Incremental reconstruction of sharp edges on mesh surfaces

Limited by the regular grids in computing, many modelling approaches (e.g. field-based methods) sample 3D shape insensitive to sharp features therefore exhibit aliasing errors, by which a lot of sharp edges and corners are lost on the reconstructed surface. An incremental approach for recovering sharp edges on an insensitive sampled triangular mesh is presented in this paper, so that shape approximation errors are greatly reduced. Either chamfered or blended sharp edges on an input triangular mesh could be successfully reconstructed by the signals inherent in the mesh. As a non-iterative method, our approach could be finished in a very short time comparing to those diffusion-based sharp-feature reproducers. The region embedding sharp features is first identified through normal variations. The positions of vertices in the sharp-feature embedded region are then predicted progressively from outer to the inner of sharp regions so that sharp edges could be recovered in the sense of region shrinking.     

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.     

深度图像的法向指导 GPU 滤波

深度相机获取深度图像由于硬件精度问题,往往会丢失大量细节信息。因此,对深度图像的滤 波,已经成为深度视觉领域一个重要的课题。然而,现阶段大多数滤波的方法对于深度图像中的尖锐特征保留 能力不足,往往会出现过光滑现象。针对深度图像滤波中的尖锐特征难以保留的问题,提出了一种新的深度图 像的联合双边滤波方法。首先求解深度图像每个像素的法向,以投票的方式对法向的权重进行计算以进行联合 双边滤波,最后根据滤波后的法向更新顶点坐标。该方法引入了高精度的纹理作为指导信息,能获取更可信的 滤波效果。另外,该方法基于点云的局部信息,不需要求解很大的矩阵,且基于 GPU 并行,运算效率极高。 实验表明,该方法能更好地保留法向的边界,具有更好的几何特征保留能力。     

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。     

Sharpen&Bend: recovering curved sharp edges in triangle meshes produced by feature-insensitive sampling

Various acquisition, analysis, visualization, and compression approaches sample surfaces of 3D shapes in a uniform fashion without any attempt to align the samples with sharp edges or to adapt the sampling density to the surface curvature. Consequently, triangle meshes that interpolate these samples usually chamfer sharp features and exhibit a relatively large error in their vicinity. We present two new filters that improve the quality of these resampled models. EdgeSharpener restores the sharp edges by splitting the chamfer edges and forcing the new vertices to lie on intersections of planes extending the smooth surfaces incident upon these chamfers. Bender refines the resulting triangle mesh using an interpolating subdivision scheme that preserves the sharpness of the recovered sharp edges while bending their polyline approximations into smooth curves. A combined Sharpen&Bend postprocessing significantly reduces the error produced by feature-insensitive sampling processes. For example, we have observed that the mean-squared distortion introduced by the SwingWrapper remeshing-based compressor can often be reduced by 80 percent executing EdgeSharpener alone after decompression. For models with curved regions, this error may be further reduced by an additional 60 percent if we follow the EdgeSharpening phase by Bender.     

Mesh filtering algorithm using an adaptive 3D convolution kernel applied to a volume-based vector distance field

This paper addresses the problem of feature preserving mesh filtering, which occurs in surface reconstruction of scanned objects, which include acquisition noise to be removed without altering sharp edges. We propose a method based on a vector field distance transform of the mesh to process. It is a volume-based implicit surface modeling, which provides an alternative representation of meshes. We use an adaptive 3D convolution kernel applied to the voxels of the distance transform model. Weights of the kernel elements are determined according to the angle between the vectors of the implicit field. We also propose a new adaptation of the Marching Cubes algorithm in order to extract the isosurface from the vector implicit field after the filtering process. We compare our method to the previous one introduced using the vector field representation and to other feature preserving adaptive filtering algorithms. According to error metric evaluations, we show that our new design provides high quality filtering results while better preserving geometric features.     

自适应尺度的双边纹理滤波方法

目前已有的结构保持的纹理平滑方法主要是利用矩形片内的统计量来区分纹理和结构,但是所用的矩形片边长是单一尺度的,这将导致含有尖锐结构或结构在多个尺度上的图像出现纹理过平滑或未平滑的现象。为此,提出一种自适应尺度的双边纹理滤波方法。首先,通过对局部区域进行统计分析,从给定候选值中自适应地为每个像素选取合适的矩形片边长,对于均匀的纹理区域,选取较大的矩形片边长,对于邻近特征边的区域选取较小边长;其次,利用自适应的矩形片边长计算引导图像;最后,对原始图像进行引导双边滤波。实验结果表明,所提方法能够在保持图像结构的同时更好地平滑纹理。     

三角网格特征边识别的一种有效方法

三角网格特征边识别在数字几何处理和计算机辅助制造(CAM)的模具加工中都有 着广泛的应用,该文指出了近年来有关网格特征边识别算法的各种弊端及原因,给出了一种鲁 棒的网格特征边识别新算法。该算法以网格特征点的识别为基础,能够识别以往算法常遗漏的 一些二面法向夹角比较小的网格边,增强了对C1 不连续网格边的识别能力。众多数值例子支 持了这个结论。     

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.     

强边缘提取网络用于非均匀运动模糊图像盲复原

基于深度学习的非均匀运动图像去模糊方法已经获得了较好的效果. 然而, 现有的方法通常存在对边缘恢复不清晰的问题. 因此, 本文提出一种强边缘提取网络(Strong-edge extraction network, SEEN), 用于提取非均匀运动模糊图像的强边缘以提高图像边缘复原质量. 设计的强边缘提取网络由两个子网络SEEN-1和SEEN-2组成, SEEN-1实现双边滤波器的功能, 用于提取滤除了细节信息后的图像边缘. SEEN-2实现L₀平滑滤波器的功能, 用于提取模糊图像的强边缘. 本文还将对应网络层提取的强边缘特征图与模糊特征图叠加, 进一步利用强边缘特征. 最后, 本文在GoPro数据集上进行了验证实验, 结果表明: 本文提出的网络可以较好地提取非均匀运动模糊图像的强边缘, 复原图像在客观和主观上都可以达到较好的效果.     

Feature-preserving surface mesh smoothing via suboptimal Delaunay triangulation

A method of triangular surface mesh smoothing is presented to improve angle quality by extending the original optimal Delaunay triangulation (ODT) to surface meshes. The mesh quality is improved by solving a quadratic optimization problem that minimizes the approximated interpolation error between a parabolic function and its piecewise linear interpolation defined on the mesh. A suboptimal problem is derived to guarantee a unique, analytic solution that is significantly faster with little loss in accuracy as compared to the optimal one. In addition to the quality-improving capability, the proposed method has been adapted to remove noise while faithfully preserving sharp features such as edges and corners of a mesh. Numerous experiments are included to demonstrate the performance of the method.     

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.     

Extracting Sharp Features from RGB‐D Images

Sharp edges are important shape features and their extraction has been extensively studied both on point clouds and surfaces. We consider the problem of extracting sharp edges from a sparse set of colour‐and‐depth (RGB‐D) images. The noise‐ridden depth measurements are challenging for existing feature extraction methods that work solely in the geometric domain (e.g. points or meshes). By utilizing both colour and depth information, we propose a novel feature extraction method that produces much cleaner and more coherent feature lines. We make two technical contributions. First, we show that intensity edges can augment the depth map to improve normal estimation and feature localization from a single RGB‐D image. Second, we designed a novel algorithm for consolidating feature points obtained from multiple RGB‐D images. By utilizing normals and ridge/valley types associated with the feature points, our algorithm is effective in suppressing noise without smearing nearby features.     

Detection of Salient Curvature Features on Polygonal Surfaces

We develop an approach for stable detection of perceptually salient curvature features on surfaces approximated by dense triangle meshes. The approach explores an "area degenerating" effect of the focal surface near its singularities and combines together a new approximations of the mean and Gaussian curvatures, nonlinear averaging of curvature maps, histogram-based curvature extrema filtering, and an image processing skeletonization procedure adapted for triangular meshes. Finally we use perceptually significant curvature extrema triangles to enhance the Garland-Heckbert mesh decimation method.     

Evolution of T-spline level sets for meshing non-uniformly sampled and incomplete data

Given a large set of unorganized point sample data, we propose a new framework for computing a triangular mesh representing an approximating piecewise smooth surface. The data may be non-uniformly distributed, noisy, and may contain holes. This framework is based on the combination of two types of surface representations, triangular meshes and T-spline level sets, which are implicit surfaces defined by refinable spline functions allowing T-junctions. Our method contains three main steps. Firstly, we construct an implicit representation of a smooth (C ² in our case) surface, by using an evolution process of T-spline level sets, such that the implicit surface captures the topology and outline of the object to be reconstructed. The initial mesh with high quality is obtained through the marching triangulation of the implicit surface. Secondly, we project each data point to the initial mesh, and get a scalar displacement field. Detailed features will be captured by the displaced mesh. Finally, we present an additional evolution process, which combines data-driven velocities and feature-preserving bilateral filters, in order to reproduce sharp features. We also show that various shape constraints, such as distance field constraints, range constraints and volume constraints can be naturally added to our framework, which is helpful to obtain a desired reconstruction result, especially when the given data contains noise and inaccuracies.     

Feature‐Preserving Surface Reconstruction From Unoriented,Noisy Point Data

We propose a robust method for surface mesh reconstruction from unorganized, unoriented, noisy and outlier‐ridden 3D point data. A kernel‐based scale estimator is introduced to estimate the scale of inliers of the input data. The best tangent planes are computed for all points based on mean shift clustering and adaptive scale sample consensus, followed by detecting and removing outliers. Subsequently, we estimate the normals for the remaining points and smooth the noise using a surface fitting and projection strategy. As a result, the outliers and noise are removed and filtered, while the original sharp features are well preserved. We then adopt an existing method to reconstruct surface meshes from the processed point data. To preserve sharp features of the generated meshes that are often blurred during reconstruction, we describe a two‐step approach to effectively recover original sharp features. A number of examples are presented to demonstrate the effectiveness and robustness of our method.     

具有特殊效果的混合细分方法

提出了基于三角形和四边形的混合控制网格的细分曲面尖锐特征、半尖锐特征生成和控制方法,避免了已有方法仅局限于初始控制网格为单一的三角形或单一的四边形网格的缺陷.通过局部修改混合细分规则,在光滑混合曲面上产生了刺、尖、折痕、角的尖锐特征效果,并对尖锐特征处局部细分矩阵进行了详细的特征分析,讨论了极限曲面的收敛性及光滑性.同时,用特征处的离散曲率来控制特征处的尖锐程度,实现了半尖锐的特征效果,并通过自适应细分方法,把尖锐特征、半尖锐特征的生成统一起来.该方法具有多分辨率表示能力强、局部性好、简单易操作的特点.实验结果表明,该算法效果好,成功地解决了混合曲面特殊效果生成问题.     

带尖锐特征的Loop细分曲面拟合系统

实现了一个基于带尖锐特征的Loop细分曲面的三角网格拟合系统,其基本原理来自文献,但在系统设计层面对原算法作了相当大的补充和完善．整个系统框架包括尖锐特征提取、保持尖锐特征的三角网格简化、保持尖锐特征的网格平滑和拓扑优化、基于最近点策略的重采样和线性拟合系统求解．所得到的拟合曲面质量较原来的结果有了显著提高。     

Fitting polynomial surfaces to triangular meshes with Voronoi squared distance minimization

This paper introduces Voronoi squared distance minimization (VSDM), an algorithm that fits a surface to an input mesh. VSDM minimizes an objective function that corresponds to a Voronoi-based approximation of the overall squared distance function between the surface and the input mesh (SDM). This objective function is a generalization of the one minimized by centroidal Voronoi tessellation, and can be minimized by a quasi-Newton solver. VSDM naturally adapts the orientation of the mesh elements to best approximate the input, without estimating any differential quantities. Therefore, it can be applied to triangle soups or surfaces with degenerate triangles, topological noise and sharp features. Applications of fitting quad meshes and polynomial surfaces to input triangular meshes are demonstrated.     

Lattice-Based High-Dimensional Gaussian Filtering and the Permutohedral Lattice

High-dimensional Gaussian filtering is a popular technique in image processing, geometry processing and computer graphics for smoothing data while preserving important features. For instance, the bilateral filter, cross bilateral filter and non-local means filter fall under the broad umbrella of high-dimensional Gaussian filters. Recent algorithmic advances therein have demonstrated that by relying on a sampled representation of the underlying space, one can obtain speed-ups of orders of magnitude over the naïve approach. The simplest such sampled representation is a lattice, and it has been used successfully in the bilateral grid and the permutohedral lattice algorithms. In this paper, we analyze these lattice-based algorithms, developing a general theory of lattice-based high-dimensional Gaussian filtering. We consider the set of criteria for an optimal lattice for filtering, as it offers a good tradeoff of quality for computational efficiency, and evaluate the existing lattices under the criteria. In particular, we give a rigorous exposition of the properties of the permutohedral lattice and argue that it is the optimal lattice for Gaussian filtering. Lastly, we explore further uses of the permutohedral-lattice-based Gaussian filtering framework, showing that it can be easily adapted to perform mean shift filtering and yield improvement over the traditional approach based on a Cartesian grid.