A dynamic balanced flow for filtering point-sampled geometry

3D point data acquisition has become a practical approach for generating complex 3D shapes. Subsequent smoothing or denoising operations on these raw data sets are required before performing sophisticated modeling operations. Based on covariance analysis and constructed directional curvature, a new approach of anisotropic curvature flow is developed for filtering the point data set. By introducing a forcing term, a balanced flow equation is constructed, which allows the anisotropic diffusion flow to be restricted in the flow diffusion band of the original surface. Thus, the common problem of shape shrinkage that puzzles most current denoising approaches for point-sampled geometry is avoided. Applying dynamic balance techniques, the equation converges to the solution quickly with appealing physical interpretations. The algorithms operate directly on the discrete sample points, requiring no vertex connectivity information. They are shown to be computationally efficient, robust and simple to implement.     

一种基于带噪声的三角网格模型的光顺算法

为了去除三角网格模型中的噪声,提出了一种基于均值漂移的特征保持的网格光顺算法。该方法在对模型中的三角形的法向量进行滤波的基础上鲁棒地计算了顶点的法向量,利用均值漂移方法自适应地聚类出顶点的邻域。结合顶点间几何特征的相似性,将改进后的双边滤波算子应用于顶点的位置更新,从而完成模型的光顺。实验结果证明了网格光顺算法的有效性。利用这种网格算法,可以达到光顺带噪声的三角网格模型的目的,并在光顺的同时,有效地保持了模型中原有的特征。     

Touch-based haptics for interactive editing on point set surfaces

A modeling paradigm for haptics-based editing on point set surfaces exploits implicit surfaces, physics-based modeling, point-sampled surfaces, and haptic. We propose a point-based geometry representation that we initially designed for dynamic physics-based sculpting, but can easily generalize to other relevant applications such as data modeling and human-computer interaction. By extending the idea of the local reference domain in the moving least square (MLS) surface model to the construction of a local and global surface distance field, we naturally incorporate Hua and Qin's dynamic implicit volumetric model into our deformation of the point-based geometry, which not only facilitates topology change but also affords dynamic sculpting and deformation.     

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.     

A Gradient-Domain Based Geometry Processing Framework for Point Clouds

The use of point clouds is becoming increasingly popular. We present a general framework for performing geometry filtering on point-based surface through applying the meshless local Petrol-Galelkin (MLPG) to obtain the solution of a screened Poisson equation. The enhancement or smoothing of surfaces is controlled by a gradient scale parameter. Anisotropic filtering is supported by the adapted Riemannian metric. Contrary to the other approaches of partial differential equation for point-based surface, the proposed approach neither needs to construct local or global triangular meshes, nor needs global parameterization. It is only based on the local tangent space and local interpolated surfaces. Experiments demonstrate the efficiency of our approach.     

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.     

Improved,feature-centric EMD for 3D surface modeling and processing

Since late 1990s, Empirical Mode Decomposition (EMD) starts to emerge as a powerful tool for processing non-linear and non-stationary signals. Nonetheless, the research on exploring EMD-relevant techniques in the domain of geometric modeling and processing is extremely rare. Directly applying EMD to coordinate functions of 3D shape geometry will not take advantage of the attractive EMD properties. To ameliorate, in this paper we articulate a novel 3D surface modeling and processing framework founded upon improved, feature-centric EMD, with a goal of realizing the full potential of EMD. Our strategy starts with a measure of mean curvature as a surface signal for EMD. Our newly-formulated measure of mean curvature is computed via the inner product of Laplacian vector and vertex normal. Such measure is both rotation-invariant and translation-invariant, facilitates the computation of different scale features for original surfaces, and avoids boundary shrinkage when processing open surfaces. Moreover, we modify the original EMD formulation by devising a feature-preserving multiscale decomposition algorithm for surface analysis and synthesis. The key idea is to explicitly formulate details as oscillation between local minima and maxima. Within our novel framework, we could accommodate many modeling and processing operations, such as filter design, detail transfer, and feature-preserving smoothing and denoising. Comprehensive experiments and quantitative evaluations/comparisons on popular models have demonstrated that our new surface processing methodology and algorithm based on the improved, feature-centric EMD are of great value in digital geometry processing, analysis, and synthesis.     

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.     

Fuzzy vector median-based surface smoothing

This paper proposes a novel approach for smoothing surfaces represented by triangular meshes. The proposed method is a two-step procedure: surface normal smoothing through fuzzy vector median (FVM) filtering followed by integration of surface normals for vertex position update based on the least square error (LSE) criteria. Median and Order Statistic-based filters are extensively used in signal processing, especially image processing, due to their ability to reject outliers and preserve features such as edges and monotonic regions. More recently, fuzzy ordering theory has been introduced to allow averaging among similarly valued samples. Fuzzy ordering theory leads naturally to the fuzzy median, which yields improved noise smoothing over traditional crisp median filters. This paper extends the fuzzy ordering concept to vector-based data and introduces the fuzzy vector median filter. The application of FVM filters to surface normal smoothing yields improved results over previously introduced normal smoothing algorithms. The improved filtering results, coupled with LSE vertex position update, produces surface smoothing that minimizes the effects of noise while simultaneously preserving detail features. The proposed method is simple to implement and relatively fast. Simulation results are presented showing the performance of the proposed method and its advantages over commonly used surface smoothing algorithms. Additionally, optimization procedures for FVM filters are derived and evaluated.     

基于噪声分类的双边滤波点云去噪算法

针对三维点云数据模型在去噪光顺中存在不同尺度噪声的问题,提出一种基于噪声分类的双边滤波点云去噪算法。该算法首先将噪声细分为大尺度和小尺度噪声,并使用统计滤波结合半径滤波对大尺度噪声进行去除;然后对三维点云数据进行曲率估计,并对现有点云双边滤波进行改进,增强其鲁棒性和保特征性;最后使用改进的双边滤波对小尺度噪声进行光顺,实现三维点云数据模型的去噪、光顺。与单独使用双边滤波、Fleishman双边滤波相比,改进算法在三维点云数据模型光顺平均误差指标上分别降低了50.53%和21.67%。实验结果表明,该改进算法对噪声进行尺度的细分既提高了计算效率,又避免了过光顺和细节失真,较好地保持模型中的几何特征。     

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。     

矿区遥感图像去噪方法研究

去噪是矿区遥感图像得以有效应用的重要预处理步骤。现有的基于统计、基于域变换、基于学习等遥感图像去噪方法普遍存在细节过度平滑、纹理保持不足等问题。基于引导滤波良好的边缘保持特性,提出了迭代引导滤波方法,通过对残差信息进行引导映射,并迭代进行引导滤波及超参数收缩,增强了遥感图像边缘特征提取效果;将迭代引导滤波与传统的小波软阈值、非局部均值(NLM)滤波、三维块匹配(BM3D)滤波等去噪方法结合,有效提高了传统方法的峰值信噪比,其中NLM滤波、BM3D滤波的去噪性能提升效果最明显;将迭代引导滤波与BM3D滤波融合,通过BM3D滤波初步获取去噪图像,得到残差数据,然后采用迭代引导滤波对残差数据进行处理,在提升图像去噪效果的同时,很好地保持了图像细节特征;将迭代引导滤波与BM3D滤波融合方法用于矿区遥感图像的煤矸石场识别及滑坡区域边缘识别,取得了较好的效果。     

点云模型的噪声分类去噪算法

针对三维点云模型数据在去噪平滑过程中存在的不同尺度噪声和算法计算耗时问题,提出了点云模型的噪声分类去噪算法。该算法根据噪声点分布特性,将其分为大尺度和小尺度噪声,先利用统计滤波结合半径滤波去除大尺度噪声;然后使用快速双边滤波对小尺度噪声进行平滑,实现点云模型的去噪和平滑。与传统的双边滤波相比,利用快速双边滤波对点云模型数据进行平滑,有效地提高了计算效率。实验结果表明,该算法对点云噪声进行快速平滑去除的同时又能有效地保持被扫描物体的几何特征。     

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.     

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.     

Segmenting point-sampled surfaces

Extracting features from point-based representations of geometric surface models is becoming increasingly important for purposes such as model classification, matching, and exploration. In an earlier paper, we proposed a multiphase segmentation process to identify elongated features in point-sampled surface models without the explicit construction of a mesh or other surface representation. The preliminary results demonstrated the strength and potential of the segmentation process, but the resulting segmentations were still of low quality, and the segmentation process could be slow. In this paper, we describe several algorithmic improvements to overcome the shortcomings of the segmentation process. To demonstrate the improved quality of the segmentation and the superior time efficiency of the new segmentation process, we present segmentation results obtained for various point-sampled surface models. We also discuss an application of our segmentation process to extract ridge-separated features in point-sampled surfaces of CAD models.     

A quasi-Monte Carlo method for computing areas of point-sampled surfaces

A novel and efficient quasi-Monte Carlo method for computing the area of a point-sampled surface with associated surface normal for each point is presented. Our method operates directly on the point cloud without any surface reconstruction procedure. Using the Cauchy-Crofton formula, the area of the point-sampled surface is calculated by counting the number of intersection points between the point cloud and a set of uniformly distributed lines generated with low-discrepancy sequences. Based on a clustering technique, we also propose an effective algorithm for computing the intersection points of a line with the point-sampled surface. By testing on a number of point-based models, experiments suggest that our method is more robust and more efficient than those conventional approaches based on surface reconstruction.     

邻域自适应的三维点云滤波算法

针对现有的点云滤波算法存在的精度丢失和收缩的不足,提出邻域自适应选择的算法,有效地改善了点云滤波中丢失精度的问题.算法首先针对原始点和均值点滤波出现的收缩问题,提出混合增采样策略.其次采用邻域自适应选择保持特征部分的滤波精度.最后定义每个采样点以对应的似然函数,并按照其梯度方向进行迭代,通过最大似然估计得到最优滤波结果...     

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.     

Detail-generating geometry completion for point-sampled geometry

In this paper, we present a novel method for detail-generating geometry completion over point-sampled geometry. The main idea consists of converting the context-based geometry completion into the detail-based texture completion on the surface. According to the influence region of boundary points surrounding a hole, a smooth patch covering the hole is first constructed using radial base functions. By applying region-growing clustering to the patch, the patching units for further completion with geometry details is then produced, and using the trilateral filtering operator formulated by us, the geometry-detail texture of each sample point on the input geometry is determined. The geometry details on the smooth completed patch are finally generated by optimizing a constrained global texture energy function on the point-sampled surfaces. Experimental results demonstrate that the method can achieve efficient completed patches that not only conform with their boundaries, but also contain the plausible 3D surface details.