分形维数

基于分形维数的肺部软组织CT图像的纹理特征研究

The study on the texture characteristic of CT image of Lung tissue based on fractal dimension

TB2钛合金扩散连接与分形维数

Diffusion welding of TB_2 titanium alloy and fractal dimension

基于多重分形维数的GIS局部放电模式识别

PD pattern recognition based on multi-fractal dimensions in GIS

MATLAB环境下图像分形维数的计算

Estimation of Fractal Dimensions of Images Based on MATLAB YANG

薄型PVC材料断裂痕迹分形维数的研究

The Study of Fractal Dimensions of Crack in Thin PVC Slice

实验结果表明，冲击韧性αK的对数值随分形维数DF增加成单调上升的直线关系。

Experimental results show that the logarithms of impact tough-ness increase monotonically with the increase of fractal dimension .

反常分形维数dq随q的增加而增加.这表明在强子－强子碰撞中多粒子产生具有自相似级联的性质。

It shows that the multiparticle production in hadron hadron collisions possesses a self-similar cascade property .

XLPE介质中水树枝的分形维数估计

The Fractal Dimension Estimate of Water Tree in XLPE Dielectric

利用VISUALBASIC（简称VB）完成了基于Windows平台的分形维数计算程序的设计，并以直线、矩形、康托尘、科赫曲线等分形图形对其进行了检验。

Programming of the fractal dimension based on Windows platform can be done using Visual Basic and Validated by means of lines , rectangles , Cantor Dust and Koch Curve .

通过对图像各个子图的改进不规则分形维数的计算，得到各个子图的指标函数J曲线；

By the calculation of the fractal dimension of each sub-image , the J plot of sub-images is made as a goal function .

根据CT对原状土柱各断面的扫描图像，得到了各断面土壤大孔隙的分形维数，为进一步研究土壤大孔隙的水力性质奠定了基础。

This study obtain fractal dimension of macropore in every section base on the scanning images of undisturbed soil by CT . It establishes the base for further study the hydraulic characteristics of macropores .

Zr及Zr-4合金的循环耗散能、分形维数与疲劳寿命的关系

The relationship between plastic dissipated energy , fractal dimension and fatigue - lifetime of zirconium and zircaloy-4

Cantor展开与分形维数

Cantor Expansions and Fractal Dimensions

对枝系构型因素进行PCA排序可将其划分为三类：第一类包括各级分枝长度；第二类包括逐步分枝率和分形维数；

Factors affecting branching architecture can be divided into three classes by PCA ordination : the first class included branch length on the second and third level ;

关于一类Weierstrass函数的分形维数

On fractal dimensions of a Weierstrass-type function

首次将Sierpinski分形维数引入磨粒图像的定量分析。

Sierpinski fractal dimension was introduced to the quantitative analysis of wear particle image for the first time .

采用位置空间重整化群方法，对简立方格子（SC）键渗流模型进行了研究，得到了临界值pc、模型在相变点的分形维数D和临界指数γ。

The renormalization group approach is used to treat the problem of bond percolation on simple cubic lattice . The threshold p_c , the fractal dimension D and the critical exponent γ are obtained .

并设计了大量实验，分别对硫酸铝和聚合氯化铝（PAC）絮凝剂，在变化水力条件和投药量的基础上分析了絮凝过程中的流动电流值和絮体分形维数变化规律。

Through a lot of experiments , we obtained the streaming current and fractal dimension of aluminum sulfate and PAC on different hydraulic condition or different dosage .

进一步分析还发现，分解后的1／f部分的分形维数变化量与基础G耐力呈正相关；非1／f部分的复杂度和近似熵变化量与基础G耐力呈负相关。

The further analysis demonstrates that the changes of fractal dimension in 1 / f after decomposition are direct correlated with relaxed G tolerance , and the changes of complexity and approximate entropy are negative correlated with relaxed G tolerance .

依据Bond裂纹学说，提出了一种以井底返出的岩屑为对象的岩石可钻性测试方法，并建立了岩石可钻性极值和岩屑分形维数的关系模型。

According to Bond crack theory , this paper sets forth a new rock drillability testing method which takes the detritus from the bottom hole as the research subject . A correlation model of drillability grades and cuttings fractal dimensions is established .

在Hausdorff维数和分配维数的基础上，采用拓扑映射技术，提出了振动波形长度分形维数的定义和计算公式，并对其数学严密性进行了证明。

Based on Hausdorff dimension and Divider dimension , the definition and computing formula of Length fractal dimension ( D_L ) on vibration waveform are proposed using topology mapping .

对试验所获得的磨粒图像的Sierpinski分形维数分析发现：磨粒图像Sierpinski分形维数的大小与磨粒尺寸分布和磨粒重叠程度有关。

Results showed that the Sierpinski fractal dimension of wear particle image was depended on the distribution of wear particle size and particle overlapping .

利用垂直截面法测量了08F钢经不同形变氮化复合后冲击断裂表面的分形维数。

Fractal dimension of impact fracture surface of08F steel was measured by vertical section method .

同时，采用多种技术和手段研究了JMS中的絮体样品的微观形貌和物理特性，并计算了絮体样品的表面分形维数DS。

While , the microstructure and physical characteristics of the flocs formed in the JMS were studied by utilizing several technologies and apparatus , and the surface fractal dimensions DS of the flocs were given .

根据结构网络图，可分别求出结构面和结构体的分形维数D（PF）和D（VF）。

According to the figure of structural network , D_ ( PF ) and D_ ( VF ), the fractal dimensions of the structural plane and body are calculated , respectively .

测定不同分形维数的级配骨料对混凝土试件的28d强度的影响，并结合实际工程案例进行研究。

The effect of grading aggregate with different fractal dimension on concrete sample strength at 28 days is tested . The practical construction is studied .

改进的差分计盒方法被应用到计算路面图像的分形维数上，其分割结果与Sobel算子进行比较。

The improved DBC approach is applied to calculate the fractal dimension of pavement surface images and the segmentation results are compared with those of the Sobel operator .

前人关于有价证券分形维数的研究是在假定维数恒定的情况下进行的，这就使得Hurst指数未能很好发挥其应有的投资指导作用。

Previous work on fractal dimension of stock was done on the assumption that dimension is constant , which makes Hurst index not exert due guidance action of investment .

运用小角X-射线散射（SAXS）技术，定量地分析了杂化介孔二氧化硅产物SiO2骨架、介观孔洞以及纳米结构整体的分形维数在陈化处理过程中的演变过程。

Small angle X-ray scattering ( SAXS ) technology was adopted to investigate the evolution of silica framework , meso-pores and structure fractal dimensions of hybrid mesoporous silica during aging treatment .

本文主要讨论分形维数（FD）理论在纹理图像特征提取方面的应用，首先我们系统地分析了图像处理中分形维数估计的一般计算方法，然后在此基础上做了改进。

We focus on Fractal Dimension ( FD ) feature extraction method of fractal-based theory for texture image segmentation in this dissertation . We first study general methods of estimating fractal dimension in image analysis .