l1优化在网格去噪中的应用

目的 网格去噪是计算机图形学中的经典问题,而如何在去除噪声的同时保持网格的特征结构是这一研究方向所面临的最大挑战。方法 提出一种具有稀疏性的全局网格去噪方法,该方法源于信号处理理论中稀疏表示的基本思想,通过优化全局能量函数来去除网格模型的噪声,同时能够保持网格模型的特征结构。该方法共分为两个步骤,第1步为网格面法向量的滤波,首先建立全局优化模型,对噪声网格的面法向量进行滤波优化,其中引入l₁范数来保证解的稀疏性,使得优化后新的面法向量能够保持网格的特征结构;第2步为网格曲面的重建,根据第1步得到的新的面法向量,按照面法向量的定义,建立最小二乘意义下的网格顶点的重建模型,求解得到新的网格曲面。结果 由于该模型是全局方法,避免了现有滤波方法可能出现的不收敛等问题,能够取得比较满意的去噪效果。结论 大量实验结果表明,本文方法在去除噪声的同时,能较好地保持网格的特征结构,尤其对于CAD模型有很好的实验效果。     

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。     

基于局部特征匹配的网格去噪算法

由于三维扫描设备精度不足以及各类人为因素的影响,扫描获取的三维模型不可避免地包含了噪声信息。如何有效地去除扫描模型中的噪声一直是一个经典热门问题。文中提出了一个数据驱动的算法,通过分析已有的噪声模型和对应原始模型数据,建立噪声模型局部几何特征与原始模型法向量之间的数据映射关系,再利用此信息局部特征匹配得到去噪后网格。实验结果表明,该方法可以有效地对网格进行去噪,在去除噪声的同时,可以很好地保持网格的特征结构。     

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.     

基于面法向量谱变换的网格光顺算法

微分坐标是刻画网格模型几何细节特征的有力工具,面法向量作为网格模型的一阶微分量,计算简单、不易受噪声影响,能真实反映网格模型的细节特征。基于此,提出一种改进的网格光顺去噪算法,使用信号处理技术中的谱网格处理方法,通过分解面法向量的拉普拉斯矩阵,将网格模型的面法向量变换到频谱域中,利用低频滤波器去除高频噪声得到连续的面法向量信号,基于三角面片重心约束条件重建网格顶点坐标,得到光顺的网格模型。实验结果表明,该算法使用的面法向量不易受到噪声影响,比顶点法向量更鲁棒,大幅提高了谱分解的效率,并且能克服光顺过程中产生的体积收缩、变形和过光滑等现象。     

利用面片法向均值滤波的混合型网格去噪方法

通过对面片法向均值滤波去噪方法的研究,提出了一种改进的混合型去噪算法。通过取值顶点的一环正常边二面角的平均,将顶点分为噪声顶点和一般顶点,然后对噪声顶点利用Laplacian方法进行平移去噪,同时将保持特征的面片法向均值滤波去噪方法作用于一般顶点。实验结果表明：这种混合方法能有效地去除大小噪声,并且在去噪过程中能保持网格的特征。     

面向可展特征的网格模型去噪方法

可展特征是三维网格模型的常见几何特征。为了更好地对具备可展特征的网格模型进行去噪,提出一种面向可展特征的网格模型去噪方法。首先基于变分形状逼近策略分割可展区域,识别出网格模型上可展特征区域,并对分割区域进行基于可展性度量的合并和划分,改进现有 L 0 去噪算法中针对非均匀噪声网格的正则优化表达项,引入三角网格顶点的可展度量项,利用可展特征的曲面法向量 L 0 范数的优化问题求解实现网格模型的去噪。通过对多个模型数据集中的大量模型数据进行处理,验证了该方法的有效性。实验表明,结合模型的可展特性的去噪方法在保持模型的几何特征特别是可展特征上效果优于已有方法。     

基于面法向规范化的重加权全局双边滤波

在网格去噪中,由于面法向对于噪声非常敏感,当网格噪声较大时,依赖于2个高斯函数的双边滤波器难以找到合适的方差参数来自适应地区分噪声和特征附近的法向变化,导致出现无法有效地去除噪声或者破坏网格的结构特征的问题.为此,提出一种改进的基于面法向的全局双边滤波算法.首先通过面法向规范化加强对噪声和特征附近面法向变化的区分,应用规范化后的法向量计算双边滤波中刻画法向变化的权重,以克服参数选择难题;其次根据重加权的思想加大对噪声的惩罚力度,进一步提高了降噪效果.大量实验结果表明,该算法无论从视觉上还是从数值上都取得了比现有算法更好的降噪结果.     

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.     

基于RPCA视频去噪算法的自适应优化方法

传统去噪算法不能在尽量滤除噪声的同时很好地保持原始图像信息。针对这种情况,提出基于鲁棒主成分分析的自适应视频去噪算法。首先根据视频数据的低秩性和噪声的稀疏性,利用加速近端梯度方法重建出原始视频的低秩部分和稀疏部分,实现噪声的初步分离;其次利用自适应中值滤波器进行预滤波处理,提高块匹配精度,进一步去除视频噪声;最后引入自适应奇异值阈值法,增强图像细节边缘信息,降低迭代优化算法的时间复杂度。实验结果表明,该方法不仅能极大程度地恢复出原始视频序列,还能自适应地去除干扰噪声。不论从客观指标PSNR值还是从主观视觉,该方法与传统去噪方法相比都具有很大的优势。     

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.     

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.     

Efficient mesh denoising via robust normal filtering and alternate vertex updating

The most challenging problem in mesh denoising is to distinguish features from noise. Based on the robust guided normal estimation and alternate vertex updating strategy, we investigate a new feature-preserving mesh denoising method. To accurately capture local structures around features, we propose a corner-aware neighborhood (CAN) scheme. By combining both overall normal distribution of all faces in a CAN and individual normal influence of the interested face, we give a new consistency measuring method, which greatly improves the reliability of the estimated guided normals. As the noise level lowers, we take as guidance the previous filtered normals, which coincides with the emerging rolling guidance idea. In the vertex updating process, we classify vertices according to filtered normals at each iteration and reposition vertices of distinct types alternately with individual regularization constraints. Experiments on a variety of synthetic and real data indicate that our method adapts to various noise, both Gaussian and impulsive, no matter in the normal direction or in a random direction, with few triangles flipped.     

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.     

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.     

A modified LOT model for image denoising

In image processing, it is often desirable to remove the noise and preserve image features. Due to the strong edge preserving ability, the total variation (TV) based regularization has been widely studied. However, it produces undesirable staircase effect. To alleviate the staircase effect, the LOT model proposed by Lysaker et al. (IEEE Trans Image Process 13(10): 1345–1357, 2004) has been studied, which is called the two-step method. After that, this method has started to appear as one of the more effective methods for image denoising, which includes two energy functions: one is about the normal field, the other is about the reconstruction image using the normal field obtained in the first step. However, the smoothed normal field is only related to the original noisy image in the first step, which is not enough. In this paper, we proposed a modified LOT model for image denoising, which lets the reconstruction vector field be related to the restored image. In addition, to compute the new model, we design a relaxed alternative direction method. The numerical experiments show that the new model can obtain the better results compared with some state-of-the art methods.

     

基于两步的网格平滑

在三角网格的生成过程中,不可避免地会出现噪声,如何有效地消除这些噪声已经成为当前计算机图形学领域的一个重要课题,提出了一个简单的,能有效去除噪声,同时能很好的保持网格尖边特征的算法.该算法通过两步来实现,第一步对三角网格的三角面面法矢量进行平滑,第二步依据面法矢量调整新的顶点坐标.此算法在伪三角的帮助下,能很好保持曲面的几何特征,防止曲面收缩.实验结果说明了实验的有效性.     

A two-stage filter for high density salt and pepper denoising

Image restoration is an important and interesting problem in the field of image processing because it improves the quality of input images, which facilitates postprocessing tasks. The salt-and-pepper noise has a simpler structure than other noises, such as Gaussian and Poisson noises, but is a very common type of noise caused by many electronic devices. In this article, we propose a two-stage filter to remove high-density salt-and-pepper noise on images. The range of application of the proposed denoising method goes from low-density to high-density corrupted images. In the experiments, we assessed the image quality after denoising using the peak signal-to-noise ratio and structural similarity metric. We also compared our method against other similar state-of-the-art denoising methods to prove its effectiveness for salt and pepper noise removal. From the findings, one can conclude that the proposed method can successfully remove super-high-density noise with noise level above 90%.