应用于地下水模拟的多尺度有限体积元方法

应用多尺度有限体积元方法模拟地下水流动问题,其中地下渗透场系数采用二维对数正态随机场.与传统的有限体积元法相比,多尺度有限体积元法的基函数具有能够反映单元内参数变化的优点,所以这种方法能在大尺度上捕捉解的小尺度特征获得较精确的解.文中算例分别对均匀、各向同性和各向异性对数正态随机场的二维地下水流动问题用传统数值模拟方法和多尺度有限体积元方法进行了计算.计算结果表明多尺度有限体积元方法收敛,且与传统数值模拟方法相比,多尺度有限体积元方法既节省计算量,又有较高的精度.     

各向异性小波收缩用于图像分割

已经证明2维情况下一般各向异性扩散与HAAR小波收缩在一定条件下是等价的,基于此等价性的各向异性小波收缩结合了小波收缩与各向异性扩散两种方法的优势。将各向异性小波收缩用于多尺度图像分割,提出一种对多尺度各向异性扩散分割方法的改进方法——多尺度各向异性小波收缩图像分割算法。该算法利用各向异性小波收缩对图像中像素灰度值进行扩散,在尽可能保持边缘的情况下,使同质区域内相邻像素灰度随尺度数增加趋于相同,构造基于尺度的空间栈,从而完成对目标的分割,是一种非监督图像分割方法。对比实验结果表明,该算法在有效处理区域内部不一致性的同时,能够准确地定位目标边缘,实现同质区域的融合,完成分割任务,且该算法收敛速度高于多尺度各向异性扩散分割方法。     

基于高斯尺度空间的山脊主脉提取方法

山脊线有主脉和支脉之分,主脉连贯突出且长度较长,控制了地形整体特征和态势,支脉则相对短小、分布于主脉两侧,反映了地形局部变化与细节。然而,现有方法提取的山脊线包含支脉多,提取结果偏差大、连续性差,无法支持实际应用。为此,结合多尺度分析与图像融合理论,提出了一种主脉的提取方法。新方法以不同参数的高斯核函数对数字高程(DEM)数据做多尺度分解,分别提取各尺度下山脊线,再以高斯尺度参数构造各尺度山脊线权重,采用加权平均法融合各尺度山脊线,获得更能体现宏观地形特征的主脉。实验结果表明,该方法简单易行,提取的主脉清晰、连续,与实际地形较为相符。     

基于多尺度非局部约束的单幅图像超分辨率算法

多尺度结构自相似性是指图像中的大量物体具有相同尺度以及不同尺度相似结构的性质.本文提出了一种基于多尺度非局部约束的单幅图像超分辨率算法,结合多尺度非局部方法和多尺度字典学习方法将蕴含在图像多尺度自相似结构中的附加信息加入到重建图像中.多尺度非局部方法在图像金字塔的不同层中搜索相似图像块,并利用多尺度相似图像块间的关系建立非局部约束项,通过正则化约束获取多尺度自相似结构中的附加信息;多尺度字典学习方法将图像金字塔作为字典学习的样本,通过字典学习使样本中的多尺度相似图像块 在字典下具有稀疏表示形式,从而获取多尺度自相似结构中的附加信息.实验表明, 与ScSR、SISR、NLIBP、CSSS、ASDSAR和mSSIM等算法相比,本文的算法取得了更好的超分辨率重建效果.     

结合多尺度体素和高阶条件随机场的点云分类

针对利用经典高阶条件随机场模型进行点云分类时,由于海量节点和无向边导致的点云分类效率低的问题,提出一种结合多尺度体素和高阶条件随机场的点云分类方法.首先以多尺度体素代替海量离散点云作为无向图图模型节点,减少节点和无向边的数量;然后使用超体分割结果作为高阶团,并基于此设计了一种非监督分布性空间上下文作为高阶团特征向量,用于改善分类结果;最后结合构建的图模型和各阶特征向量,采用经典高阶条件随机场模型实现点云数据的自动分类.采用Oakland标准数据集作为实验数据,实验结果表明,该方法在有效地保证分类精度的前提下,高阶条件随机场点云分类模型的分类效率提高了5～10倍.     

基于融合分层条件随机场的道路分割模型

为了在道路检测中结合图像的多尺度特征以及点云的空间结构特征,使检测算法能有效地排除道路场景中的阴影、光线等干扰,本文提出一种基于融合分层条件随机场的图像和点云融合的道路分割模型．首先,利用Meanshift算法产生多个尺度的超像素分割,建立基于图像的多尺度分层条件随机场．将点云数据投影到图像平面,再建立基于点云的多尺度分层条件随机场．在条件随机场的像素层和点云层之间建立连接,构造多尺度的融合模型．然后,针对多尺度融合模型中图像层的每一层和点云层的每一层,分别提取对应尺度的图像特征或点云特征．每一层用梯度提升树算法根据提取的特征训练1个分类器,利用每一层的分类器得到对应层的数据项代价．最后,使用α扩张算法对融合模型进行联合优化求解．在KITTI Road数据集上的实验结果表明,该方法具有良好的道路检测性能．     

基于有向地形表面特征的尺度不变性地形匹配

针对条带地形的地形匹配定位,提出了航带地形的有向地形表面特征描述及匹配方法。在航带的一维方向上检测极值点,同时利用区域中心的极值点及其地形表面的切线作为参考,利用地形极值点相对于参考点和参考线的相对位置关系构造地形的具有不变性的特征,基于特征的距离计算和比较,实现了具有抵抗尺度变化等相似变换的地形匹配方法。仿真实验证明了该方法的有效性,对于从序列图像重建地形的匹配定位具有重要意义。     

基于局部最优分析的纺织品瑕疵检测方法

针对复杂的含有周期变化图案的纺织品瑕疵检测,提出改进Markov随机场模型的无监督纺织品瑕疵检测方法.应用随机场实现周期性纺织品图像的瑕疵检测,利用Markov邻域特性,综合判断瑕疵区域.结合周期图像分割,确定Markov随机场最小图像块计算单元,降低算法的计算复杂度.在随机场势函数定义中,综合考虑相邻图像块的差异特性,结合Markov随机场的全局性判断瑕疵点的位置.引入模糊相似关系矩阵概念,求解改进后的模型参数,使所有图像块的局部能量达到最优.实验表明,文中方法对样本的查全率较高.     

自相似网络通信量的多尺度预测研究

自相似性是网络的普遍属性,并且对网络性能具有重要影响。在网络性能研究中,利用自相似的长程相关性来进行预测对于有效分配和利用网络资源以保证网络QoS及提高网络性能是非常有意义的。然而,由于自相似通信量同时具有长程相关和短程相关性的多尺度性和非线性使得通信量的预测非常困难。文章在充分考虑自相似网络通信量这些特性的基础上,提出了利用人工神经网络来进行预测的方法。我们首先根据研究目标构建了多时间尺度预测的人工神经网络,并且对输入/输出向量处理、参数选择和学习算法进行了讨论;然后,我们利用FARIMA为模型合成的同时具有LRD和SRD性质的通信量trace进行了多尺度预测的实验研究,结果表明可以利用该算法进行多时间尺度预测,这对于优化网络控制策略是非常有意义的。     

基于无参数Markov随机场模型的彩色纹理综合方法

提出一种基于多尺度、无参数Markov随机场模型和KL变换的彩色纹理综合方法。该方法能捕捉原始纹理的高阶统计特性,综合出与原始纹理视觉一致的彩色纹理图像。实验结果证明该方法对彩色纹理图像的综合非常有效。     

各向异性的分形地形生成方法研究

传统的分形地形生成方法得到的地形是各向同性的,为了使生成的分形地形具有各向异性特征,提出了一种新的分形地形生成方法,该方法利用组合分形布朗曲面模型,将具有不同特征的两种分形布朗曲面相融合,使得生成的地形具有各向异性特征.对组合分形布朗曲面算法进行了仿真实验,生成了最终的分形地形.对仿真结果的分析表明,生成的分彤地形的特征具有各向异性特征,和实际的自然地形特征相符合,从而证明了该算法的有效性.     

Multi-scale anisotropic heat diffusion based on normal-driven shape representation

Multi-scale geometric processing has been a popular and powerful tool in graphics, which typically employs isotropic diffusion across scales. This paper proposes a novel method of multi-scale anisotropic heat diffusion on manifold, based on the new normal-driven shape representation and Edge-weighted Heat Kernels (EHK). The new shape representation, named as Normal-Controlled Coordinates (NCC), can encode local geometric details of a vertex along its normal direction and rapidly reconstruct surface geometry. Moreover, the inner product of NCC and its corresponding vertex normal, called Normal Signature (NS), defines a scalar/heat field over curved surface. The anisotropic heat diffusion is conducted using the weighted heat kernel convolution governed by local geometry. The convolution is computed iteratively based on the semigroup property of heat kernels toward accelerated performance. This diffusion is an efficient multi-scale procedure that rigorously conserves the total heat. We apply our new method to multi-scale feature detection, scalar field smoothing and mesh denoising, and hierarchical shape decomposition. We conduct various experiments to demonstrate the effectiveness of our method. Our method can be generalized to handle any scalar field defined over manifold.     

Smooth anisotropic sources with application to three-dimensional surface mesh generation

Isotropic sources are extended to take anisotropy into account in order to obtain a smooth anisotropic sizing field for anisotropic mesh generation. Different types of anisotropic sources are described to represent boundary layers on surfaces and in volume that guarantee a smooth anisotropic field. This allows to us resolve multiple boundary layer intersections properly and naturally provides a smooth transition between the anisotropic boundary layer sizing and the isotropic region. Furthermore, the interaction between a smooth anisotropic sizing field and curvature is studied, and estimates of the tangential size spacing are provided for first and second order approximation of the geometry to ensure smoothness of the sizing field. It is also shown that, in order to get a smooth size variation, volumetric and surface meshing can not be decoupled. The filtering of the sources in order to obtain a computationally efficient method is described. Numerical examples demonstrate our method.     

一种计算各向异性分形维数的新方法

分形维数是描述分形的重要参数,分形维数的计算是分形几何研究的重要内容。传统上分形维数的计算是基于各向同性这一假设所得到的维数计算方法,不适合具有各向异性特性的自然地形的维数计算。基于微分统计法,提出并实现了一种计算各向异性分形维数的新方法,该算法通过保留方向信息,达到了计算不同方向上不同分形维数的目的。利用频谱合成法生成的各向异性分形曲面进行实验的结果表明,算法是正确且有效的。     

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.     

Framework for Capturing and Editing of Anisotropic Effect Coatings

Coatings are used today for products, ranging from automotive production to electronics and everyday use items. Product design is taking on an increasingly important role, where effect pigments come to the fore, offering a coated surface extra optical characteristics. Individual effect pigments have strong anisotropic, azimuthaly‐dependent behaviour, typically suppressed by a coating application process, randomly orienting pigment particles resulting in isotropic appearance. One exception is a pigment that allows control of the azimuthal orientation of flakes using a magnetic field. We investigate visual texture effects due to such an orientation in a framework allowing efficient capturing, modelling and editing of its appearance. We captured spatially‐varying BRDFs of four coatings containing magnetic effect pigments. As per‐pixel non‐linear fitting cannot preserve coating sparkle effects, we suggest a novel method of anisotropy modelling based on images shifting in an angular domain. The model can be utilized for a fast transfer of desired anisotropy to any isotropic effect coating, while preserving important spatially‐varying visual features of the original coating. The anisotropic behaviour was fitted by a parametric model allowing for editing of coating appearance. This framework allows exploration of anisotropic effect coatings and their appearance transfer to standard effect coatings in a virtual environment.     

A Theoretical Framework for Convex Regularizers in PDE-Based Computation of Image Motion

Many differential methods for the recovery of the optic flow field from an image sequence can be expressed in terms of a variational problem where the optic flow minimizes some energy. Typically, these energy functionals consist of two terms: a data term, which requires e.g. that a brightness constancy assumption holds, and a regularizer that encourages global or piecewise smoothness of the flow field. In this paper we present a systematic classification of rotation invariant convex regularizers by exploring their connection to diffusion filters for multichannel images. This taxonomy provides a unifying framework for data-driven and flow-driven, isotropic and anisotropic, as well as spatial and spatio-temporal regularizers. While some of these techniques are classic methods from the literature, others are derived here for the first time. We prove that all these methods are well-posed: they posses a unique solution that depends in a continuous way on the initial data. An interesting structural relation between isotropic and anisotropic flow-driven regularizers is identified, and a design criterion is proposed for constructing anisotropic flow-driven regularizers in a simple and direct way from isotropic ones. Its use is illustrated by several examples.     

Scattering characteristics of an anisotropic medium sphere

Based on the invariable displacement current of anisotropic media, a theoretical model for electromagnetic reconstructing anisotropic media and a basic method for selecting electromagnetic field are proposed. Taking the gypsum crystal as an example, the analytical solution of bi‐axial medium scattering is presented by using the spherical vector wave function of electromagnetic field. The electromagnetic wave scattering of the anisotropic medium spheres are simulated in radiation of electromagnetic waves of different frequency. The electromagnetic analysis of the simulation results shows that the electromagnetic mechanism is consistent with the results of relevant literature. When the anisotropic medium degenerates to the isotropic medium, the results obtained by the model are completely consistent with those obtained by Mie theory.     

NURBS 曲面光顺方法综述

NURBS 曲线、曲面的光顺处理是CAD/CAM 中非常重要的问题。在研 究了NURBS 曲面光顺中的几种常用方法的基础上,针对现有光顺算法在多尺度特征并存曲 面光顺中的不足,提出利用各向异性小波在表达高维信息的优势,将各向异性小波融入曲面 的多分辨率分析中的思想,应用于NURBS 曲面光顺,以达到对曲面特征的保存。