基于几何矩的 CAD 模型形状匹配算法及应用

基于矩方法及其理论,提出了一个基于几何矩的形状匹配算法,用于识别 CAD 模型中具有相 似形状特征的几何体。该算法采用一组满足平移、旋转、缩放不变性的几何矩不变量对三维几何体的形状特征 进行描述,并根据形状特征向量的相似程度评估几何体之间的相似性。为提高几何矩计算的准确性和效率,对 CAD 模型的三角面片数据进行了预处理,并采用递归算法实现各阶几何矩的快速计算。形状匹配算法被应用 于 CAE 软件的相似几何体拾取中,能够通过 GUI 交互的方式实时拾取与目标几何体形状特征相似的几何体, 取得了良好的应用效果。     

不规则形状图象矩特征的一种快速准确算法

介绍了一种基于边缘点计算矩特征的方法,该算法实现思路清晰,编程实现简单,结果准确,且可应用到其他形状特征的计算中。     

不规则形状图象矩特征的一种快速准确算法

介绍了一种基于边缘点计算矩特征的方法，该算法实现思路清晰，编程实现简单，结果准确，且可应用到其他形状特征的计算中。     

一种新的二维图像几何矩快速计算方法

几何矩是二维图像形状特征的有效描述,本文提出了一种新的快速计算二维图像几何矩的方法,通过分离二维矩为计算两步一维矩,并将阶数高的一维矩计算中的乘法运算转换为加法运算,能够大幅度地提高计算二维图像几何矩的计算速度。本文从理论上证明了新算法的有效性与时间复杂度,并进行了实验分析,验证了新算法的运算速度效率。     

基于最小外接圆补偿机制的形状图像检索

提出了一种新的基于最小外接圆补偿机制的二值形状图像检索算法,其不仅提取了目标区域的特征,而且补偿了目标最小外接圆下的背景区域特征。提取常用于描述区域特征的Hu不变矩和Zernike不变矩作为图像特征,不变矩特征具有平移、缩放、旋转不变性。图像相似度用归一化特征向量的欧氏距离表示。该方法不仅计算简单,而且可有效补偿人眼的视觉感受。通过大量实验表明,该算法较仅基于目标区域的检索算法取得了更好的检索精度和回召率。     

利用角点坐标计算图象的矩不变量

本文提出了一种直接利用角点坐标计算形状的方法，并导出了低阶矩的闭合形式，最后给出了计算M．K．Hu提出的七个矩不变量的算法。该算法计算的是经典不变矩的精确值，但大大地筒化了计算。     

基于形状不变矩的t-混合模型的图像分类

提出一种基于物体形状不变矩特征,采用t-混合模型计算后验概率的统计形状分类的方法:采用Hu形状不变矩作为图像特征,用t-混合模型的EM迭代算法,估计出模型中未知参数,计算出形状类别的后验概率。实验结果表明,物体序列的形状不变矩具有良好的统计分布性质,按其后验概率分类的准确性较高。     

轮廓矩不变量及其在物体形状识别中的应用

为了有效地刻画物体的形状特征，在基于区域的Hu矩不变量的基础上，构造了一种基于物体轮廓曲线的新的矩不变量，即轮廓矩不变量。该不变量不仅独立于物体本身的颜色和灰度级，而且具有平移、旋转和尺度不变性，因此可将轮廓矩不变量应用于物体形状的识别，为了能快速地进行物体形状识别，还讨论了小波边缘检测和轮廓的获取问题及其算法。实验表明，基于这种轮廓矩的识别算法具有很好的识别率。     

一种新的快速计算Legendre矩的方法

正交矩在模式识别，图像分析等领域有成功的应用，但由于正交矩的复杂性，有关正交矩的快速算法研究尚未得到很好的解决，该文提出一种 新的快速计算Ｌegendre矩的方法，该方法把基于像素点的二维Ｌegendre矩转换为线段的形式来计算，在计算出所有线段的积分后，使用扩展的Ｈatamian滤波方法来计算一维的Ｌegendre矩。结果显示新的算法有效地降低了计算的复杂度，并且，该方法能用于处理任意形状的物体。     

相对矩及在几何形状识别中的应用

在计算机视觉中,几何形状的识别具有十分重要的意义,而一般几何形状可以分为区域和结构两类。Hu提出的不变矩是用于区域形状识别的几何特征,但对于结构则因不满足缩放不变的条件而不适用。为此对Hu提出的区域不变矩和Chen提出的区域不变矩快速算法进行了扩展,并定义了对于结构和区域均满足平移、缩放、旋转不变的相对矩,从而统一了区域和结构的矩特征计算公式,而且与Hu的不变矩相比,更具有一般性,利用相对矩进行的识别实验表明,相对矩是对区域、封闭和不封闭结构的形状进行识别的有效特征,尤其在识别封闭和不封闭结构时,比傅立叶描述子等传统方法简便。     

基于AutoCAD计算截面对任意轴的静距和惯性矩的程序设计

本文以二维绘图软件AutoCAD为平台,利用VBA开发工具,依据平面图形的平行移轴公式、转轴公式,实现了计算截面对任意轴的静距和惯性矩的程序设计。从而简化了计算过程,减少重复性工作。     

具有线性加法复杂度的二值图象不变矩计算方法

不变矩方法是模式识别的一个重要方法,然而由于不变矩计算复杂,从而限制了它的应 用.本文运用格林定理,将不变矩计算由平面域转化为曲线域.在此基础上,提出了边界跟踪 迭代的不变矩计算方法.新方法不仅不需要乘法,而且加法次数亦从O(N2)降低到O(N).     

A unified methodology for the efficient computation of discrete orthogonal image moments

A novel methodology is proposed in this paper to accelerate the computation of discrete orthogonal image moments. The computation scheme is mainly based on a new image representation method, the image slice representation (ISR) method, according to which an image can be expressed as the outcome of an appropriate combination of several non-overlapped intensity slices. This image representation decomposes an image into a number of binary slices of the same size whose pixels come in two intensities, black or any other gray-level value. Therefore the image block representation can be effectively applied to describe the image in a more compact way. Once the image is partitioned into intensity blocks, the computation of the image moments can be accelerated, as the moments can be computed by using decoupled computation forms. The proposed algorithm constitutes a unified methodology that can be applied to any discrete moment family in the same way and produces similar promising results, as has been concluded through a detailed experimental investigation.     

Novel moment invariants for improved classification performance in computer vision applications

A novel set of moment invariants based on the Krawtchouk moments are introduced in this paper. These moment invariants are computed over a finite number of image intensity slices, extracted by applying an innovative image representation scheme, the image slice representation (ISR) method. Based on this technique an image is decomposed to a several non-overlapped intensity slices, which can be considered as binary slices of certain intensity. This image representation gives the advantage to accelerate the computation of image's moments since the image can be described in a number of homogenous rectangular blocks, which permits the simplification of the computation formulas. The moments computed over the extracted slices seem to be more efficient than the corresponding moments of the same order that describe the whole image, in recognizing the pattern under processing. The proposed moment invariants are exhaustively tested in several well known computer vision datasets, regarding their rotation, scaling and translation (RST) invariant recognition performance, by resulting to remarkable outcomes.     

基于小波和不变矩的图像copy-move篡改盲检测

针对数字图像取证中一类常见的复制粘贴图像伪造,本文提出了一种基于小波变换和不变矩提取的检测算法。该算法利用小波变换提取图像的低频分量,对低频分量分块进行不变矩特征提取,然后将特征矢量进行按行字典排序,并且配合图像块的偏移位置信息,进行图像复制伪造区域的检测和定位。实验表明该算法能够较精确地定位出复制和粘贴的图像伪造区域,并有效地减少了运算量,提高了检测效率。     

Exact and fast algorithm for two-dimensional image wavelet moments via the projection transform

Wavelet moments are perfect representations of moments in multiresolution wavelet domain, which integrates the theory of moment invariants into wavelet analysis. However, the calculations of moments are very complicated in terms of computational complexity, so it is difficult to implement them in real time. An exact and fast projection-based algorithm for two-dimensional wavelet moments is presented in this paper. In our approach, the computation of a two-dimensional wavelet moment of order of r is performed in (r+1) different one-dimensional spaces. Since only additions are required to perform the projection transform, the total computational complexity can be greatly reduced.     

Application of maximum entropy principle for reliability-based design optimization

The maximum entropy principle (MEP) is used to generate a natural probability distribution among the many possible that have the same moment conditions. The MEP can accommodate higher order moment information and therefore facilitate a higher quality PDF model. The performance of the MEP for PDF estimation is studied by using more than four moments. For the case with four moments, the results are compared with those by the Pearson system. It is observed that as accommodating higher order moment, the estimated PDF converges to the original one. A sensitivity analysis formulation of the failure probability based on the MEP is derived for reliability-based design optimization (RBDO) and the accuracy is compared with that by finite difference method (FDM). Two RBDO examples including a realistic three-dimensional wing design are solved by using the derived sensitivity formula and the MEP-based moment method. The results are compared with other methods such as TR-SQP, FAMM + Pearson system, FFMM + Pearson system in terms of accuracy and efficiency. It is also shown that an improvement in the accuracy by including more moment terms can increase numerical efficiency of optimization for the three-dimensional wing design. The moment method equipped with the MEP is found flexible and well adoptable for reliability analysis and design.