Image analysis by Gaussian-Hermite moments

Orthogonal moments are powerful tools in pattern recognition and image processing applications. In this paper, the Gaussian-Hermite moments based on a set of orthonormal weighted Hermite polynomials are extensively studied. The rotation and translation invariants of Gaussian-Hermite moments are derived algebraically. It is proved that the construction forms of geometric moment invariants are valid for building the Gaussian-Hermite moment invariants. The paper also discusses the computational aspects of Gaussian-Hermite moment, including the recurrence relation and symmetrical property. Just as the other orthogonal moments, an image can be easily reconstructed from its Gaussian-Hermite moments thanks to the orthogonality of the basis functions. Some reconstruction tests with binary and gray-level images (without and with noise) were performed and the obtained results show that the reconstruction quality from Gaussian-Hermite moments is better than that from known Legendre, discrete Tchebichef and Krawtchouk moments. This means Gaussian-Hermite moment has higher image representation ability. The peculiarity of image reconstruction algorithm from Gaussian-Hermite moments is also discussed in the paper. The paper offers an example of classification using Gaussian-Hermite moment invariants as pattern feature and the result demonstrates that Gaussian-Hermite moment invariants perform significantly better than Hu's moment invariants under both noise-free and noisy conditions.     

Image analysis by Krawtchouk moments

A new set of orthogonal moments based on the discrete classical Krawtchouk polynomials is introduced. The Krawtchouk polynomials are scaled to ensure numerical stability, thus creating a set of weighted Krawtchouk polynomials. The set of proposed Krawtchouk moments is then derived from the weighted Krawtchouk polynomials. The orthogonality of the proposed moments ensures minimal information redundancy. No numerical approximation is involved in deriving the moments, since the weighted Krawtchouk polynomials are discrete. These properties make the Krawtchouk moments well suited as pattern features in the analysis of two-dimensional images. It is shown that the Krawtchouk moments can be employed to extract local features of an image, unlike other orthogonal moments, which generally capture the global features. The computational aspects of the moments using the recursive and symmetry properties are discussed. The theoretical framework is validated by an experiment on image reconstruction using Krawtchouk moments and the results are compared to that of Zernike, pseudo-Zernike, Legendre, and Tchebyscheff moments. Krawtchouk moment invariants are constructed using a linear combination of geometric moment invariants; an object recognition experiment shows Krawtchouk moment invariants perform significantly better than Hu's moment invariants in both noise-free and noisy conditions.     

Image analysis by Tchebichef moments

This paper introduces a new set of orthogonal moment functions based on the discrete Tchebichef polynomials. The Tchebichef moments can be effectively used as pattern features in the analysis of two-dimensional images. The implementation of the moments proposed in this paper does not involve any numerical approximation, since the basis set is orthogonal in the discrete domain of the image coordinate space. This property makes Tchebichef moments superior to the conventional orthogonal moments such as Legendre moments and Zernike moments, in terms of preserving the analytical properties needed to ensure information redundancy in a moment set. The paper also details the various computational aspects of Tchebichef moments and demonstrates their feature representation capability using the method of image reconstruction.     

基于复Contourlet域的支持向量机和Krawtchouk矩的双水印算法

为了进一步提高基于支持向量机(SVM)水印算法的 鲁棒性,提出了一种 基于复Contourlet域的SVM和Krawtchouk矩的双水印算法。首先从RGB宿主 图像中提取B 分量和G分量,并且充分利用Krawtchouk矩不变量的平移、旋转、缩放不变性 和Krawtchouk矩良好 的局部重构特性,计算B分量图像的Krawtchouk低阶矩不变量 ,由此构造鲁棒水印;然后对G分量图 像进行两级复Contourlet分解,在其低频分量中,利用SVM建立图像尺度内的 局部相关性训练模型, 并根据预测结果自适应地实现数字水印图像的嵌入和提取。大量实验结果表明,本文算法不 仅具有较好的 不可感知性,而且对中值滤波、加性噪声和JPEG压缩之类的常规图像处理,以及缩放、旋转 和剪切等几 何攻击,均具有较好的鲁棒性能,其性能优于基于小波域的SVM和基于Contourlet域的SVM水 印算法。     

Radial Tchebichef moment invariants for image recognition

Radial Tchebichef moments as discrete orthogonal moments in the polar coordinate have been successfully used in the field of image recognition. However, the scale invariant property of these moments has not been studied due to its complexity of the problem. In this paper, we present a method to construct a set of scale and rotation invariants extracted from radial Tchebichef moments, named radial Tchebichef moment invariants (RTMI). Experimental results show the efficiency and the robustness to noise of the proposed method for recognition tasks.     

2D and 3D image localization,compression and reconstruction using new hybrid moments

In this article, we will present a new set of hybrid polynomials and their corresponding moments, with a view to using them for the localization, compression and reconstruction of 2D and 3D images. These polynomials are formed from the Hahn and Krawtchouk polynomials. The process of calculating these is successfully stabilized using the modified recurrence relations with respect to the n order, the variable x and the symmetry property. The hybrid polynomial generation process is carried out in two forms: the first form contains the separable discrete orthogonal polynomials of Krawtchouk–Hahn (DKHP) and Hahn–Krawtchouk (DHKP). The latter are generated as the product of the discrete orthogonal Hahn and Krawtchouk polynomials, while the second form is the square equivalent of the first form, it consists of discrete squared Krawtchouk–Hahn polynomials (SKHP) and discrete polynomials of Hahn–Krawtchouk squared (SHKP). The experimental results clearly show the efficiency of hybrid moments based on hybrid polynomials in terms of localization property and computation time of 2D and 3D images compared to other types of moments; on the other hand, encouraging results have also been shown in terms of reconstruction quality and compression despite the superiority of classical polynomials.

     

采用径向Tchebichef矩不变量的飞机型号识别

针对几何矩非正交性对目标描述的不足以及连续正交矩在处理数字图像方面存在离散化误差的缺陷,为了提高识别精度,提出了一种利用离散正交的Tchebichef矩结合全局特征和局部特征的飞机型号识别方法。首先,根据几何矩和Tchebichef矩之间的关系,利用归一化几何中心矩、圆谐函数得到径向Tchebichef矩的旋转、尺度和平移(RST)不变量;然后,利用径向Tchebichef矩提取飞机目标的局部和全局特征构成特征向量;最后,利用Matlab构造了四类飞机的样本集,采用支持向量机(SVM)作为分类器识别测试样本飞机型号,分析了几何矩、Zernike矩和本文方法在识别精度上的差异以及训练样本集大小对识别精度的影响。实验结果表明,本文提出的算法提高了识别精度,并且在训练样本集较小时仍能获得90%以上的识别精度。     

An Energy Efficient Protocol to Mitigate Hot Spot Problem Using Unequal Clustering in WSN

Iris recognition under less constrained environment poses a challenge to be considered for high-security applications. In this paper, discrete orthogonal moment-based features including Tchebichef, Krawtchouk and Dual-Hahn are proposed which prove to be effective for both near-infrared and visible images. The local as well as global features are extracted from localized iris regions till 15th order with invariance (scale, rotation, translation and illumination) properties and tolerance to noise. The performance of the moment-based features is evaluated on four publicly available databases: CASIA-IrisV4-Interval, IITD.v1, UPOL and UBIRIS.v2. It is found that the proposed method gives encouraging results in terms of accuracy, equal error rate and decidability index as compared to the competing techniques available in the literature.     

基于Krawtchouk不变矩的仿射攻击不变性局部水印算法

本文提出了一种基于原始图像Krawtchouk不变矩实现的仿射攻击不变性局部水印算法.具体介绍了Krawtchouk不变矩的构造方法,水印是事先产生的且与原始图像无关,通过将水印嵌入到图像的Krawtchouk不变矩中实现仿射攻击不变性.这种基于Krawtchouk矩的水印算法是局部水印技术,即水印的嵌入只是影响到部分原始图像,因此该算法对剪切攻击具有很好的鲁棒性.检测过程中采用独立分量分析技术实现真正意义上的盲检测.文中具体分析了所提出算法的计算复杂度,实验数据说明这种水印算法对通用水印测试软件Stirmark具有很好的鲁棒性.     

彩色图像的四元数径向矩仿射不变量

为了研究彩色图像的不变量特性,本文把传统灰度图像的不变量理论推广到四元数层面上来,定义了彩色图像的四元数径向矩并构造了该矩函数的仿射不变量。采用四元数对彩色图像建模,可以充分利用彩色图像整体信息,实现彩色图像RGB通道的并行处理。实验结果表明,彩色图像的四元数径向矩仿射不变量的稳定性要优于L.V.Gool等人提出的彩色矩仿射不变量,其数值稳定性(σ/μ值)提高了一个数量级。本文所提出的四元数径向仿射不变量可以作为模式识别中彩色目标的特征描述子。     

Some computational aspects of discrete orthonormal moments

Discrete orthogonal moments have several computational advantages over continuous moments. However, when the moment order becomes large, discrete orthogonal moments (such as the Tchebichef moments) tend to exhibit numerical instabilities. This paper introduces the orthonormal version of Tchebichef moments, and analyzes some of their computational aspects. The recursive procedure used for polynomial evaluation can be suitably modified to reduce the accumulation of numerical errors. The proposed set of moments can be used for representing image shape features and for reconstructing an image from its moments with a high degree of accuracy.     

基于Tchebichef不变矩的多比特抗几何攻击图像盲水印算法

现有的大多数水印算法对旋转、平移和尺度变换等几何攻击的鲁棒性比较差,微小的几何攻击都有能导致水印检测器失效,因此水印算法对几何攻击具有鲁棒性非常重要。本文提出了一种基于Tchebichef不变矩实现的多比特几何攻击不变性图像盲水印算法。文中具体介绍了Tchebichef不变矩的构造方法,水印是事先产生的与原始图像无关的信号,嵌入过程中将水印嵌入到图像的Tchebichef不变矩中实现几何攻击不变性。水印检测过程中采用独立分量分析技术实现真正意义上的多比特水印盲检测。文中具体分析了所提出的水印算法的计算复杂度,实验过程中采用通用水印测试软件Stirmark对所提出的水印算法进行鲁棒性测试,实验数据说明这种水印算法对Stirmark具有很好的鲁棒性。     

基于兴趣点不变矩的图像拼接

提出了一种基于兴趣点不变矩(IPIM)的图像拼接技术.利用Harris角检测器获取图像中的兴趣点,计算兴趣点邻域的平移、旋转及尺度不变矩,通过比较各兴趣点邻域不变矩的欧式距离提取出初始特征点对,根据几何变换模型剔除伪特征对,最后利用正确映射模型实现图像的拼接.实验表明,该方法对平移以及任意角度的旋转具有良好的鲁棒性,对于具有小尺度变换的图像仍然具有很好的拼接效果.     

Localized affine transform resistant watermarking in region-of-interest

Many proposed image watermarking techniques are sensitive to affine transforms, such as rotation, scaling and translation. In this paper, a localized affine transform resistant watermarking is designed utilizing Krawtchouk transform and dual channel detection. Watermark is inserted into the significant Krawtchouk invariant moment. Watermarking based on Krawtchouk moments is local, which permits to the watermark to be embedded at the most significant information-wise portion. Watermark embedding intensity is modified according to the results of performance analysis. The convergence of closed loop embedding system is proved. An optimum watermark detector is designed with the introduction of dual channel detection utilizing high order spectra detection and likelihood detection. The detector extracts watermark blindly utilizing Independent Component Analysis. The computational aspects of the proposed watermarking are discussed. Experimental results demonstrate that this watermarking is robust with respect to attacks produced by watermark benchmark—Stirmark.     

Tchebichef矩在图像数字水印技术中的应用

提出了一种利用原始图像的Tchebichef矩来增加水印顽健性的方法,即利用原始图像的一个或多个Tchebichef矩的值来估计水印图像所经过的几何变换的参数以及图像增强等图像处理操作的参数,并将这一过程作为水印检测的预处理过程。实验中将多种不同的水印信息在不同的图像处理域(包括DWT、DCT、FFT以及空间域等)实现水印信息的嵌入。为了检测这种估计算法的顽健性,本文实验中的几何攻击是由Stirmark产生的。计算机模拟实验证明这种估计方法简单,估计精度很高,增加了图像水印技术对几何攻击的顽健性,而且可在任何处理域中实现,具有很好的实用价值。1     

基于双正交小波变换的矩不变量

寻找相对于尺度、平移、旋转不变的小波不变量是多尺度分析在模式识别中的关键问题.矩是一种理论和应用上比较成熟的方法,本文将矩与多尺度小波分解的近似系数联系起来,利用空间基函数的双正交性推导得到了双正交小波矩不变量,并用实验验证了结果的正确性.同时以Haar小波为例对结论中的限制条件进行了理论分析和实验验证,结果表明可以计算高于平滑阶数的小波矩,且计算精度符合要求.由此获得了比较完善的理论和实验结果,最后指出了它在实际应用中所需注意的问题.     

基于局部Tchebichef矩的鲁棒图像水印算法

针对目前基于图像不变特征水印算法不能同时有效抵抗常规图像处理和几何攻击这一问题,提出了一种基于局部Tchebichef矩(LTMs)的图像水印新算法。首先,利用Harris-Laplace检测算子提取载体图像多尺度空间中的特征点,并通过特征选择策略获得稳定且分离的局部圆形特征区域;然后,结合主方向对齐,得到具有旋转、缩放和平移(RST)不变性的局部圆形特征区域;最后,计算局部特征区域的Tchebichef矩,采用量化调制Tchebichef低阶矩幅值将水印嵌入到局部特征区域中。实验结果表明,本文算法在获得很好的不可见性的同时,对常规图像处理、几何攻击及组合攻击具有较好的鲁棒性。