彩色图像四元数矩不变量的研究

为了研究彩色图像的矩不变量特性,采用四元数进行彩色图像处理,以充分利用彩色图像的整体信息,实现彩色图像RGB并行处理。本文把传统灰度图像的矩不变量理论推广应用到四元数层面上来,定义了彩色图像的四元数矩并构造了该矩函数的仿射不变量。实验结果表明:所提出的彩色图像的四元数矩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σ/u值提高了2个数量级。所提出的四元数仿射矩不变量可以作为模式识别中彩色目标的特征描述子来实现彩色图像目标的识别与跟踪。     

基于离散四元数傅里叶变换的双随机相位加密技术

应用光学图像加密的思想,将离散四元数傅里叶变换(DQFT)与双随机相位加密技术相结合,提出了一种应用于彩色图像的双随机相位加密新技术. 基于DQFT的双随机相位加密技术可将彩色图像作为一个整体进行加密,从而在保持了系统的保密性能的同时,有效地降低了复杂性. 阐述了加密和解密的原理,并通过实验对其鲁棒性进行了验证. 关键词： 四元数 离散四元数傅里叶变换(DQFT) 双随机相位加密     

基于四元数实矩阵和对数极坐标的彩色图像零水印算法

为了提高空间域彩色图像零水印算法的水印嵌入、检测的精度,以及抵抗旋转几何变换的能力,提出一种基于对数极坐标和四元数实矩表示的抗旋转攻击空间域零水印算法。将原始彩色图像使用四元数实矩阵来表征,计算实数字矩阵的Hu不变矩;利用7个Hu不变矩来设计和构建零水印信息;在水印检测前,通过对数极坐标校正算法,对可能遭受旋转攻击的待检测图像进行旋转角度的遍历,而后进行水印的提取。实验获得了良好的图象视觉效果,对于旋转几何攻击具有很强的鲁棒性,同时对于滤波,JPEG压缩,剪切攻击也具有一定的鲁棒性。     

基于Radon变换和四元数实矩阵的彩色图像零水印算法

为了提高空间域彩色图像零水印算法的水印嵌入和检测精度以及抵抗旋转几何变换的能力,提出了一种基于Radon变换和四元数实矩阵表示的抗旋转攻击空间域零水印算法。首先将原始彩色图像使用四元数实矩阵来表征,并计算实数字矩阵的Radon变换不变矩;然后利用少量低阶Radon变换不变矩来设计和构建零水印信息;在水印检测前,通过Radon变换几何校正算法对可能遭受旋转攻击的待检测图像进行旋转角度的校正,然后进行水印的提取。实验结果表明,该方法可以获得良好的图像视觉效果,对于旋转几何攻击具有很强的鲁棒性,同时对滤波、JPEG压缩和剪切攻击也具有一定的鲁棒性。     

彩色图像处理的可交换 Clifford 代数方法

采用可交换Clifford代数对彩色图像建模,充分利用彩色图像作为一个整体所具有的潜在颜色信息,实现彩色图像各颜色分量的并行处理,可完成彩色图像的整体处理。本文分析了彩色图像的表示方法,系统研究了一类可交换Clifford代数-Clcom2,定义了Clcom2上元素的四则运算规则、单位元、逆元、共轭、范数等。给出了基于可交换Clifford代数的彩色图像表示方法,并介绍了一个Clcom2架构下的彩色图像处理实例：彩色图像边缘检测。与传统的四元数彩色图像表示方法相比,本文所提出的方法最大限度地去除了数据冗余,其算法复杂度也大大降低。结果显示,基于可交换Clifford代数的彩色图像表示方法可以应用到彩色图像处理中。     

四元数在量子力学中的应用

把双四元数推广到了二级双四元数，并设计了一种态函数的四元数表示法，从而用四元数表述了相对论量子力学，使四元数物理学形成了系统，用四元数表示的算符和状态，对于导出算符间的对易关系和状态的洛伦兹变换性质是方便的。     

八元数神经网络模型：256色图像的识别

首次把八元数引入到神经网络中，提出了八元数离散神经网络模型，并用信噪比理论初步考察了模型的稳定性和存贮容量。八元数神经网络模型可应用于高精度的２５６级的灰度图像或２５６值的彩色图像的识别中。     

四元数在力学和电磁学中的应用

用双四元数表述了相对论力学和电磁规律,所用的方法能够适用于相对论性物理学科的不同领域,有利于形成系统的四元数物理学,由于四元数本身结构上的特点,使得四元数形式的物理量具备了反映四维时空中时间与空间内在联系的功能,从而用了数表述的相对论性物理学在一定程度上为揭示一些貌视无关的自然规律之间本质上的联系提供了可能性。     

三维转动的四元数表述

用四元数表达三维的旋转与使用矩阵相比具有两个优点：第一．几何意义明确;第二,计算简单．因此,四元数在数学、物理学和计算机图形学中具有很高的应用价值．本文详细叙述了四元数的这一功能,讨论了四元数的定义、运算、性质、几何意义和它的3种表达形式,给出了使用四元数处理点的各种几何变换的一般结论．     

双目视觉中基于对偶四元数的三维运动估计

针对现有的三维运动估计算法在精度、效率和稳定性等综合性能上的不足,提出了一种结合双目视觉三维重建和利用对偶四元数表达运动参数的新算法。该算法以双目视觉系统为基础,采用SIFT算法进行图像特征点的提取和匹配;根据匹配关系进行三维特征点重建,以获取三维场景中运动目标的结构参数;利用对偶四元数可同时表示刚体的旋转和平移运动的特点,实现目标对象运动参数的表达和求解。通过实验将提出的算法与现有算法(包括奇异值分解法、正交分解法和单位四元数分解法)进行比较,结果表明,该算法具有更加简洁的表达形式,在保持传统算法精度和稳定性优势的基础上提高了计算效率,具有更优的综合性能。     

Quaternion higher-order spectra and their invariants for color image recognition

This paper describes an invariants generation method for color images, which could be a useful tool in color object recognition tasks. First, by using the algebra of quaternions, we introduce the definition of quaternion higher-order spectra (QHOS) in the spatial domain and derive its equivalent form in the frequency domain. Then, QHOS invariants with respect to rotation, translation, and scaling transformations for color images are constructed using the central slice theorem and quaternion bispectral analysis. The feature data are further reduced to a smaller set using quaternion principal component analysis. The proposed method can deal with color images in a holistic manner, and the constructed QHOS invariants are highly immune to background noise. Experimental results show that the extracted QHOS invariants form compact and isolated clusters, and that a simple minimum distance classifier can yield high recognition accuracy.     

A geometric correction based robust color image watermarking scheme using quaternion Exponent moments

Most of the existing color image watermarking schemes was designed to mark grayscale images or use the color components, which ignore the significant correlation between different color channels. Recently, several approaches were developed to process the color channels intrinsically, but they always cannot counterattack geometric distortions. It is a challenging work to design a robust color image watermarking scheme against geometrical distortions. In this paper, we propose a geometric correction based robust color image watermarking approach using quaternion Exponent moments (QEMs). The novelty of our approach is that (1) the QEMs are derived to deal with the color images in a holistic manner, and (2) the QEMs are exploited for estimating the geometric distortions parameters in order to permit watermark extraction. Experimental results confirm the validity of our approach and its higher robustness against geometrical distortions compared to alternative watermarking methods in the literature.     

Double-Color-Image Compression-Encryption Algorithm Based on Quaternion Multiple Parameter DFrAT and Feature Fusion with Preferable Restoration Quality

To achieve multiple color images encryption, a secure double-color-image encryption algorithm is designed based on the quaternion multiple parameter discrete fractional angular transform (QMPDFrAT), a nonlinear operation and a plaintext-related joint permutation-diffusion mechanism. QMPDFrAT is first defined and then applied to encrypt multiple color images. In the designed algorithm, the low-frequency and high-frequency sub-bands of the three color components of each plaintext image are obtained by two-dimensional discrete wavelet transform. Then, the high-frequency sub-bands are further made sparse and the main features of these sub-bands are extracted by a Zigzag scan. Subsequently, all the low-frequency sub-bands and high-frequency fusion images are represented as three quaternion signals, which are modulated by the proposed QMPDFrAT with three quaternion random phase masks, respectively. The spherical transform, as a nonlinear operation, is followed to nonlinearly make the three transform results interact. For better security, a joint permutation-diffusion mechanism based on plaintext-related random pixel insertion is performed on the three intermediate outputs to yield the final encryption image. Compared with many similar color image compression-encryption schemes, the proposed algorithm can encrypt double-color-image with higher quality of image reconstruction. Numerical simulation results demonstrate that the proposed double-color-image encryption algorithm is feasibility and achieves high security.     

基于扩展目标的不变矩跟踪算法

 提出基于边缘区域的不变矩计算方法，在此基础上，针对在运动中形状、尺寸和方位不断变化的扩展目标，提出一种以不变矩作为跟踪特征，粗、精阶段相结合的相关跟踪算法，并根据目标图像的相关性给出一种新的跟踪置信度。实验结果显示算法迅速、有效、匹配精度高，对于复杂背景，较强噪声和运动状态发生变化条件下的扩展目标跟踪稳定可靠。     

几种边界特征描述方法的比较研究

在图像处理与模式识别领域经常根据物体的边界来识别物体。对物体边界特征描述的三种主要方法,即基于极半径函数的傅里叶描述子、边界序列矩和改进的不变矩进行了比较研究,给出了实验结果和结论。     

基于Zernike正交矩的亚像素图像线宽测量算法

针对图像内的细窄线宽,提出了一种基于Zernike正交矩的亚像素图像线宽检测算法。该算法具有明确的几何模型,通过计算图像的2阶和4阶Zernike正交矩,推导出了亚像素线宽表达式。根据数字图像的离散性,给出了计算正交矩所需的模板系数,并分析了由离散性造成的原理误差。将所提出的亚像素线宽检测技术应用于安瓿内异物粒径的标定实验,结果表明:该算法可有效地测量弱小目标在图像中的亚像素线宽值,从而得到了异物粒径大小与亚像素线宽之间的标定曲线。     

Strange magnetic moments of octet baryons under SU (3) breaking

Magnetic moments of octet baryons are parameterized to all orders of the flavor SU(3) breaking with the irreducible tensor technique in order to extract the contribution of each flavor quark to the magnetic moments of the octet baryons. The not-yet measured magnetic moment of ∑⁰ is predicted to be 0.649μ_N. Our parameterized forms for the magnetic moments are explicitly flavor-dependent, and hence each flavor component of the magnetic moments can be evaluated directly via the flavor projection operator. It is found that the strange magnetic moment of the nucleon is suppressed due to the small isoscalar anomalous magnetic moment of the nucleon. In particular, the strange magnetic form factor of the nucleon turns out to be positive, G_N^s(0)=0.428μ_N, which is consistent with recent data.     

Moment Systems Derived from Relativistic Kinetic Equations

In this paper, we are interested in the derivation of macroscopic equations from kinetic ones using a moment method in a relativistic framework. More precisely, we establish the general form of moments that are compatible with the Lorentz invariance and derive a hierarchy of relativistic moment systems from a Boltzmann kinetic equation. The proof is based on the representation theory of Lie algebras. We then extend this derivation to the classical case and general families of moments that obey the Galilean invariance are also constructed. It is remarkable that the set of formal classical limits of the so-obtained relativistic moment systems is not identical to the set of classical moments quoted in Ref. 21 and one could use a new physically relevant criterion to derive suitable moment systems in the classical case. Finally, the ultra-relativistic limit is considered.