用反调和平均曲率流实现网格保特征平滑

利用反调和平均曲率流，提出一种各向异性、快速的不规则三角网格去噪算法．模型中选择的各向异性演化权函数比较简单，同时保持了网格的几何特征．分别用显式格式和半隐式格式实现了此平滑算法．提供的数值例子显示了模型的有效性．     

Anisotropic diffusion in vector field visualization on Euclideandomains and surfaces

Vector field visualization is an important topic in scientific visualization. Its aim is to graphically represent field data on two and three-dimensional domains and on surfaces in an intuitively understandable way. Here, a new approach based on anisotropic nonlinear diffusion is introduced. It enables an easy perception of vector field data and serves as an appropriate scale space method for the visualization of complicated flow pattern. The approach is closely related to nonlinear diffusion methods in image analysis where images are smoothed while still retaining and enhancing edges. Here, an initial noisy image intensity is smoothed along integral lines, whereas the image is sharpened in the orthogonal direction. The method is based on a continuous model and requires the solution of a parabolic PDE problem. It is discretized only in the final implementational step. Therefore, many important qualitative aspects can already be discussed on a continuous level. Applications are shown for flow fields in 2D and 3D, as well as for principal directions of curvature on general triangulated surfaces. Furthermore, the provisions for flow segmentation are outlined     

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.     

非线性扩散图像去噪中的耦合自适应保真项研究

讨论了一种基于非线性扩散方程的图像去噪方法.在讨论了图像去噪的3个基本要求的基础上,总结了平均曲率运动去噪模型和总变差去噪模型中利用保真项的不足.将利用图像的局部信息构造的自适应保真项引入到方向扩散去噪模型中,克服了原有方法在耦合保真项上的不足,使新的非线性扩散去噪模型能够在有效地去除噪声的同时很好地保持目标尖角、边缘等重要的几何结构.实验结果表明,耦合自适应保真项的扩散方程能够很好地保持图像中目标的几何结构,同时具有良好的去噪能力.     

Adaptive Continuous-Scale Morphology for Matrix Fields

In this article we consider adaptive, PDE-driven morphological operations for 3D matrix fields arising e.g. in diffusion tensor magnetic resonance imaging (DT-MRI). The anisotropic evolution is steered by a matrix constructed from a structure tensor for matrix valued data. An important novelty is an intrinsically one-dimensional directional variant of the matrix-valued upwind schemes such as the Rouy-Tourin scheme. It enables our method to complete or enhance anisotropic structures effectively. A special advantage of our approach is that upwind schemes are utilised only in their basic one-dimensional version, hence avoiding grid effects and leading to an accurate algorithm. No higher dimensional variants of the schemes themselves are required. Experiments with synthetic and real-world data substantiate the gap-closing and line-completing properties of the proposed method.     

Extracting lines of curvature from noisy point clouds

We present a robust framework for extracting lines of curvature from point clouds. First, we show a novel approach to denoising the input point cloud using robust statistical estimates of surface normal and curvature which automatically rejects outliers and corrects points by energy minimization. Then the lines of curvature are constructed on the point cloud with controllable density. Our approach is applicable to surfaces of arbitrary genus, with or without boundaries, and is statistically robust to noise and outliers while preserving sharp surface features. We show our approach to be effective over a range of synthetic and real-world input datasets with varying amounts of noise and outliers. The extraction of curvature information can benefit many applications in CAD, computer vision and graphics for point cloud shape analysis, recognition and segmentation. Here, we show the possibility of using the lines of curvature for feature-preserving mesh construction directly from noisy point clouds.     

基于局部方差改进的超声图像各向异性扩散去噪算法

针对各向异性扩散算法不能有效区分强噪声和弱边缘的缺点,提出了一种基于图像局部统计特征改进的算法。该算法在对图像进行各向异性扩散去噪的过程中,使用梯度阈值找到图像中灰度变化较大的点,再通过计算局部方差和局部去心方差的差值判断该点是否为噪声点,若是噪声点则使用均值滤波处理。对仿真图像和临床超声图像的实验结果表明:与传统的各向异性扩散算法相比,改进的算法在图像去噪和特征保留的能力上得到了良好的提升。     

基于各向异性扩散活动轮廓模型的左心室MRI分割

结合各向异性扩散算法与梯度矢量流活动轮廓模型,提出了基于各向异性扩散活动轮廓模型并应用于心脏核磁共振图像分割;模型采用各向异性扩散方程构造活动轮廓模型的外部能量函数,得到边界更加清晰的分段平滑图像,运用梯度矢量流将边缘图梯度散射到平坦区域,可以有效抑制噪声,同时保持了目标边界;对左心室核磁共振图像的分割实验表明,该模型可以克服噪声和伪影的干扰,与原梯度矢量流模型相比具有更高的精确性和可靠性,有利于实现自动分割.     

基于剪切波和改进P-M扩散的图像去噪

针对多尺度几何分析方法去噪时产生的伪Gibbs效应和各向异性扩散模型产生的阶梯效应,提出一种基于剪切波的改进各向异性扩散图像去噪方法。首先对噪声图像进行剪切波变换得到不同尺度的系数矩阵,然后利用改进的各向异性扩散方程对变换后的系数进行处理,实现建立在对图像精细分析基础上的各向异性扩散模型。实验结果表明,该方法能较好地抑制噪声和保持边缘,同时有效地抑制伪Gibbs效应,取得良好的视觉效果。     

基于各向异性扩散方程的多层次并行图像去噪

针对利用各向异性扩散方程的去噪模型在求解中存在计算量大、耗时长、影响实时性等缺点,本文充分利用并行知识,提出了有效的解决方案。即基于各向异性扩散去噪模型,设计工作站机群平台,对噪声图像进行条状重叠的数据划分,以便实现算法节点内与节点间的两级并行策略:在机群结点内部采用共享内存结构,机群节点间采用分布内存结构,以二者的最优结合实现并行的层次结构化,从而得到一种高效的多层次并行图像去噪算法。实验结果表明,在基于混合模型的并行环境下,该算法能在一定程度上提高原算法的计算效率,不仅有效地缩短了运行时间,而且仍能获得与其相当的图像去噪质量。     

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。     

An improved speckle-reduction algorithm for SAR images based on anisotropic diffusion

This paper mainly studies the algorithm of anisotropic diffusion for speckle noise removal of SAR images. Because the Gauss curvature driven diffusion method is sensitive to the noise and is of low efficiency on suppressing the speckle noise, an improved denoising algorithm is proposed. The new algorithm introduces the difference curvature as the diffusion coefficients of the function, which solves the problem that Gauss curvature driven diffusion is sensitive to the speckle noise, further, Tukey’s biweight function is used to control the curvature diffusion model, which can not only better protect edges, but also automatically control the diffusion. Numerical experiments show that the improved algorithm can preserve the information of textures, edges while inhibiting the speckle of SAR images.     

几何特征保持的文物点云去噪算法

三维激光扫描是一种快速获取高精度点云的新技术,但由于受物体本身的构造、粗糙程度、纹理以及测量环境等因素的影响,获取的点云数据大多存在孤立的噪声点。针对文物点云数据模型中复杂噪声难以去除的问题,提出一种几何特征保持的点云去噪算法。首先通过栅格划分删除点云中的大尺度噪声;然后定义点云中数据点的曲率因子和密度因子,并通过对其加权构造模糊C均值聚类（Fuzzy C-means clustering, FCM）的目标函数;最后采用该特征加权FCM算法删除小尺度噪声,从而实现点云的去噪处理。实验结果表明,该几何特征保持的去噪算法对文物点云数据具有良好的去噪效果,是一种有效的点云去噪算法。     

小波域上图像非线性扩散滤波

提出一个小波域上图像扩散滤波恢复新模型。主要思想是把原图像作为最精细尺度下的小波子带，根据噪声分布的特点，导出保护较大尺度下信息的泛函模型代替小波阈值除噪，对泛函求变分得：Euler-Lagrange方程。新的滤波方法能避免小波阈值除噪的伪Gibbs现象，改进了同类型非线性扩散方程滤波的效果。利用可加算子分裂(AOS)格式求非线性扩散方程的数值解。实例的数值计算说明对图像滤波和保护边缘的有效性。     

扩散方程的动力学分析

扩散方程－热力学中用于描述热量分布及其变化规律的方程，已在另一门完全不同的学科－计算机视觉中获得了广泛的应用，扩散方程及其变化形式，可用来产生尺度空间及检测边缘，本文从数值解法及动力学分析的角度，分析了线性扩散方程，非线性扩散方程以及偏置的非线性扩散方程，扩散方程的数值迭代解事实上这是一个动力学系统的映身函数，所以扩散过程的稳态是该动力学系统的不动点，扩散方程所产生的尺度空间就是该动力学系统的轨道     

一种改进的各向异性扩散图像去噪方法

研究了基于图像特征方向的正交坐标系,分析了在此框架下的各向异性扩散图像去噪原理。然后根据人类视觉系统的一些特性提出了一种改进的各向异性扩散方法。该方法避免了各向异性扩散方程的不适定问题。实验结果表明,该方法在噪声消除和边缘保留方面能获得较好的效果。     

Image Compression with Anisotropic Diffusion

Compression is an important field of digital image processing where well-engineered methods with high performance exist. Partial differential equations (PDEs), however, have not much been explored in this context so far. In our paper we introduce a novel framework for image compression that makes use of the interpolation qualities of edge-enhancing diffusion. Although this anisotropic diffusion equation with a diffusion tensor was originally proposed for image denoising, we show that it outperforms many other PDEs when sparse scattered data must be interpolated. To exploit this property for image compression, we consider an adaptive triangulation method for removing less significant pixels from the image. The remaining points serve as scattered interpolation data for the diffusion process. They can be coded in a compact way that reflects the B-tree structure of the triangulation. We supplement the coding step with a number of amendments such as error threshold adaptation, diffusion-based point selection, and specific quantisation strategies. Our experiments illustrate the usefulness of each of these modifications. They demonstrate that for high compression rates, our PDE-based approach does not only give far better results than the widely-used JPEG standard, but can even come close to the quality of the highly optimised JPEG2000 codec.     

On Using Anisotropic Diffusion for Skeleton Extraction

We present a novel and effective skeletonization algorithm for binary and gray-scale images, based on the anisotropic heat diffusion analogy. We diffuse the image in the direction normal to the feature boundaries and also allow tangential diffusion (curvature decreasing diffusion) to contribute slightly. The proposed anisotropic diffusion provides a high quality medial function in the image: it removes noise and preserves prominent curvatures of the shape along the level-sets (skeleton features). The skeleton strength map, which provides the likelihood of a point to be part of the skeleton, is defined by the mean curvature measure. Finally, thin and binary skeleton is obtained by non-maxima suppression and hysteresis thresholding of the skeleton strength map. Our method outperforms the most related and the popular methods in skeleton extraction especially in noisy conditions. Results show that the proposed approach is better at handling noise in images and preserving the skeleton features at the centerline of the shape.     

散乱点云分割技术研究与实现

点云分割是根据空间、几何和纹理等特征对点云进行划分,使得同一划分内的点云具有相似的特征。首先对获取的散乱点云数据进行去噪、填补空洞和畸变等预处理,然后计算最小包围立方体分割点云空间并构建八叉树加速邻域点的搜索,为每个点构造最小二乘邻域,分析散乱点云数据的高斯曲率和平均曲率,再通过区域生长法得到低噪声的精确分块,自适应、智能化地对点云进行分块。经实验验证,该方法可以获得较好的分割效果。     

Robust structure from motion with affine camera via low-rank matrix recovery

We present a novel approach to structure from motion that can deal with missing data and outliers with an affine camera. We model the corruptions as sparse error. Therefore the structure from motion problem is reduced to the problem of recovering a low-rank matrix from corrupted observations. We first decompose the matrix of trajectories of features into low-rank and sparse components by nuclear-norm and l1-norm minimization, and then obtain the motion and structure from the low-rank components by the classical factorization method. Unlike pervious methods, which have some drawbacks such as depending on the initial value selection and being sensitive to the large magnitude errors, our method uses a convex optimization technique that is guaranteed to recover the low-rank matrix from highly corrupted and incomplete observations. Experimental results demonstrate that the proposed approach is more efficient and robust to large-scale outliers.