Feature-Preserving Mesh Denoising via Anisotropic Surface Fitting

We propose in this paper a robust surface mesh denoising method that can effectively remove mesh noise while faithfully preserving sharp features. This method utilizes surface fitting and projection techniques. Sharp features are preserved in the surface fitting algorithm by considering an anisotropic neighborhood of each vertex detected by the normal-weighted distance. In addition, to handle the mesh with a high level of noise, we perform a pre-filtering of surface normals prior to the neighborhood searching. A number of experimental results and comparisons demonstrate the excellent performance of our method in preserving important surface geometries while filtering mesh noise.     

Bilateral normal filtering for mesh denoising

Decoupling local geometric features from the spatial location of a mesh is crucial for feature-preserving mesh denoising. This paper focuses on first order features, i.e., facet normals, and presents a simple yet effective anisotropic mesh denoising framework via normal field denoising. Unlike previous denoising methods based on normal filtering, which process normals defined on the Gauss sphere, our method considers normals as a surface signal defined over the original mesh. This allows the design of a novel bilateral normal filter that depends on both spatial distance and signal distance. Our bilateral filter is a more natural extension of the elegant bilateral filter for image denoising than those used in previous bilateral mesh denoising methods. Besides applying this bilateral normal filter in a local, iterative scheme, as common in most of previous works, we present for the first time a global, noniterative scheme for an isotropic denoising. We show that the former scheme is faster and more effective for denoising extremely noisy meshes while the latter scheme is more robust to irregular surface sampling. We demonstrate that both our feature-preserving schemes generally produce visually and numerically better denoising results than previous methods, especially at challenging regions with sharp features or irregular sampling.     

Robust Feature-Preserving Mesh Denoising Based on Consistent Subneighborhoods

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.     

Robust mesh smoothing

This paper proposes a vertex-estimation-based, feature-preserving smoothing technique for meshes. A robust mesh smoothing operator called mean value coordinates flow is introduced to modify mean curvature flow and make it more stable. Also the paper proposes a three-pass vertex estimation based on bilateral filtering of local neighbors which is transferred from image processing settings and a Quasi-Laplacian operation, derived from the standard Laplacian operator, is performed to increase the smoothness order of the mesh rapidly whilst denoising meshes efficiently, preventing volume shrinkage as well as preserving sharp features of the mesh. Compared with previous algorithms, the result shows it is simple, efficient and robust.     

保特征的联合滤波网格去噪算法

目的 在去噪的过程中保持网格模型的特征结构是网格去噪领域研究的热点问题。为了能够在去噪中保持模型特征,本文提出一种基于变分形状近似（VSA）分割算法的保特征网格去噪算法。方法 引入变分形状近似分割算法分析并提取噪声网格模型的几何特征,分3步进行去噪。第1步使用变分形状近似算法对网格进行分割,对模型进行分块降噪预处理。第2步通过分析变分形状近似算法提取分割边界中的特征信息,将网格划分为特征区域与非特征区域。对两个区域用不同的滤波器联合滤波面法向量。第3步根据滤波后的面法向量,使用非迭代的网格顶点更新方法更新顶点位置。结果 相较于现有全局去噪方法,本文方法可以很好地保持网格模型的特征,引入的降噪预处理对于非均匀网格的拓扑结构保持有着很好的效果。通过对含有不同程度高斯噪声的网格模型进行实验表明,本文算法无论在直观上还是定量分析的结果都相较于对比的方法有着更好的去噪效果,实验中与对比算法相比去噪效果提升15%。结论 与现有的网格去噪算法对比,实验结果表明本文算法在中等高斯噪声下更加鲁棒,对常见模型有着比较好的去噪效果,能更好地处理不均匀采样的网格模型,恢复模型原有的特征信息和拓扑结构。     

青铜器纹饰特征增强及自动提取

目的 青铜器是我国的文化瑰宝,然而出土青铜器大多破损、变形,需要修复以进行保护。随着3维激光扫描技术及数字几何处理研究的发展,文物数字化修复技术得到了广泛的重视。在青铜器修复过程中需要将相邻碎片的纹饰对准,以保证纹饰的连续性,从而保证修复质量。因此,青铜器纹饰特征的有效提取是青铜器修复过程中的一项重要工作,鉴于青铜器纹饰特征一般具有比较明显的尖锐边,本文提出并实现了一种青铜器尖锐特征增强及自动提取算法。方法 首先,为了减少网格均匀度对特征提取的不利影响,提出一种加权法向距离;其次,为了增强尖锐特征提取效果,提出一种逆双边滤波算法,并利用该算法获得反锐化掩膜,增强法向距离间的差异性,使得大的更大,小的更小;最后,采用Otsu算法自动确定分割阈值,依据该阈值把网格顶点分为特征点集和非特征点集,实现青铜器纹饰特征的提取。结果 对实际3维激光扫描获得的青铜器模型,分别采用本文算法和Tran等人提出的尖锐特征自动提取算法进行了纹饰特征提取,包括采用两种算法进行了纹饰特征增强前后纹饰特征提取实验,本文使用的3个模型点数在6 000至80万之间,这些模型都可以在1 s到10 s之间得到最终的提取结果,具有较高的效率。同时,本文算法可以更为准确地提取尖锐特征点,且得到的特征点更为连续,有利于进一步的处理。结论 采用本文提出的青铜器纹饰提取算法,能够自动、高效地提取青铜器纹饰特征。     

A new feature-preserving mesh-smoothing algorithm

We present a novel mesh denoising and smoothing method in this paper. Our approach starts by estimating the principal curvatures and mesh saliency value for each vertex. Then, we calculate the uniform principal curvature of each vertex based on the weighted average of local principal curvatures. After that, we use the weighted bi-quadratic Bézier surface to fit the neighborhood of each vertex using the least-square method and obtain the new vertex position by adjusting the parameters of the fitting surface. Experiments show that our smoothing method preserves the geometric feature of the original mesh model efficiently. Our approach also prevents the volume shrinkage of the input mesh and obtains smooth boundaries for non-closed mesh models.     

Bilateral recovering of sharp edges on feature-insensitive sampled meshes

A variety of computer graphics applications sample surfaces of 3D shapes in a regular grid without making the sampling rate adaptive to the surface curvature or sharp features. Triangular meshes that interpolate or approximate these samples usually exhibit relatively big error around the insensitive sampled sharp features. This paper presents a robust general approach conducting bilateral filters to recover sharp edges on such insensitive sampled triangular meshes. Motivated by the impressive results of bilateral filtering for mesh smoothing and denoising, we adopt it to govern the sharpening of triangular meshes. After recognizing the regions that embed sharp features, we recover the sharpness geometry through bilateral filtering, followed by iteratively modifying the given mesh's connectivity to form single-wide sharp edges that can be easily detected by their dihedral angles. We show that the proposed method can robustly reconstruct sharp edges on feature-insensitive sampled meshes.     

Mean shift denoising of point-sampled surfaces

This paper presents an anisotropic denoising/smoothing algorithm for point-sampled surfaces. Motivated by the impressive results of mean shift filtering on image denoising, we extend the concept to 3D surface smoothing by taking the vertex normal and the curvature as the range component and the vertex position as the spatial component. Then the local mode of each vertex on point-based surfaces is computed by a 3D mean shift procedure dependent on local neighborhoods that are adaptively obtained by a kdtree data structure. Clustering pieces of point-based surfaces of similar local mode provides a meaningful model segmentation. Based on the adaptively clustered neighbors, we finally apply a trilateral point filtering scheme that adjusts the position of sample points along their normal directions to successfully reduce noise from point-sampled surfaces while preserving geometric features.     

一种带噪声的密集三角网格细分曲面拟合算法

实现了一个从带噪声的密集三角形拟合出带尖锐特征的细分曲面拟合系统.该系统包括了一种改进的基于图像双边滤波器的网格噪声去除方法,模型的尖锐特征提取以及保持尖锐特征的网格简化和拓扑优化.为了处理局部细节特征和模型数据量问题,提出了自适应细分方法,并将根据给定精度估计最少细分深度引入到细分曲面拟合系统中,使得拟合得到的细分曲面模型具有良好的细节特征和数据量小等特点.大量3D模型实验结果和实际工程应用结果表明了该细分曲面拟合系统的有效性.     

保持特征的三角网格曲面去噪技术综述与展望

三角网格曲面去噪是计算机图形学领域一个经典问题,近年来不断涌现出各种新的去噪方法.该文主要关注保持特征的三角网格曲面去噪技术,总结了三角网格的几何表示以及一系列特征结构,依据算法类型将现有去噪技术分为优化法、滤波法、数据驱动法3类.针对不同的去噪模型和所利用的网格属性,对各分类下的去噪方法进行分析、讨论;简述了4类常用评估准则,从尖锐特征保持能力、体积保持、异常值去除能力、有无顶点漂移现象、有无面片翻转现象5个方面展示不同算法的优缺点;并根据这些算法存在的共性问题提出三角网格曲面去噪技术发展方向.     

快速网格去噪声算法

消除网格噪声是构造完美三维模型过程中必不可少的一步。通过把图像处理领域中的双向滤波引入到三维网格上，Fleishman等虽已提出了一种快速、简单的网格去噪声算法，但该算法效率较低，且不够稳定，为此提出用准柯西函数和泰勒多项式函数取代该算法所采用的高斯函数，并改进和完善了其中的细节部分，以使算法的效率和稳定性得到进一步提高。最后还讨论了如何选择合适的参数，以达到最佳效果的问题。     

面向法向域网格建模的非线性引导滤波

网格建模是数字几何处理领域的基础性研究问题.为了提高网格建模的简便性和鲁棒性,首先提出了一种非线性的引导滤波算法.滤波过程在法向域进行,滤波后的法向是引导网格法向的局部二次变换;然后,应用上述算法研究了建模方面的2个重要问题:网格去噪和网格平滑,其中的难点在于如何构造合适的引导网格.针对去噪问题,每次迭代时利用双边法向滤波得到引导网格;针对平滑问题,引导网格以高斯滤波结果作为初始值,进而结合原始网格不断进行更新;最后,在形状复杂或特征丰富的网格模型上进行了去噪、平滑等实验,结果表明,该算法简单实用、鲁棒,去噪时能够有效地去除强噪声,保持模型的几何特征;平滑时能够提取出中小尺度的特征,保留大尺度的特征.     

Surface interpolation of meshes by geometric subdivision

Subdivision surfaces are generated by repeated approximation or interpolation from initial control meshes. In this paper, two new non-linear subdivision schemes, face based subdivision scheme and normal based subdivision scheme, are introduced for surface interpolation of triangular meshes. With a given coarse mesh more and more details will be added to the surface when the triangles have been split and refined. Because every intermediate mesh is a piecewise linear approximation to the final surface, the first type of subdivision scheme computes each new vertex as the solution to a least square fitting problem of selected old vertices and their neighboring triangles. Consequently, sharp features as well as smooth regions are generated automatically. For the second type of subdivision, the displacement for every new vertex is computed as a combination of normals at old vertices. By computing the vertex normals adaptively, the limit surface is G¹ smooth. The fairness of the interpolating surface can be improved further by using the neighboring faces. Because the new vertices by either of these two schemes depend on the local geometry, but not the vertex valences, the interpolating surface inherits the shape of the initial control mesh more fairly and naturally. Several examples are also presented to show the efficiency of the new algorithms.     

Coarse‐to‐Fine Normal Filtering for Feature‐Preserving Mesh Denoising Based on Isotropic Subneighborhoods

State‐of‐theart normal filters usually denoise each face normal using its entire anisotropic neighborhood. However, enforcing these filters indiscriminately on the anisotropic neighborhood will lead to feature blurring, especially in challenging regions with shallow features. We develop a novel mesh denoising framework which can effectively preserve features with various sizes. Our idea is inspired by the observation that the underlying surface of a noisy mesh is piecewise smooth. In this regard, it is more desirable that we denoise each face normal within its piecewise smooth region (we call such a region as an isotropic subneighborhood) instead of using the anisotropic neighborhood. To achieve this, we first classify mesh faces into several types using a face normal tensor voting and then perform a normal filter to obtain a denoised coarse normal field. Based on the results of normal classification and the denoised coarse normal field, we segment the anisotropic neighborhood of every feature face into a number of isotropic subneighborhoods via local spectral clustering. Thus face normal filtering can be performed again on the isotropic subneighborhoods and produce a more accurate normal field. Extensive tests on various models demonstrate that our method can achieve better performance than state‐of‐theart normal filters, especially in challenging regions with features.     

5–6–7 Meshes: Remeshing and analysis

We introduce a new type of meshes called 5–6–7 meshes. For many mesh processing tasks, low- or high-valence vertices are undesirable. At the same time, it is not always possible to achieve complete vertex valence regularity, i.e. to only have valence-6 vertices. A 5–6–7 mesh is a closed triangle mesh where each vertex has valence 5, 6, or 7. An intriguing question is whether it is always possible to convert an arbitrary mesh into a 5–6–7 mesh. In this paper, we answer the question in the positive. We present a 5–6–7 remeshing algorithm which converts a closed triangle mesh with arbitrary genus into a 5–6–7 mesh which (a) closely approximates the original mesh geometrically, e.g. in terms of feature preservation and (b) has a comparable vertex count as the original mesh. We demonstrate the results of our remeshing algorithm on meshes with sharp features and different topology and complexity.     

Guided Mesh Normal Filtering

The joint bilateral filter is a variant of the standard bilateral filter, where the range kernel is evaluated using a guidance signal instead of the original signal. It has been successfully applied to various image processing problems, where it provides more flexibility than the standard bilateral filter to achieve high quality results. On the other hand, its success is heavily dependent on the guidance signal, which should ideally provide a robust estimation about the features of the output signal. Such a guidance signal is not always easy to construct. In this paper, we propose a novel mesh normal filtering framework based on the joint bilateral filter, with applications in mesh denoising. Our framework is designed as a two‐stage process: first, we apply joint bilateral filtering to the face normals, using a properly constructed normal field as the guidance; afterwards, the vertex positions are updated according to the filtered face normals. We compute the guidance normal on a face using a neighboring patch with the most consistent normal orientations, which provides a reliable estimation of the true normal even with a high‐level of noise. The effectiveness of our approach is validated by extensive experimental results.     

Fast and effective feature-preserving mesh denoising

We present a simple and fast mesh denoising method, which can remove noise effectively, while preserving mesh features such as sharp edges and corners. The method consists of two stages. Firstly, noisy face normals are filtered iteratively by weighted averaging of neighboring face normals. Secondly, vertex positions are iteratively updated to agree with the denoised face normals. The weight function used during normal filtering is much simpler than that used in previous similar approaches, being simply a trimmed quadratic. This makes the algorithm both fast and simple to implement. Vertex position updating is based on the integration of surface normals using a least-squares error criterion. Like previous algorithms, we solve the least-squares problem by gradient descent, but whereas previous methods needed user input to determine the iteration step size, we determine it automatically. In addition, we prove the convergence of the vertex position updating approach. Analysis and experiments show the advantages of our proposed method over various earlier surface denoising methods.     

Feature-preserving mesh denoising based on vertices classification

In this paper, we present an effective surface denoising method for noisy surfaces. The two key steps in this method involve feature vertex classification and an iterative, two-step denoising method depending on two feature weighting functions. The classification for feature vertices is based on volume integral invariant. With the super nature of this integral invariant, the features of vertices can be fixed with less influence of noise, and different denoising degrees can be applied to different parts of the pending surface. Compared with other methods, our approach produces better results in feature-preserving.