超复数

一种基于超复数系的数字全息图像生成方法

A Method Based on Hypercomplex Number System for Fractal Digital Hologram Synthesis

可交换超复数Julia集的生成与研究

The Generation and Study of Communicative Hypercomplex Julia Set

时空推动用Hamilton超复数表示

Time-space boost represented by Hamilton super-complex number

本论文通过从图像超复数梯度信息矩阵中来获取超复数Harris响应，给出了超复数Harris响应的彩色图像质量指标。

Hypercomplex gradient information matrix is presented to compute Hypercomplex Harris response of color image .

因此，超复数Harris响应的变化程度就反映了彩色图像的失真程度。

Hence , the degree of change in hypercomplex Harris response is related to quality degradation of color image .

最后，提出基于超复数空间的彩色边缘检测和Bayer图像自适应彩色重建算法

Finally , a quaternion based color edge detector is proposed and a self-adaptive color reconstruction algorithm for Bayer pattern is developed

并根据该模型利用特殊的四阶累积量切片分析了加性高斯有色噪声中二维谐波频率估计及联合Hamilton四元数和超复数在二维谐波频率估计中的应用前景。

The corresponding four order cumulant was defined to restrain the additive Gauss noise and the frequency was extracted using the properties of Hamilton quaternion and hypercomplex .

其次，结合矩阵分析中奇异值分解（SVD）的计算方法，实现了超复数奇异值分解，并将其应用于超声彩色图像压缩中。

Secondly , the paper realizes the hypercomplex Singular Value Decomposition ( SVD ) combined with the SVD computation method in matrix analysis , and put it into practice of ultrasonic color images compression .

基于超复数奇异值分解（也称四元数奇异值分解QSVD）提出一种全新的图形化与数值化相结合的彩色图像质量评估测度，不仅能判断图像失真等级，还能判断不同的失真类型。

Based on hypercomplex singular value decomposition also called quaternion singular value decomposition ( QSVD ), we present a novel color image quality measure that can be used as a graphical or a scalar measure to predict the distortion introduced by a wide range of noise sources .

客观评估彩色图像质量的超复数奇异值分解法

Hypercomplex Singular Value Decomposition Approach to Objectively Assessing Color Image Quality

四维复空间的超复数和单位球

Super - complex and unit ball of four-dimensional complex space

残差超复数偶对分解的多光谱和全色图像融合方法

Residual Error Hypercomplex Symplectic Decomposition Approach to Multispectral and Panchromatic Image Fusions

彩色图像超复数空间的自适应水印算法

An Adaptive Watermarking Algorithm in the Hypercomplex Space of a Color Image

超复数空间彩色边缘检测器的实现

Realization of Color Edge Detector in Quaternion Space

四元数和超复数在加性高斯噪声背景下二维谐波频率估计中的应用

Two-dimensional harmonics frequency estimation in additive gaussian noise background based on quaternion and hypercomplex

一种超复数鲁棒相关图像配准算法

A Picture Matching Algorithm of Robust Hypercomplex Correlation

经过超复数傅里叶变换，得到原始图像的相位信息。

With hypercomplex Fourier transformation , the phase information of the original image could be obtained .

另外，本文还利用超复数自适应稀疏表示字典对彩色图像进行了质量评估。

This paper proposes a method to evaluate color image quality by using hypercomplex adaptive sparse dictionary .

通过把彩色图像映射到超复数空间进行处理，产生色差边缘图像。

The original image is firstly mapped into the quaternion space , and a color difference edge image is produced .

根据此分析结果，本论文提出一种残差超复数偶对分解的多光谱与全色图像融合方法。

In this dissertation , a residual error hypercomplex symplectic decomposition approach to multispectral and panchromatic images fusion is presented .

上述结果表明：矢量水听器的超复数测量模型为矢量水听器的信号处理开辟了一个新的天地。

The results show that the hypercomplex model of acoustic vector sensor breaks a new path for the signal processing field .

提出超复数空间彩色图像边缘检测器的一种新实现方法&基于超复数空间旋转变换的彩色边缘检测。

A new approach is presented for the realization of color edge detector in the quaternion space rotation transform based color edge detector .

并对颜色空间变换方法中的超复数空间变换方法提出了归一化的色差边缘检测算法。

Furthermore , we make some improvements on the method of super complex number space transformation , and bring forth a unitary color difference edge detection method .

然后，实现了两种基本的小波压缩方法，对超复数小波的幅值-相位表示形式设计了简单的量化标准，并进行压缩指标分析。

Then , the paper realizes two basic wavelet compression methods and design simple quantization standard to the magnitude-phase representation of hypercomplex wavelet combined with compression indices analysis .

为了保证嵌入水印的载体图像仍然可以用三色分量进行传输，本论文研究了在超复数频域嵌入水印的前提条件，以及提出了如何满足该条件的方法。

We explore the prerequisite to ensure that the watermarked host image can also be transferred in three channels , which can be satisfied by our proposed technique .

在此基础上，本论文研究了人类视觉系统对彩色载体图像的纹理、边缘和亮度的掩蔽特性与嵌入水印强度的关系，据此关系进而提出了彩色图像在超复数空间的自适应水印算法。

Furthermore , based on different mask properties of the human vision system about texture , edge and luminance of the color host images , the selected frequency spectras are weighted adaptively .

超复数可以很方便的表示彩色图像的3通道分量，并且结合分析变换手段，可以使得分解系数离散稀疏，更有利于提取有用信息。

The hypercomplex algebra is convenient to represent the 3 channels of color images that makes the coefficients of decomposition are sparse and it is helpful to extract significant information combined with transform methods .

同时超复数傅立叶变化扩展了经典傅立叶变换处理的信号范围，作为彩色图像处理的新理论也待扩展其适用范围。

Meanwhile the hypercomplex Fourier transform extends the processing signal field compared with the classical Fourier transform . As a new theory in color image processing field , its application range should be extended .

多光谱和全色图像融合适用的超复数主元加权方法如果将能谱实验数据的对数拟合成直线以求得粒子温度，则最好对温度误差的平方和极小化。

Hypercomplex principle component weighted approach to multispectral and panchromatic images fusions However , if a straight line is fitted for logarithmic spectrum data to give the particle temperature , it is better to minimize the temperature square error sum .