广义Gray码及其在数字图像置乱中的应用

以图像信息安全问题为背景，讨论了广义Gray码及其在数字图像中的置乱作用，推广了丁玮等人（1999年）的相关结果。给出了图像置乱变换的周期，得到了周期性的一个充分必要条件。     

基于Arnold变换的图像逆置乱算法

针对Arnold变换的周期依赖于图像的阶数这一特性,提出了一种反变换算法.该算法通过分析加密图像任一点处两坐标分量间关系,得到原图像相应点的坐标,从而实现图像的解密.该反变换也可作为图像置乱的正变换,相应的反变换就是Arnold变换.在此基础上,把二维反变换算法推广到m维的情形.实验结果表明,对于已应用Arnold变换进行预处理的置乱图像,在无须计算原图像变换周期的前提下可快速实现图像的逆置乱,该过程具有确定性,其迭代次数与预处理置乱次数相等.     

基于Gray-Scott系统的图像加密

首先给出了从Gray-Scott系统中提取8位整型伪随机序列的一种有效算法,接着提出了一种使用随机序列的图像像素位置置乱算法,在此基础上结合像素值改变技术设计了一套有效的图像加密方法.数值模拟及安全性分析说明加密方法有效.     

多小波图像插值算法研究

与单小波变换一样,多小波变换同样具有多分辨分析的特性,1次多小波变换可以将图像分解成4个低频子带和12个高频子带,而且原图像的大小是每个子带的4倍.根据多小波变换的这一特点,利用原图像与经过1次多小波变换后的各高频子带的信息,并考虑各子带的分形维数,提出了一种新颖的灰度图像插值算法.实验结果表明,与传统的插值算法相比,例如双线性插值与双三次多项式插值,该算法的插值效果较好,且克服了单小波插值中出现的斑点干扰.     

基于Logistic映射和超混沌系统的图像加密方案

利用Logistic映射和一个超混沌系统产生一个复杂的混沌时间序列,对图像进行置乱操作,重新排列图像的各像素,再进行两轮扩散操作,得到一个新的基于Logistic映射和超混沌系统的图像加密方案,并进行仿真实验和性能测试。实验证明,该加密方案有较好的密码学特性,能够对抗统计分析攻击、差分攻击等。     

基于自适应小波变换和矢量量化的图像压缩编码

运用小波变换进行图像压缩的算法其核心都是小波变换的多分辨率分析以及对不同尺度的小波系数的量化和编码 .本文提出了一种基于能量的自适应小波变换和矢量量化相结合的压缩算法 .即在一定的能量准则下 ,根据子图像的能量大小决定是否进行小波分解 ,然后给出恰当的小波系数量化 .在量化过程中 ,采用一种改进的LBG算法进行码书的训练 .实验表明 ,本算法广泛适用于不同特征的数字图像 ,在取得较高峰值信噪比的同时可以获得较高的重建图像质量 .     

基于上下文光谱角映射的无监督图像变化检测方法

对传统遥感图像变化检测方法未充分利用像素上下文信息的问题,提出一种无需关于像素的概率分布假设、基于上下文光谱角映射的无监督图像变化检测方法.方法避免了在图像分析过程中将像素看作独立单元,通过引入图像的空间上下文信息特征,在对像素变化类别的判别测试阶段加以利用,从而达到提高变化检测精确度的效果.对卫星图像的实施过程首先利用上下文光谱角映射创建一幅相似图像,然后用K均值聚类算法将其分为有变化和无变化的两类来生成映射图像.实验从定量和定性的两方面与最大似然估计法(MLC)比较,结果显示所提方法比已有方法有所改进,对于二时刻图像和多光谱图像的变化检测问题有更好的适用性.     

基于Curvelet变换的数字水印算法

数字水印技术能起到版权保护的作用,从数字水印的鲁棒性与不可感知性要求出发,介绍了Curvelet变换的多方向、多分辨、带通特点及各层的系数特征,提出了一种基于Curvelet变换和HVS的图像数字水印技术,这种数字水印方法是将数字水印嵌入到原始图像经Curvelet变换后的高频系数构成的矩阵当中.仿真实验表明该算法简单有效,原图像与嵌入水印后图像差异小,水印提取准确,不仅能保证数字水印不可感知性,而且在对嵌入水印图像进行裁剪、加噪、旋转及涂改等攻击后具有较强的鲁棒性.     

简单1维数字流形的积空间中数字复叠的笛卡尔积的Deck变换群

首先提出了简单1维数字流形的概念,接着研究了简单1维数字流形的具有C-相容邻接关系的笛卡尔积空间中的数字图像.进一步,为了研究数字复叠的笛卡尔积的Deck变换群,利用半径2-(k_(i2),k_(i1))-局部同胚的性质来体现数字复叠的笛卡尔积的Deck变换群在从数字拓扑的角度来比较数字积空间时的优势.此外,通过强调C-相容的必要性修正了文献(Han S E.Comparison among digital fundamental groups and its applications[J].Information Sciences,2008,178(8):2091-2104)中的一个错误.利用本文的方法,可以从本质上区分数字积图像,从而使得数字图像的研究内容更加丰富.     

手部软组织红外热像图处理与K-L变换分析

首先对手部软组织的红外热像图进行图像处理,包括灰度化、降噪、增强、分割,其中图像分割采用Otsu算法选择适当的阈值,从而将目标图像与背景分割.然后将处理后图像的像素值代入K-L变换,得到样本的特征空间,将所有样本都投影到该特征空间得到投影系数.最后利用欧式距离公式,最终判断手部软组织的病变情况.     

Using Conventional Edge Detectors and Postsmoothing for Segmentation of Spotted Microarray Images

Segmentation of spotted microarray images is important in generating gene expression data. It aims to distinguish foreground pixels from background pixels for a given spot of a microarray image. Edge detection in the image processing literature is a closely related research area, because spot boundary curves separating foregrounds from backgrounds in a microarray image can be treated as edges. However, for generating gene expression data, segmentation methods for handling spotted microarray images are required to classify each pixel as either a foreground or a background pixel; most conventional edge detectors in the image processing literature do not have this classification property, because their detected edge pixels are often scattered in the whole design space and consequently the foreground or background pixels are not defined. In this article, we propose a general postsmoothing procedure for estimating spot boundary curves from the detected edge pixels of conventional edge detectors, such that these conventional edge detectors together with the proposed postsmoothing procedure can be used for segmentation of spotted microarray images. Numerical studies show that this proposal works well in applications.

Datasets and computer code are available in the online supplements.     

I-binomial scrambling of digital nets and sequences

The computational complexity of the integration problem in terms of the expected error has recently been an important topic in Information-Based Complexity. In this setting, we assume some sample space of integration rules from which we randomly choose one. The most popular sample space is based on Owen's random scrambling scheme whose theoretical advantage is the fast convergence rate for certain smooth functions.This paper considers a reduction of randomness required for Owen's random scrambling by using the notion of i-binomial property. We first establish a set of necessary and sufficient conditions for digital (0,s)-sequences to have the i-binomial property. Then based on these conditions, the left and right i-binomial scramblings are defined. We show that Owen's key lemma (Lemma 4, SIAM J. Numer. Anal. 34 (1997) 1884) remains valid with the left i-binomial scrambling, and thereby conclude that all the results on the expected errors of the integration problem so far obtained with Owen's scrambling also hold with the left i-binomial scrambling.     

Geometric Encoding of Color Images

Formal analysis and computer recognition of 2D color images is an important branch of modern computer geometry. However, the present methods, in spite of their longstanding high development, are not quite satisfactory and seem to be much worse than (unknown) algorithms used by our brain to analyze visual information. Almost all existing algorithms omit colors and deal with gray scale transformations only. However, in many cases color information is important and has to be proceeded. In this paper a fundamentally new method of encoding and analyzing color digital images is proposed. The main idea of this method is that a full-color digital image is encoded by a special two-dimensional surface in the three-dimensional space. After that the surface is analyzed by methods of differential geometry rather than traditional gradient-based or Hessian-based methods (like SIFT, GLOH, SURF, Canny operator, and many other well-known algorithms).     

基于方向信息测度的最小模糊度准则边缘检测

将像素点的方向信息测度作为判别边缘点的特性指标,借用Huang等构造的自适应确定分割阈值的思想,本文提出了一种基于方向信息测度的最小模糊度准则边缘检测方法。文中提出的方法,一方面由于采用了方向信息测度,可以很好地将边缘点和非边缘点区分开来;另一方面通过最小化模糊度,自适应地将给定图像的所有像素点按照方向信息测度分成两类,从而达到提取边缘的目的。实验结果证明,我们提出的方法能够很好地判别边缘点,有效地提取图像的边缘。     

An affine interpretation of Bäcklund transformations

The paper is devoted to an affine interpretation of Bäcklundmaps (Bäcklund transformations are a particular case of Bäcklund maps) for second order differential equations with unknown function of two arguments. Note that up to now there are no papers where Bäcklund transformations are interpreted as transformations of surfaces in a space other than Euclidean space. In this paper, we restrict our considerations to the case of so-called Bäcklund maps of class 1. The solutions of a differential equation are represented as surfaces of an affine space with induced connection determining a representation of zero curvature. We show that, in the case when a second order partial differential equation admits a Bäcklund map of class 1, for each solution of the equation there is a congruence of straight lines in an affine space formed by the tangents to the affine image of the solution. This congruence is an affine analog of a parabolic congruence in Euclidean space. The Bäcklund map can be interpreted as a transformation of surfaces of an affine space under which the affine image of a solution of the differential equation is mapped into a particular boundary surface of the congruence.     

A Jordan surface theorem for three-dimensional digital spaces

Many applications of digital image processing now deal with three-dimensional images (the third dimension can be time or a spatial dimension). In this paper we develop a topological model for digital three space which can be useful in this context. In particular, we prove a digital, three-dimensional, analogue of the Jordan curve theorem. (The Jordan curve theorem states that a simple closed curve separates the real plane into two connected components.) Our theorem here is a digital topological formulation of the Jordan-Brouwer theorem about surfaces that separate three-dimensional space into two connected components.     

The Almost Pasting Property of Digital Continuity

The pasting property plays a significant role in studying a continuous map in general topology. Unlike the pasting property, digital continuity has some intrinsic features. In this paper we prove that digital continuity has the almost pasting property instead of the pasting one. Furthermore, as a digital version of the straightness of a metric space, we introduce the notion of k-straightness of a digital space (X,k) and study its properties which can be used in image synthesis and digital image weaving.     

VT and VF classification using trajectory analysis

Visual classification of Ventricular Fibrillation (VF) and Ventricular Tachycardia (VT) patterns is a hard task for cardiologists. VT and VF signals are apparently similar in the time domain but their underlying information is totally different. In this paper, an image-based technique is presented which extracts discriminative information from the trajectories of VT and VF signals in the state space. In this way, first, signals are sketched in the state space by the delay time method. Then, the state space is considered as an image and trajectories of VT and VF signals are considered as two different images. The purpose is to design some masks, apply them on the images, and finally classify these masked images by a box counting method. These masks are designed to remove the common information between the two patterns and just discriminative pixels are flagged. After applying the masks, flagged pixels are counted and a threshold is determined through the cross validation phase under the receiver operator curve (ROC) criterion to classify the VT and VF trajectory images. The signals are selected from two different data sets include MIT/BIH and CCU of the Royal Infirmary of Edinburgh. Our experiments show brilliant results which provide 100% classification rate on the training and testing phases. Even, through the cross validation phase, the results remained the same also, so thep value is determined as less than 0.0001, that experimentally shows no over-fitting is occurred.     

Side-scan sonar image processing using thin plate splines and control point matching

The development of reliable software tools to aid human interpretation of complex digital images is of increasing importance. In particular, change detection requires that two or more images be carefully overlaid (registered) using digital techniques that compensate for picture distortions caused by sensor motion, ambient conditions, etc.We are primarily interested in small scale changes that occur in a given underwater scene observed at different times. In this paper we describe our use of thin plate splines in registering pairs of digital images composed of millions of pixels. We also review work on selecting and matching the control points needed for image registration.     

A new color image cryptosystem via hyperchaos synchronization

This paper proposes a novel color image cryptosystem based on synchronization of two different six-dimensional hyperchaotic systems. In the transmitter end, we apply the drive system to generate the diffusion matrices and scrambling ones, which are used to change the image pixel value and position, respectively. Thus the ciphered image is obtained. In the receiver, synchronization of two nonidentical hyperchaotic systems can be achieved by designing the appropriate controllers. The response system is employed to yield the corresponding diffusion matrices and scrambling ones using the same generation method in the encryption algorithm. Then the cipher-image can be decrypted by the decryption algorithm, which is similar to that of the encryption process but in the reversed order. The experimental results show that the presented image cryptosystem has high security and can resist noise and crop attacks.