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.
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.
@cite_28 @cite_21 @cite_0 @cite_23 @cite_5
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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. In this paper, we introduce a feature-preserving denoising algorithm. It is built on the premise that the underlying surface of a noisy mesh is piecewise smooth, and a sharp feature lies on the intersection of multiple smooth surface regions. A vertex close to a sharp feature is likely to have a neighborhood that includes distinct smooth segments. By defining the consistent subneighborhood as the segment whose geometry and normal orientation most consistent with those of the vertex, we can completely remove the influence from neighbors lying on other segments during denoising. Our method identifies piecewise smooth subneighborhoods using a robust density-based clustering algorithm based on shared nearest neighbors. In our method, we obtain an initial estimate of vertex normals and curvature tensors by robustly fitting a local quadric model. An anisotropic filter based on optimal estimation theory is further applied to smooth the normal field and the curvature tensor field. This is followed by second-order bilateral filtering, which better preserves curvature details and alleviates volume shrinkage during denoising. The support of these filters is defined by the consistent subneighborhood of a vertex. We have applied this algorithm to both generic and CAD models, and sharp features, such as edges and corners, are very well preserved. 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. One of the main challenges in editing a mesh is to retain the visual appearance of the surface after applying various modifications. In this paper we advocate the use of linear differential coordinates as means to preserve the high-frequency detail of the surface. The differential coordinates represent the details and are defined by a linear transformation of the mesh vertices. This allows the reconstruction of the edited surface by solving a linear system that satisfies the reconstruction of the local details in least squares sense. Since the differential coordinates are defined in a global coordinate system they are not rotation-invariant. To compensate for that, we rotate them to agree with the rotation of an approximated local frame. We show that the linear least squares system can be solved fast enough to guarantee interactive response time thanks to a precomputed factorization of the coefficient matrix. We demonstrate that our approach enables to edit complex detailed meshes while keeping the shape of the details in their natural orientation.