基于数值微分的图像融合方法

提出一种基于数值微分的图像融合方法。用精确求解离散数据导数的数值微分方法取代传统的邻域差分来求解图像梯度,将求解得到的图像梯度应用到基于偏微分方程的图像融合模型中,改进基于偏微分方程的图像融合数值化方案。将改进前后的方法进行对比实验,结果表明,应用改进方法得到的融合图像的质量指标和图像收敛性较优。     

基于变分法和偏微分方程的图像彩色化方法

针对传统的图像彩色化算法易产生的图像边缘颜色模糊等问题,提出一种基于变分法和偏微分方程的图像彩色化算法,结合整体变分(TV)模型和金兹堡一朗道(GL)模型的特点,通过求泛函极值建立偏微分方程,使图像的光滑区域和边界区域都能有效的实现颜色扩散,对偏微分方程进行数值求解得到彩色化结果.实验结果表明,与其它偏微分方程彩色化技术相比,该方法能得到清晰自然的彩色化图像和较高的图像质量.     

一种基于各向异性扩散的图像处理方法

图像修复的方法有很多种,目前最常用的有基于偏微分方程（PDE）和基于纹理合成的修复方法。在图像的修复和去噪上,偏微分方程都有很好的应用,但对于含有噪声的破损图像的修复,传统的方法是先去除噪声再进行修复。在BSCB模型的基础上加以改进,提出了一种新的修复方法,结合现有的图像修复和图像去噪两种技术的优势,对图像破损区域修复的同时进行整幅图像的去噪,修复和去噪的过程都是各项异性扩散的过程,能很好地保留图像的边缘信息。通过数值实验也表明该方法的有效性。     

一种基于各向异性扩散的图像处理方法

图像修复的方法有很多种,目前最常用的有基于偏微分方程(PDE)和基于纹理合成的修复方法.在图像的修复和去噪上,偏微分方程都有很好的应用,但对于含有噪声的破损图像的修复,传统的方法是先去除噪声再进行修复.在BSCB模型的基础上加以改进,提出了一种新的修复方法,结合现有的图像修复和图像去噪两种技术的优势,对图像破损区域修复的同时进行整幅图像的去噪,修复和去噪的过程都是各项异性扩散的过程,能很好地保留图像的边缘信息.通过数值实验也表明该方法的有效性.     

基于PDE正则化的超分辨率图像重构方法

采用非线性扩散模型建立超分辨率图像重构的偏微分方程,利用各向异性扩散方程的方向选择平滑的特性,在重构高分辨率图像的同时能够很好地消除系统噪声,保持细节信息。实验结果表明,该方法有效地提高了重构的图像质量,在视觉观察和数值评价上都优于原有正则化方法,并且对不同噪声水平的图像具有很好的鲁棒性。     

基于耦合偏微分方程的图像去噪方法

本文基于Perona-Malik模型和四阶偏微分方程提出了耦合偏微分方程的平滑方法。实验表明,该方法能很好兼顾图像噪声消除和边缘保持,避免了二阶偏微分方程处理图像常出现的块效应,使图像平滑自然。     

浅谈解的存在唯一性定理在《偏微分方程数值解》中的应用

从一个新的角度讨论常微分方程中解的存在唯一性定理在偏微分方程数值解法中的重要应用。给出一类伪双曲型偏微分方程的新的分裂混合有限元数值格式,将该格式转化成常微分方程系统,利用解的存在唯一性定理证明该系统是存在唯一解的。通过简短的讨论、概述明确解的存在唯一定理在偏微分方程数值解中的应用方法．并希望能够在教学科研未来的发展中有新的观念。     

数字图像处理中的偏微分方程方法综述

数字图像处理中的偏微分方程(PDE)方法近年来发展非常迅速,PDE方法旨在建立偏微分方程的数学模型,而后令图像遵循此偏微分方程变化,最终达到预想的效果。通过偏微分方程处理图像之后得到的效果是用传统方法达不到的。现结合国内外研究现状详细地阐述了图像去噪、图像复原、图像分割、图像增强这4类PDE模型,同时也分析了偏微分方程建立、偏微分方程求解和偏微分方程实现这3个主要的过程。     

Level Set方法在轮廓界面追踪问题中的应用

运用LevelSet方法研究图像轮廓追踪问题。首先,运用差分法检测出图像的初始轮廓线,然后采用基于LevelSet方法的偏微分方程数值解理论来进行图像轮廓界面的提取。Matlab实验结果表明,该方法可以测出模糊或离散的边界,得到精确的图像轮廓界面。     

具有纹理保持能力的四阶偏微分方程去噪方法

虽然四阶偏微分方程图像去噪方法能得到较好的分段光滑的结果,但这类方法常破坏图像的纹理信息。提出了一种具有保持图像纹理信息能力的四阶偏微分方程去噪模型。利用垂直于梯度方向的图像二阶导数设计了一种新的代价函数。证明了该函数解的存在性与唯一性并给出了其对应的Euler-Lagrange方程。在实验方面,用大量真实的纹理图像验证了新方法。实验结果表明,新方法在去噪的同时图像的边缘与细节得到了较好的保持。     

On the normal vector estimation for point cloud data from smooth surfaces

Reliable estimation of the normal vector at a discrete data point in a scanned cloud data set is essential to the correct implementation of modern CAD/CAM technologies when the continuous CAD model representation is not available. A new method based on fitted directional tangent vectors at the data point has been developed to determine its normal vector. A local Voronoi mesh, based on the 3D Voronoi diagram and the proposed mesh growing heuristic rules, is first created to identify the neighboring points that characterize the local geometry. These local Voronoi mesh neighbors are used to fit a group of quadric curves through which the directional tangent vectors are obtained. The normal vector is then determined by minimizing the variance of the dot products between a normal vector candidate and the associated directional tangent vectors. Implementation results from extensive simulated and practical point cloud data sets have demonstrated that the present method is robust and estimates normal vectors with reliable consistency in comparison with the existing plane fitting, quadric surface fitting, triangle-based area weighted average, and triangle-based angle weighted average methods.     

Point-tangent/point-normal B-spline curve interpolation by geometric algorithms

We introduce a novel method to interpolate a set of data points as well as unit tangent vectors or unit normal vectors at the data points by means of a B-spline curve interpolation technique using geometric algorithms. The advantages of our algorithm are that it has a compact representation, it does not require the magnitudes of the tangent vectors or normal vectors, and it has C² continuity. We compare our method with the conventional curve interpolation methods, namely, the standard point interpolation method, the method introduced by Piegl and Tiller, which interpolates points as well as the first derivatives at every point, and the piecewise cubic Hermite interpolation method. Examples are provided to demonstrate the effectiveness of the proposed algorithms.     

规则特征曲面点云法向估计

目的 针对特征曲面点云法矢估计不准确,点云处理时容易丢失曲面的细节特征等问题,提出基于高斯映射的特征曲面散乱点云法向估计法。方法 首先,用主成分分析法粗略地估算点云法向和特征点;其次,将特征点的各向同性邻域映射到高斯球,用K均值聚类法对高斯球上的数据分割成多个子集,以最优子集对应的各向异性邻域拟合曲面来精确估算特征点的法向量;最后,通过测试估计法向与标准法向的误差来评价估计法矢的准确性,并且将估计的法向应用到点云曲面重建中来比较特征保留效果。结果 本文方法估计的法向最小误差接近0,对噪声有较好的鲁棒性,重建的曲面能保留曲面的尖锐特征,相比于其他法向估计法,所提出的方法估计的法向更准确。结论 本文方法能够比较准确的估算尖锐特征曲面法向量,对噪声鲁棒性强,具有较高的适用性。     

基于模糊极大似然估计聚类的点云数据分块

对散乱点云数据采用微切平面法进行法矢估计,对法矢方向进行全局协调性调整。采用稳定性较好的二次曲面拟合法估算点云数据的高斯曲率和平均曲率。将点的坐标、法矢和曲率合并为八维特征向量,通过模糊极大似然估计聚类技术,将具有类似几何特征的向量聚为一类,从而实现点云数据的分块。实验证明该方法有效。     

On computer generation of random vectors by transformations of uniformly distributed vectors

The paper discusses a general method of computer generation of random vectors based on transformations of uniformly distributed vectors. This method is then applied to build up efficient algorithms for generatingq-exponential random vectors and multivariate normal ort-distributed vectors. Comparisons and connections with other similar algorithms are also presented.     

Discrete plane segmentation and estimation from a point cloud using local geometric patterns

This paper presents a method for segmenting a 3D point cloud into planar surfaces using recently obtained discretegeometry results. In discrete geometry, a discrete plane is defined as a set of grid points lying between two parallel planes with a small distance, called thickness. In contrast to the continuous case, there exist a finite number of local geometric patterns （LGPs） appearing on discrete planes. Moreover, such an LGP does not possess the unique normal vector but a set of normal vectors. By using those LGP properties, we first reject non-linear points from a point cloud, and then classify non-rejected points whose LGPs have common normal vectors into a planar-surface-point set. From each segmented point set, we also estimate the values of parameters of a discrete plane by minimizing its thickness.     

基于拓扑映射的背向面去除算法

场景往往由多边形逼近表示,提出的背向面去除算法首先将场景中的多边形法向量正则化为单位向量,并将起始点移至原点,这些单位向量必定位于单位圆球上;然后将单位圆球分成若干个中心对称的区域,每个区域进行拓扑映射得到参考平面,可以求得每个多边形法向量所在的区域,并求出多边形法向量在区域边界圆盘面上的拓扑映射坐标．对同一场景而言,这些计算只需进行一次,称为前置运算．当视点向量位置改变时,则需动态计算视点向量和正背向分界线在每个区域的拓扑映射坐标;然后在一维射影直线上根据视点向量、法向量和分界线之间的拓扑映射坐标位置关系,判断该多边形是否为背向面．实验结果表明,算法运行可靠,有较高的检测速度,尤其是对同一场景,当视点变化时的多次检测效果显著．     

多边形和多面体顶点法矢的数值估计

证明了两个定量，定理1揭示了三点多边的外接圆在中点处的法矢与两个边界法矢的关系；定理2揭示了四面体外接球面在中点处的法矢与三个相邻三角平面的法矢量的关系，给出了一个判别二维多维边形和三维多面体顶点法矢计算方法优劣的准则，在此基础上，提出一种用于估计三维多面体顶部的法矢量的计算方法，两个例子说明文中给出的准则和算法的合理性和实用性。     

基于支持向量的Kernel判别分析

提出了一种新的基于支持向苗的核化判别分析方法（SV—KFD）．首先深入地分析了支持向量机（SVM）以及核化费舍尔判别分析（Kernel Fisher）方法的相互关系．基于作者证明的SVM本身所同有的零空间性质;SVM分类面的法向量在基于支持向量的类内散度矩阵条件下,具有零空间特性,提山了利用SVM的法向量定义核化的决策边界特征矩阵（Kernelized Decision Boundary Feature Matrix,KDBFM）的方法．进一步结合均值向量的差向量构建扩展决策边界特征矩阵（Ex—KDBFM）．最后以支持向量为训练集合,结合零空间方法来计算投影空间,该投影空间被用来从原始图像中提取判别特征．以人脸识别为例,作者在FERET和CAS—PEAL—R1大规模人脸图像数据怍上对所提出的方法进行了实验验证,测试结果表明该方法具有比传统核判别分析方法更好的识别性能．     

Normal and Abnormal Tissue Classification in Positron Emission Tomography Oncological Studies

Positron Emission Tomography (PET) imaging is increasingly used in radiotherapy environment as well as for staging and assessing treatment response. The ability to classify PET tissues, as normal versus abnormal tissues, is crucial for medical analysis and interpretation. For this reason, a system for classifying PET area is implemented and validated. The proposed classification is carried out using k-nearest neighbor (KNN) method with the stratified K-Fold Cross-Validation strategy to enhance the classifier reliability. A dataset of eighty oncological patients are collected for system training and validation. For every patient, lesion (abnormal tissue) and background (normal tissue around the lesion) are contoured on PET images using a semi-automatic method. Then 160 vectors are obtained to train and validate the KNN. Each vector is composed by thirty Standardized Uptake Values (SUVs) characterizing the area under investigation (lesion or background). In one case, vectors are labeled as normal or abnormal tissues by a nuclear medicine physician using a semi-automatic method; in other cases, Fuzzy C-means (FCM) and k-means are used for labelling vectors in an unsupervised manner. This study aims to evaluate the performance of the proposed classifier comparing it to the Linear Kernel Support Vector Machine (KSVM). The method accuracy is evaluated by comparison with the gold standard in terms of correct classification. Experimental results show that the KNN method achieves the highest classification accuracy using the semi-automatic labelling training (Sensitivity: 86.25%; Specificity: 90.00%; Negative Predictive Value: 88.37%; Precision: 89.81%; Accuracy: 88.12%; Error: 11.87%). In addition, the proposed method shows real-time performance; it could be applied to the field classification of PET images assisting physicians into discrimination of normal and abnormal tissue during radiation treatment planning.