Viscosity solutions for geodesic active contour under geometrical conditions

This paper addresses the issue of introducing geometrical constraints into segmentation processes in image analysis. This question has emerged from the analysis of classical tools: indeed, usual methods such as deformable models, fast marching prove to be fruitless when image data are missing or of poor quality or when the image owns homogeneous-textured regions. To cope with these hindrances, the idea developed hereafter consists of integrating geometrical constraints in the modelling to make the segmentation process easier to handle.

We have devised a geodesic active contour-based model, in which we are trying to determine a curve that best approaches the given points (geometrical data) while detecting the object under consideration (see also Apparato et al., Segmentation of medical image sequence under constraints: application to non-invasive assessment of pulmonary arterial hypertension, Int. J. Comput. Math. 5(2004), pp. 527–536 and Gout and Vieira-Testé C. Gout and S. Vieira-Testé, An algorithm for segmentation under interpolation conditions using deformable models, Int. J. Comput. Math. 80(1) (2003), pp. 47–54 where other approaches are given for this kind of problems). In this paper the main results concern the study of the existence and uniqueness of the viscosity solution of this problem (following three different approaches). We also give numerical examples on real data sets.     

由影调恢复物体外形的唯一性

研究了当投射的平行光垂直于图像平面时图像以及成像物体区域内部的几何特性 与边界特性,讨论了由一般物体所成的像唯一地求解SFS问题的条件,并由此提出了一个更 为一般的整体区域上的唯一性定理和局部不唯一定理,推广了本领域现有的研究结果.定理 的证明以微分几何和常微分方程几何理论为工具,其过程是构造性的,亦即在定理证明的同 时指明了由单目图像恢复物体外形且不使用正则化技术的可能途径.     

An optimal control model for a system of degenerate parabolic integro-differential equations

An initial-boundary-value problem for a system of degenerate parabolic integro-differential equations is considered. The sufficient conditions for the existence and uniqueness of its generalized solution and for the existence of at least one optimal control for a given performance functional are obtained. A stable numerical solution to the initial-boundary-value problem is derived for a locally one-dimensional case and conditions are formulated for constructing a stable numerical algorithm of the optimal control problem on a class of piecewise-smooth control functions. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 90–102, November–December 2007.     

Solving the Wiener-Hopf equation with a probabilistic kernel

Inhomogeneous Wiener-Hopf equations on a halfline with probabilistic kernels are considered. They are analyzed using the theory of isotonic and contraction operators. Necessary and sufficient conditions of existence and general sufficient conditions of uniqueness for the solutions of these equations are established. The conditions for and the rate of convergence of successive approximations of the solution are found. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 39–47, March–April 2006.     

A feature-oriented forward–backward diffusion model for intensity image restoration based on level set motion

In this paper, a new enhancing and smoothing partial differential equation coupled with time-delay regularization is presented, which is based on local geometric properties desired for image restoration. To reverse the process of image deterioration, a newly defined shock filter for edge enhancing is combined with a level set motion-based regularization equation. The balance between the backward process and the forward process is carried out by a weighting function coupled with time-delay regularization helping to identify boundary areas and homogeneous regions in a given image. The proposed model is well-posed in terms of viscosity solutions – the existence and uniqueness of periodic viscosity solution to the initial value problem of the equation is established. Numerical results for some kinds of grey-level images are demonstrated to confirm our anticipation.     

The method of successive approximation applied to find the probability for an insurance company with random premiums

A risk process that describes the evolution of the capital of an insurance company is analyzed, random premiums and claims being available. Integral equations of nonbankruptcy probability as a function of the initial capital are derived. Necessary and sufficient conditions for the existence and uniqueness of solutions of these integral equations, and convergence conditions for the method of successive approximation for finding their solutions are established __________ Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 112–127, January–February 2006.     

基于熵和独特性的角点提取算法

针对角点提取在图像配准中的应用,利用图像窗口的互相关系数定义了邻域窗口的独特性,提出一种基于熵和独特性的角点提取算法.算法首先通过Canny算子提取图像边缘,然后通过计算边缘点所在圆形邻域的熵和独特性筛选出角点,并通过不断修正剩余候选角点的独特性达到输出角点分散分布的目的.通过与Harris算法及区域特征提取的Sift算法实验对比,表明该算法能够对角点准确提取、精确定位,具有较好的抗噪性和方向无关性,且提取的角点分散分布,尤其适用于图像配准,其局限性在于不具有尺度不变性.     

Necessary and sufficient conditions of existence and uniqueness of solutions to integral equations of actuarial mathematics

Necessary and sufficient conditions of existence and uniqueness of solutions of integral equations are established for ruin probability as a function of the initial capital of an insurance company. Several sufficient conditions and correctness conditions of the problem of finding ruin probability are also established. A general method of successive approximations for solution of this problem is substantiated. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 157–164, September–October 2006.     

Stabilization of discrete‐time singular Markovian jump repeated vector nonlinear systems

This paper studies the control problem for discrete‐time singular Markovian jump systems with repeated vector nonlinearities. Sufficient conditions for stochastic stability are established, where the uniqueness of solution to the underlying system is also guaranteed. Then, a series of formulations of stabilizing conditions is further developed to design mode‐dependent and mode‐independent controllers by using the linear matrix inequality approach. Based on the proposed results, more special cases for stabilizing controller are considered. Finally, numerical examples are used to demonstrate the effectiveness and superiority of the proposed methods. Copyright © 2015 John Wiley & Sons, Ltd.     

On Robust Exponential Periodicity of Interval Neural Networks with Delays

In this Letter, based on globally Lipschitz continous activation functions, new conditions ensuring existence, uniqueness and global robust exponential stability of the periodic solution of interval-delayed neural networks with periodic input are obtained. All the results obtained are generalizations of some resent results reported in the literature for neural networks with constant input.     

Optimal worst case estimation for LPV–FIR models with bounded errors

This work presents an approximate solution method for the infinite-time nonlinear quadratic optimal control problem. The method is applicable to a large class of nonlinear systems and involves solving a Riccati equation and a series of algebraic equations. The conditions for uniqueness and stability of the resulting feedback policy are established. It is shown that the proposed approximation method is useful in determining the region in which the constrained and unconstrained optimal control problems are identical. A reactor control problem is used to illustrate the method.     

Existence and numerical simulation of solutions for nonlinear fractional pantograph equations

In this paper a method based on Sinc approximation is developed for the numerical solution of a nonlinear fractional pantograph equation. In order to use Sinc approximation, the problem needs to have an analytic solution. So we investigated the existence and uniqueness of analytic solutions in the proposed domain. Single and double exponential transformations are used to approximate the solution. Some test problems are given to demonstrate the efficiency and applicability of the methods. The results are compared with some other existing numerical methods to show the performance and good accuracy of the methods. The numerical orders of convergence show that the method has exponential rate of convergence.     

On the existence,uniqueness and nature of Carathéodory and Filippov solutions for bimodal piecewise affine dynamical systems

In this paper, we deal with the well-posedness (in the sense of existence and uniqueness of solutions) and nature of solutions for discontinuous bimodal piecewise affine systems in a differential inclusion setting. First, we show that the conditions guaranteeing uniqueness of Filippov solutions in the context of general differential inclusions are quite restrictive when applied to bimodal piecewise affine systems. Later, we present a set of necessary and sufficient conditions for uniqueness of Filippov solutions for bimodal piecewise affine systems. We also study the so-called Zeno behavior (possibility of infinitely many switchings within a finite time interval) for Filippov solutions.     

Analysis of systems of singular ordinary differential equations

Systems of ordinary differential equations with a small parameter at the derivative and specific features of the construction of their periodic solution are considered. Sufficient conditions of existence and uniqueness of the periodic solution are presented. An iterative procedure of construction of the steady-state solution of a system of differential equations with a small parameter at the derivative is proposed. This procedure is reduced to the solution of a system of nonlinear algebraic equations and does not involve the integration of the system of differential equations. Problems of numerical calculation of the solution are considered based on the procedure proposed. Some sources of its divergence are found, and the sufficient conditions of its convergence are obtained. The results of numerical experiments are presented and compared with theoretical ones. Translated from Kibemetika i Sistemnyi Analiz, No. 5, pp. 103–110, September–October, 1999.     

Impossible and ambiguous shading patterns

A smooth object depicted in a monochrome image will often exhibit brightness variation, or shading. A problem much studied in computer vision has been that of how object shape may be recovered from image shading. When the imaging conditions are such that an overhead point-source illuminates a smooth Lambertian surface, the problem may be formulated as that of finding a solution to an eikonal equation. This article will focus on the existence and uniqueness of such solutions, reporting recent results obtained. With regard to existence, shading patterns are exhibited for which there is no corresponding object shape. Specifically, a necessary and sufficient condition is presented for a circularly symmetric eikonal equation to admit exclusively unbounded solutions; additionally, a sufficient condition is given for an eikonal equation to have no solution whatsoever. In connection with uniqueness, we consider eikonal equations, defined over a disc, such that the Euclidean norm of the gradient of any solution is circularly symmetric, vanishes exactly at the disc center, and diverges to infinity as the circumference of the disc is approached. Contrary to earlier influential work, a class of such eikonal equations is shown to possess simultaneously circularly symmetric and noncircularly symmetric bounded smooth solutions.     

Positive solutions of operator equations on ordered Banach spaces and applications

This paper is concerned with an operator equation on ordered Banach spaces. The existence and uniqueness of its’ positive solutions is obtained by using the properties of cones and monotone iterative technique. As applications, we utilize the results obtained in this paper to study the existence and uniqueness of positive solutions for two classes of integral equations.     

基于最佳正弦伪随机序列的数字水印技术

论文提出了一种新的具有一定扩充性,以最佳正弦伪随机序列为水印信号的公开数字水印算法。论文先讨论了水印信号设计上应注意的问题;然后描述了最佳正弦伪随机序列的创建方法和性质;并提出了根据水印信号自身良好的自相关特性设计的水印算法;最后对算法进行抗攻击试验并对算法本身进行了简单的讨论。采用最佳正弦伪随机序列为水印信号,保证了水印信号自身具有很高的隐蔽性和信号的唯一性;同时还保证了信号具有很强的抗干扰能力。实验证明该水印算法对于噪声干扰和各种常规图像处理具有良好的鲁棒性。     

基于SIFT二次匹配方法的同名像点识别

将尺度不变特征变换（SIFT）二次匹配方法用于IRS-P5立体像对的同名像点识别。引入全局几何约束与唯一性约束,剔除误匹配,获取用于初始定位的匹配样本,完成初始匹配。根据初始定位点,获取小区域子图像,在小区域内调整SIFT匹配阈值,在唯一性约束基础上,引入偏移坐标差值约束,完成二次匹配。通过实验验证,相比于将SIFT算法直接应用于遥感影像同名像点识别,SIFT特征二次匹配算法在严格阈值下,匹配对数可增长23.07倍,可获取更密集可靠的同名像点。