基于两变量Krawtchouk矩的图像重建

传统的离散正交Krawtchouk矩的基函数由两个单变量的Krawtchouk多项式乘积构成,它割裂平面两个方向之间的联系。提出了一种新的、以两变量Krawtchouk正交多项式为基函数的图像矩,并推导了正则化后两变量多项式的简单的计算方法。重建实验结果表明,相对于同系数的单变量的离散正交矩,两变量离散正交矩的重建误差更小。     

基于Krawtchouk矩和小波变换的数字水印算法

提出了一种基于Krawtchouk矩和小波变换的抵抗几何攻击的内容认证水印算法。该方法首先对图像进行一次小波分解，然后计算其低频成分的Krawtchouk低阶矩不变量来构建水印。水印提取过程简单，只需计算所得图像的几个低阶Krawtchouk矩不变量。文中给出了实验结果，并与Alghoniemy提出的基于几何矩不变量的数字水印算法进行了比较。结果表明，该方法简单、有效，对旋转、缩放、剪切、组合攻击等几何攻击以及JPEG压缩攻击具有更高的稳健性。     

基于Krawtchouk-RBF的印章图像分类识别

为了有效地对印章图像进行分类,提出了一种基于Krawtchouk矩和RBF神经网络的印章图像分类识别方法。首先提取标准印章图像的Krawtchouk矩不变量,将其作为RBF神经网络的原始训练样本;然后提取全部待鉴印章图像的Krawtchouk矩不变量,将其作为RBF神经网络的输入量进行分类识别。实验结果表明,使用Krawtchouk矩来描述印章图像的特征并通过RBF神经网络来对其进行分类识别的方法十分有效,与同类的Brushlet-RBF法和KPCA-RBF法相比,其识别率更高,且更准确。     

一种基于Krawtchouk矩的水印算法

提出一种基于Krawtchouk矩的水印算法,通过修改一些原始Krawtchouk矩并重构图像以获得水印图像.基于Krawtchouk矩与几何矩的关系,提出采用具有平移、比例缩放和旋转不变性的几何不变矩来检测水印.实验表明,与用Krawtchouk不变矩检测相比,该算法对于大角度旋转和图像平移的几何攻击具有更好的鲁棒性.     

正交傅里叶—梅林矩的一种高效算法*

提出了一种高效计算图像正交傅里叶—梅林矩的算法。该算法通过消除正交多项式中的阶乘项和提取该图像矩的公共项以提高图像矩值的计算性能。实验分析表明,与传统的直接计算方法相比,该算法可有效节省计算时间,尤其是在计算高阶连续矩情况下性能更好。     

基于Krawtchouk矩的运动目标分类

针对视频监控系统,为了实现对运动目标的有效分类,提高其分类准确率,提出一种基于Krawtchouk矩不变量特征的运动目标分类技术.提取目标图像的低阶Krawtchouk矩不变量来描述目标,确保目标在平移、缩放、旋转条件下的不变性,选用K-means均值聚类算法进行数据聚类,达到准确分类的效果.通过实验验证了该方法的有效性,与应用Hu矩不变量进行分类的结果进行比较,表明了该方法具有较好的分类效果.     

二维Tchebichef 正交矩反变换的快速算法

提出了一种二维Tchebichef矩反变换的快速算法.借助Clenshaw递推公式,推导了一维Tchebichef矩反变换的快速算法,并将其推广至二维Tchebichef正交矩反变换的计算.与以迭代方式计算Tchebichef多项式进而计算二维Tchebichef矩反变换的方法相比,文中提出的算法有效地减少了算术运算的次数,大幅提高了计算速度.实验结果表明了该方法的有效性.     

可有效抵抗一般性几何攻击的数字水印检测方法

以回归型支持向量机理论为基础, 结合性能稳定的伪Zernike矩和Krawtchouk矩, 提出了一种可有效抵抗一般性几何攻击的强鲁棒数字图像水印检测算法. 该算法首先选取图像的低阶Krawtchouk矩作为特征向量, 然后利用SVR对几何变换参数进行训练学习并对待检测图像进行数据预测, 最后对其进行几何校正并提取水印信息. 仿真实验结果表明, 该数字图像水印检测算法不仅具有较好的不可感知性, 而且对常规信号处理和一般性几何攻击均具有较好的鲁棒性.     

结合SIFT和Krawtchouk矩不变量的图像配准方法

提出了一种基于SIFT和Krawtchouk矩不变量的图像配准方法。通过SIFT关键点检测方法检测关键点;对每个关键点计算其邻域的Krawtchouk矩不变量,并将其构成描述关键点的特征向量;计算关键点特征向量之间的欧氏距离找出相匹配的关键点对。实验结果表明,该算法的配准性能与标准SIFT算法相当,而运算速度比标准SIFT算法有较大程度提高。     

几何误差和数值误差最小化的Zernike矩

形状特征提取和表示是基于内容图像检索的重要研究内容之一.提出一种几何误差和数值误差最小化的Zernike矩方法,并且把这种方法应用于形状特征提取和表示.该方法把图像中的兴趣区域映射到单位圆里,通过计算变换后图像在Zernike多项式上的投影来取得Zernike矩,并且通过把心理生理学的研究成果引入Zernike矩的计算过程来提高系统的检索性能.通过实验对传统Zernike矩方法、几何误差和数值误差最小化的Zernike矩方法进行了比较,发现从重构角度采用几何误差和数值误差最小化的Zernike矩方法优于采用传统Zernike矩方法.而从检索角度采用几何误差和数值误差最小化的Zernike矩方法的系统比采用传统Zernike矩方法的系统具有更好的检索性能.     

鲁棒性数字图像水印技术

数字水印技术作为版权保护的重要手段已经成为了研究的热点,但是实用的鲁棒性数字水印技术不多,特别是抗几何攻击的水印算法不多.文中利用Krawtchouk不变矩对平移、旋转和缩放的不变性以及Krawtchouk矩良好的局部特性和重构性能,根据水印的容量自适应地改变某些相对稳定的低阶矩来嵌入水印,并用Rijndael加密和Arnold置乱等技术以及构造的图像特征不变矩阵生成相关的二值逻辑表来进行版权认证.实验证明,该算法不仅对JPEG压缩、裁剪、噪声等常见攻击有较强的免疫力,而且对平移、旋转、缩放等几何攻击也具有较强的免疫力.     

Improved quality of reconstructed images using floating point arithmetic for moment calculation

Zernike moments which are superior to geometric moments because of their special properties of image reconstruction and immunity to noise, suffer from several discretization errors. These errors lead to poor quality of reconstructed image and wide variations in the numerical values of the moments. The predominant factor, as observed in this paper, is due to the discrete integer implementation of the steps involved in moment calculation. It is shown in this paper that by modifying the algorithms to include discrete float implementation, the quality of the reconstructed image improves significantly and the first-order moment becomes zero. Low-order Zernike moments have been found to be stable under linear transformations while the high-order moments have large variations. The large variations in high-order moments, however, do not greatly affect the quality of the reconstructed image, implying that they should be ignored when numerical values of moments are used as features. The 11 functions based on geometric moments have also been found to be stable under linear transformations and thus these can be used as features. Pixel level analysis of the images has been carried out to strengthen the results.     

Moment-based methods for polygonal approximation of digitized curves

Object shape representation plays an important role in the area of image processing, pattern recognition and computer vision. In the past two decades, many algorithms have been suggested for creating approximated polygons. In this study, two new polygonal approximation methods based on the geometric moments and the orthogonal moments defined in terms of Legendre polynomials are proposed. The difference between the moments defined by the initial contour and those of the approximated polygon is taken as the objective function. Each algorithm provides various polygonal approximation results with different number of line segments for different application situations. For a given error bound, we can determine the optimal polygon with a minimum number of line segments. The procedures are applied to some digital curves and better results are obtained in comparison with some known methods.     

Image representation using separable two-dimensional continuous and discrete orthogonal moments

This paper addresses bivariate orthogonal polynomials, which are a tensor product of two different orthogonal polynomials in one variable. These bivariate orthogonal polynomials are used to define several new types of continuous and discrete orthogonal moments. Some elementary properties of the proposed continuous Chebyshev–Gegenbauer moments (CGM), Gegenbauer–Legendre moments (GLM), and Chebyshev–Legendre moments (CLM), as well as the discrete Tchebichef–Krawtchouk moments (TKM), Tchebichef–Hahn moments (THM), Krawtchouk–Hahn moments (KHM) are presented. We also detail the application of the corresponding moments describing the noise-free and noisy images. Specifically, the local information of an image can be flexibly emphasized by adjusting parameters in bivariate orthogonal polynomials. The global extraction capability is also demonstrated by reconstructing an image using these bivariate polynomials as the kernels for a reversible image transform. Comparisons with the known moments are performed, and the results show that the proposed moments are useful in the field of image analysis. Furthermore, the study investigates invariant pattern recognition using the proposed three moment invariants that are independent of rotation, scale and translation, and an example is given of using the proposed moment invariants as pattern features for a texture classification application.     

一种快速计算Zernike矩的改进q-递归算法

提出了一种快速计算Zernike矩的改进q-递归算法,该方法通过同时降低核函数中Zernike多项式和Fourier函数的计算复杂度以提高Zernike矩的计算效率。采用 q-递归法快速计算Zernike多项式以避免复杂的阶乘运算,再利用x轴、y轴、x=y和x=-y 4条直线将图像域分成8等分。计算Zernike矩时,仅计算其中1个区域的核函数的值,其他区域的值可以通过核函数关于4条直线的对称性得到。该方法不仅减少了核函数的存储空间,而且大大降低了Zernike矩的计算时间。试验结果表明,与现有方法相比,改进q-递归算法具有更好的性能。     

基于两变量Hahn矩的图像分析

提出了一种新的、以两变量离散正交Hahn多项式为核函数的图像矩,推导了正则化后,两变量离散正交Hahn多项式的简单的计算方法。对二值图像、灰度图像以及噪声图像的重建实验表明：相对于同系数的单变量的Hahn矩,两变量Hahn矩的重建误差更小。因此,它们能够更好地提取图像的特征。     

Accurate calculation of high order pseudo-Zernike moments and their numerical stability

The accuracy of pseudo-Zernike moments (PZMs) suffers from various errors, such as the geometric error, numerical integration error, and discretization error. Moreover, the high order moments are vulnerable to numerical instability. In this paper, we present a method for the accurate calculation of PZMs which not only removes the geometric error and numerical integration error, but also provides numerical stability to PZMs of high orders. The geometric error is removed by taking the square-grids and arc-grids, the ensembles of which maps exactly the circular domain of PZMs calculation. The Gaussian numerical integration is used to eliminate the numerical integration error. The recursive methods for the calculation of pseudo-Zernike polynomials not only reduce the computation complexity, but also provide numerical stability to high order moments. A simple computational framework to implement the proposed approach is also discussed. Detailed experimental results are presented which prove the accuracy and numerical stability of PZMs.     

参数可调的通用半正交图像矩模型

目的 为了提高以正交多项式为核函数构造的高阶矩数值的稳定性,增强低阶矩抗噪和滤波的能力,将仅具有全局描述能力的常规正交矩推广到可以局部化提取图像特征的矩模型,从频率特性分析的角度定义一种参数可调的通用半正交矩模型。方法 首先,对传统正交矩的核函数进行合理的修正,以修正后的核函数（也称基函数）替代传统正交矩中的原核函数,使其成为修改后的特例之一。经过修正后的基函数可以有效消除图像矩数值不稳定现象。其次,采用时域的分析方法能够对图像的低阶矩作定量的分析,但无法对图像的高频部分（对应的高阶矩）作更合理的表述。因此提出一种时—频对应的方法来分析和增强不同阶矩的稳定性,通过对修正后核函数的频带宽度微调可以建立性能更优的不同阶矩。最后,利用构建的半正交—三角函数矩研究和分析了通用半正交矩模型的特点及性质。结果 将三角函数为核函数的图像矩与现有的Zernike、伪Zernike、正交傅里叶—梅林矩及贝塞尔—傅里叶矩相比,由于核函数组成简单,且其值域恒定在[-1,1]区间,因此在图像识别领域具有更快的计算速度和更高的稳定性。结论 理论分析和一系列相关图像的仿真实验表明,与传统的正交矩相比,在数值稳定性、图像重构、图像感兴趣区域（ROI）特征检测、噪声鲁棒性测试及不变性识别方面,通用的半正交矩性能及效果更优。