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.     

Edge detection by spherical separation

We describe an optimization-based method for tackling the classic image processing problem known as edge detection and we formulate it in the form of a classification one. The novelty of the approach is in the use of spherical separation as a classification tool in the image processing framework. Spherical separation consists in separating by means of a sphere two given discrete point-sets in a finite dimensional Euclidean space; in our context the two sets are the edge points and the non-edge points, respectively, in the digital representation of a given image. Assuming that the center of the sphere is fixed, the problem reduces to the minimization of a convex and nonsmooth function of just one variable, which can be effectively solved by means of an “ad hoc” bisection method. The results of our experiments on some edge detection benchmark images are provided.     

基于BP神经网络的手写体数字的识别方法研究

对手写体数字的识别问题进行了讨论,提出一种基于BP神经网络的识别方法.从而提高了识别效率.主要就在识别时,数字在图片上的位置和数字本身大小方面做了改进,发现数字在图片上的大小和其在图片上的位置直接影响识别效果.具体做的是,首先提取了图片的轮廓,然后归一化成28×28的图像.这样做,不仅使得图像数字区域大小相同,而且都在图像中心上,使得识别结果变的更加理想化,达到了高识别的目的.另外,选择了容错性较好的BP网络,以200组手写体数字图像作为输入向量,以其他的110组进行识别,效率达到了90%.     

Harmonic analysis on SL(2,ℂ) and projectively adapted pattern representation) and projectively adapted pattern representation

Among all image transforms, the classical (Euclidean) Fourier transform has had the widest range of applications in image processing. Here its projective analogue, given by the double cover groupSL(2, ℂ) of the projective groupPSL(2, ℂ) for patterns, is developed. First, a projectively invariant classification of patterns is constructed in terms of orbits of the groupPSL(2, ℂ) acting on the image plane (with complex coordinates) by linear-fractional transformations. Then,SL(2, ℂ)-harmonic analysis, in the noncompact picture of induced representations, is used to decompose patterns into the components invariant under irreducible representations of the principal series ofSL(2, ℂ). Usefulness in digital image processing problems is studied by providing a camera model in which the action ofSL(2, ℂ) on the complex image plane corresponds to, and exhausts, planar central projections as produced when aerial images of the same scene are taken from different vantage points. The projectively adapted properties of theSL(2, ℂ)-harmonic analysis, as applied to the problems, in image processing, are confirmed by computational tests. Therefore, it should be an important step in developing a system for automated perspective-independent object recognition.     

Complex valued neural network with Möbius activation function

In this work, we propose a new type of activation function for a complex valued neural network (CVNN). This activation function is a special Möbius transformation classified as reflection. It is bounded outside of the unit disk and has partial continuous derivatives but not differentiable since it does not satisfy the Cauchy–Riemann equalities. However, the fixed points set of this function is a circle. Therefore, we employ this function to a specific complex valued Hopfield neural network (CVHNN) and increase the number of fixed points of the CVHNN. Using of this activation function leads us also to guarantee the existence of fixed points of the CVHNN. It is shown that the fixed points are all asymptotically stable states of the CVHNN which indicates that the information capacity is enlarged.     

数码相机定位研究

讨论了数码相机的定位问题,假设针孔镜头成像,根据射影几何的理论建立数学模型．首先,对靶标的像图形进行处理,求出其中每个图形的外切点,通过交比不变性和点的共线理论对所求的外切点进行约束从而得到最优的外切点,最后求出各个圆圆心在像平面的坐标．然后,考虑图形在成像过程中发生的“畸变”,通过空间坐标变换把在像平面局部坐标的分析...     

Blaschke product interpolation and its application to the design of digital filters

A new proof is given thatn distinct points on the unit circle can be mapped inton arbitrary points on the unit circle of the complex plane by a finite Blaschke product. A result of this proof is that the mapping can be done with at mostn?1 factors in the product. The problem is studied in the context of its application to frequency transformations used to design digital filters.     

A fractional partial differential equation based multiscale denoising model for texture image

Traditional integer‐order partial differential equation based image denoising approach can easily lead edge and complex texture detail blur, thus its denoising effect for texture image is always not well. To solve the problem, we propose to implement a fractional partial differential equation (FPDE) based denoising model for texture image by applying a novel mathematical method—fractional calculus to image processing from the view of system evolution. Previous studies show that fractional calculus has some unique properties that it can nonlinearly enhance complex texture detail in digital image processing, which is obvious different with integer‐order differential calculus. The goal of the modeling is to overcome the problems of the existed denoising approaches by utilizing the aforementioned properties of fractional differential calculus. Using classic definition and property of fractional differential calculus, we extend integer‐order steepest descent approach to fractional field to implement fractional steepest descent approach. Then, based on the earlier fractional formulas, a FPDE based multiscale denoising model for texture image is proposed and further analyze optimal parameters value for FPDE based denoising model. The experimental results prove that the ability for preserving high‐frequency edge and complex texture information of the proposed fractional denoising model are obviously superior to traditional integral based algorithms, as for texture detail rich images. Copyright © 2013 John Wiley & Sons, Ltd.     

基于迭代函数系统和编码空间的数字图像置乱方法研究

针对数字图像的安全保密问题 ,本文介绍了一种基于位置空间的数字图像置乱技术 .首先利用伴随于迭代函数系统 ( IFS)的编码空间对数字图像各像素赋予不同编码 ,然后通过对编码的特定置换使各像素位置改变以达到图像置乱的目的 .本文讨论了置乱变换对原图信息分散的规律以及变换的周期性 .理论和实践表明 ,该方法克服了图像信息量大造成的编码上的困难 ,置乱变换后原图的信息按照特定的规律分散开 ,增强了信息隐藏的不可感知性 .     

Displacement Regularization with Application to Image Zooming

We study the problem of displacement errors, i.e. errors induced by a sampling process with distorted locations of the sampling points. Starting with a non-convex regularization method, we apply a semi-group concept and derive a partial differential equation, which allows for correcting displacement errors. As main application for correction of displacement errors we consider image interpolation, in particular zooming, of digital color images. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An Interactive Icon Index: Images of the Outer Planets

Abstract

We are interested in the exploratory analysis of large collections of complex objects. As an example, we are studying a large collection of digital images that has nearly 30,000 members. We regard each image in the collection as an individual observation. To facilitate our study we construct an index of the images in the collection. The index uses a small copy of each image (an icon or a “thumbnail”) to represent the full-size version. A large number of these thumbnails are laid out in a workstation window. We can interactively arrange and rearrange the thumbnails within the window. For example, we can sort the thumbnails by the values of a function computed from them or by the values of data associated with each of them. By the use of specialized equipment (a single-frame video disk recorder/player), we can instantly access any individual full-size image in the collection as a video image. We regard our software as an early development of statistical exploratory tools for studying collections of images and other complex objects in the same way we routinely study batches of numbers. We expect that the concept of a visual index will extend to other collections of complex objects besides images, for example, time series, functions, and text.     

Digital topological method for computing genus and the Betti numbers

This paper concerns with computation of topological invariants such as genus and the Betti numbers. We design a linear time algorithm that determines such invariants for digital spaces in 3D. These computations could have applications in medical imaging as they can be used to identify patterns in 3D image.Our method is based on cubical images with direct adjacency, also called (6,26)-connectivity images in discrete geometry. There are only six types of local surface points in such a digital surface. Two mathematical ingredients are used. First, we use the Gauss-Bonnett Theorem in differential geometry to determine the genus of 2-dimensional digital surfaces. This is done by counting the contribution for each of the six types of local surface points. The new formula derived in this paper that calculates genus is g=1+(|M₅|+2⋅|M₆|−|M₃|)/8 where Mi indicates the set of surface-points each of which has i adjacent points on the surface. Second, we apply the Alexander duality to express the homology groups of a 3D manifold in the usual 3D space in terms of the homology groups of its boundary surface.While our result is stated for digital spaces, the same idea can be applied to simplicial complexes in 3D or more general cell complexes.     

Dynamical Analysis and Control Strategies of Rumor Spreading Models in Both Homogeneous and Heterogeneous Networks

In recent years, rumor propagation in social networks attracts more researchers’ attention. In this paper, we have established I2S2R rumor spreading models in both homogeneous networks and heterogeneous networks considering the effect of time delay. In the homogeneous network model, we obtain the basic reproduction number by means of the next-generation matrix. Besides, the local stability and the global stability of the equilibrium points are discussed by linearization approach of nonlinear systems and Lyapunov function. In the heterogeneous network model, we calculate the basic reproduction number through algebraic method. In addition, Lyapunov functional method and Lasalle invariance principle are applied to study the stability of equilibrium points in the complex network model. Further, we put forward some useful strategies to control the spreading of rumor based on the complex network theory. Finally, we take advantage of numerical simulations to verify the theory above and come up with necessary conclusions.

     

基于PGH矩改进SURF算法的工业散料识别研究

针对工业散料识别过程中图像特征匹配率低的问题,提出一种基于PGH矩的改进SURF图像匹配算法.首先,研究Gaussian-Hermite矩,将其扩展到复数空间中,推导出Polar-Gaussian-Hermite矩;其次,利用升降算符法计算图像PolarGaussian-Hermite矩,获得新的特征向量;最后,将原始图像提取的特征点和模板图像进行准确匹配得到最优匹配结果.实验结果表明算法能够解决缩放、旋转和曝光情况下工件匹配问题,误匹配率8%左右,满足工业散料识别系统的准确性和实时性要求.     

Theory of viscoelastic behavior of regular polymeric networks with stable points linking four chains

A regular stable network formed by flexible macromolecules connected into four functional points is considered. Each point of the network is acted on by the elastic forces from neighbors, by the force of viscous resistances, proportional to the relative velocity of the point, and by the effective force of Brownian movement. The kinetic equation is written for the network points in the case of deformation, and the moments of the second-order distribution function are calculated. The relaxation times of the system are found, and the behavior of the network in the presence of homogeneous sinusoidal deformation due to extension and shear is discussed. The complex modulus of elasticity of the network is calculated as a function of the network parameters and frequency.Branch of the Institute of Chemical Physics, Academy of Sciences of the USSR, Moscow Region. Translated from Mekhanika Polimerov, No. 2, pp. 209–216, March–April, 1970.     

Digital contracts-driven method for pricing complex derivatives

In this paper, we propose a hybrid method of nonparametric and parametric methods, that is a digital contracts-driven (DCD) method, for pricing various complex options. Differing from general nonparametric data-driven methods, in which usually the observed data are used as training data directly, in the DCD method the European-style digital contracts of the underlying assets are used as basic inputs for a learning network. The digital contracts calculated from the observed data based upon the parametric method are used as hints in the learning process, and then enable the DCD method to have superior pricing accuracy to the common data-driven method in practical applications. Some Monte Carlo simulation experiments are performed and the results demonstrate that the proposed hybrid method not only has the advantages of generality and superior accuracy as the nonparametric method, but also the robust property to financial data with noise as the parametric method.     

基于微分算子的边缘检测法在基因芯片图像识别中的应用

一种基于梯度算子和拉普拉斯算子检测医学基因芯片荧光数字图像边缘的方法．数字图像经过图像增强等预处理以后，突出了我们感兴趣的数字图像特征，根据数字图像灰度变化的趋势，用灰度变化的一阶导数(梯度算子)检测图象中的边缘区域；用灰度变化的二阶导数确定图像边缘的中心位置．最后根据某些预定的准则把满足这些准则的象素组成一条边缘．     

一类输出耦合混沌复杂动态网络不稳定平衡点的控制

研究节点输出耦合混沌复杂动态网络不稳定平衡点的控制问题,基于输出控制思想,提出网络节点不稳定平衡点的全局控制方法以及牵制控制方法,将混沌复杂动态网络的所有节点镇定到其平衡点.利用李稚普诺夫稳定性理论,得到控制器参数选择条件,以蔡氏混沌电路作为网络节点动态进行仿真研究,证明该方法的有效性.     

The Genus of a Digital Image Boundary Is Determined by Its Foreground,Background, and Reeb Graphs

We prove that the genus of the boundary of a digital image is precisely half of the sum of the cycle ranks of three particular graphs: the "foreground graph" and "background graph," which capture topological information about the digital image and its complement, respectively, and the Reeb graph, relative to the natural height function, associated with the digital image's boundary. We prove several additional results, including a characterization of when the cycle rank of the Reeb graph fails to equal the genus of the digital image's boundary (which can happen by virtue of the failure of the natural height function on the boundary of the digital image to be a Morse function).