm to generate multiple half windows (subsets) for each vertex. A half-kernel Laplacian operator for feature-preserving surface smoothing.