text: This paper presents a two-stage mesh denoising algorithm. Unlike other traditional averaging approaches, our approach uses an element-based normal voting tensor to compute smooth surfaces. By introducing a binary optimization on the proposed tensor together with a local binary neighborhood concept, our algorithm better retains sharp features and produces smoother umbilical regions than previous approaches. On top of that, we provide a stochastic analysis on the different kinds of noise based on the average edge length. The quantitative results demonstrate that the performance of our method is better compared to state-of-the-art smoothing approaches.
  @cite_28: Mesh vertices are usually represented with absolute coordinates. In some applications, this leads to problems for local operations because of global misalignment. We investigate the idea of describing mesh geometry in a differential way. These differential coordinates describe local properties of the geometry rather than the absolute position in space. The main application discussed here is the insertion of shape features from one mesh into another, given the meshes have the same connectivity. We regard this as local control overmesh morphing. Differential coordinates also prove useful for free-form modeling of meshes.
  @cite_21: In this paper, we propose a novel triangle mesh denoising method based on the differential coordinates. The proposed approach consists of the application of the mean filter to differential coordinates of the mesh and the reconstruction of mesh vertices' Cartesian coordinates to make them fit to the modified differential coordinates. The presented method is simple, stable and able to effectively remove large noise. Experimental results demonstrate that the proposed Mesh Mean Filter does not cause surface shrinkage and shape distortion during the denoising process, and preserves geometric detail features to a certain extent.
  @cite_0: In this paper, we develop methods to rapidly remove rough features from irregularly triangulated data intended to portray a smooth surface. The main task is to remove undesirable noise and uneven edges while retaining desirable geometric features. The problem arises mainly when creating high-fidelity computer graphics objects using imperfectly-measured data from the real world. Our approach contains three novel features: an implicit integration method to achieve efficiency, stability, and large time-steps; a scale-dependent Laplacian operator to improve the diffusion process; and finally, a robust curvature flow operator that achieves a smoothing of the shape itself, distinct from any parameterization. Additional features of the algorithm include automatic exact volume preservation, and hard and soft constraints on the positions of the points in the mesh. We compare our method to previous operators and related algorithms, and prove that our curvature and Laplacian operators have several mathematically-desirable qualities that improve the appearance of the resulting surface. In consequence, the user can easily select the appropriate operator according to the desired type of fairing. Finally, we provide a series of examples to graphically and numerically demonstrate the quality of our results.
  @cite_23: Surface representation and processing is one of the key topics in computer graphics and geometric modeling, since it greatly affects the range of possible applications. In this paper we will present recent advances in geometry processing that are related to the Laplacian processing framework and differential representations. This framework is based on linear operators defined on polygonal meshes, and furnishes a variety of processing applications, such as shape approximation and compact representation, mesh editing, watermarking and morphing. The core of the framework is the definition of differential coordinates and new bases for efficient mesh geometry representation, based on the mesh Laplacian operator.
  @cite_5: SUMMARY In contrast to most triangulation algorithms which implicitly assume that triangulation point locations are fixed, 'Laplacian' smoothing focuses on moving point locations to improve triangulation. Laplacian smoothing is attractive for its simplicity but it does require an existing triangulation. In this paper the effect of Laplacian smoothing on Delaunay triangulations is explored. It will become clear that constraining Laplacian smoothing to maintain a Delaunay triangulation measurably improves Laplacian smoothing. An early reference to the use of Laplacian smoothing is to be found in a papel by Buell and Bush.' They surveyed the use of Laplace's equation to generate two-dimensional meshes, and described an equipotential method2 which extends finite differences of Laplace's equation on rectangular grids to differences on triangular grids. On triangular grids, the weighted difference equations
summary: Isotropic smoothing methods are the earliest smoothing algorithms. These algorithms have low complexity but suffer from severe shrinkage and further feature blurring @cite_5 . @cite_0 introduced an implicit smoothing algorithm that produces stable results against irregular meshes and avoids the shrinkage by volume preservation. Later, the concept of the differential coordinates was introduced by Alexa @cite_28 as a local shape descriptor of a geometry. exploited the differential coordinates concept for mesh denoising by computing the mean of the differential coordinates at each vertex and then computes a smooth surface according to the mean differential coordinates @cite_21 . This method produces less shrinkage but is unable to preserve shallow features. The differential coordinates framework has been extended for a variety of mesh processing algorithms by Sorkine @cite_23 . In general, isotropic smoothing methods are prone to shrink volumes and blur features, but effective in noise removal.