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On satellite image segmentation via piecewise constant approximation of selective smoothed target mapping

APPLIED MATHEMATICS AND COMPUTATION 2021年 389卷 125615-125615页

作者： Hnatushenko, Volodymyr V. Kogut, Peter, I Uvarov, Mykola, V Dnipro Univ Technol Dept Informat Syst & Technol Av Dmytra Yavornytskoho 19 UA-49005 Dnipro Ukraine EOS Data Analyt Ukraine Gagarin Av 103a Dnipro Ukraine Oles Honchar Dnipro Natl Univ Dept Differential Equat Gagarin Av 72 UA-49010 Dnipro Ukraine EOS Data Analyt Ukraine Desyatynny Lane 5 UA-01001 Kiev Ukraine

Mostly motivated by the crop field classification problem and the automated computational methodology for the extraction of agricultural fields with a uniform crop distribution from satellite data, we propose an indirect approach for the image segmentation which is based on the concept of a piecewise constant approximation of the slope-based vegetation indices. We discuss in detail the consistency of the new statement of segmentation problem and its solvability. We mainly focus on the rigor mathematical substantiation of the proposed approach, deriving the corresponding optimality conditions, and we show that the new optimization problem is rather a flexible and powerful model of variational image segmentation problems. We illustrate the efficiency of the proposed algorithm by numerical experiences with images that have been delivered by satellite Sentinel-2. (C) 2020 Elsevier Inc. All rights reserved.

关键词： Optimal segmentation problem piecewise constant approximation Optimality conditions Existence result

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Quantitative security analysis of a dynamic network system under lateral movement-based attacks

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RELIABILITY ENGINEERING & SYSTEM SAFETY 2019年第Mar.期183卷 213-225页

作者： Yu, Shi Chang Xiaolin Rodriguez, Ricardo J. Zhang Zhenjiang Trivedi, Kishor S. Beijing Jiaotong Univ Beijing Key Lab Secur & Privacy Intelligent Trans Beijing Peoples R China Acad Gen Mil Ctr Univ Def Zaragoza Spain Beijing Jiaotong Univ Sch Elect & Informat Engn Beijing Peoples R China Duke Univ Durham NC 27708 USA

Malicious lateral movement-based attacks have become a potential risk for many systems, bringing highly likely threats to critical infrastructures and national security. When launching this kind of attacks, adversaries first compromise a fraction of the targeted system and then move laterally to the rest of the system until the whole system is infected. Various approaches were proposed to study and/or defend against lateral movement-based attacks. However, few of them studied transient behaviors of dynamic attacking and dynamic targeted systems. This paper aims to analyze the transient security of a dynamic network system under lateral movement-based attacks from the time that attack-related abnormity in the system is detected until mechanisms are designed and deployed to defend against attacks. We explore state-space modeling techniques to construct a survivability model for quantitative analysis. A phased piecewise constant approximation approach is also proposed to derive the formulas for calculating model state transient probabilities, with which we derive formulas for calculating metrics of interest. The proposed approach allows both model state transition rates and the number of model states to be time-varying during the system recovery. Numerical analysis is carried out for investigating the impact of various dynamic system parameters on system security.

关键词： Lateral movement-based attack Dynamic transient analysis Non-homogeneous continuous-time Markov chain piecewise constant approximation

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Comparison principle and stability of differential equations with piecewise constant arguments

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JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS 2013年第2期350卷 211-230页

作者： Alwan, Mohamad S. Liu, Xinzhi Xie, Wei-Chau Univ Waterloo Dept Appl Math Waterloo ON N2L 3G1 Canada Univ Waterloo Dept Civil & Environm Engn Waterloo ON N2L 3G1 Canada

This Paper studies systems of nonlinear differential equations with piecewise constant arguments (EPCA). We develop a comparison principle for this system. Then, this result is used to establish some stability properties of the system. As for the stability results we employ the Lyapunov function approach. We also show that the piecewise (constant) arguments can play as a stabilizing role in some cases where the underlying systems are unstable. A class of linear retarded EPCA are also considered in this paper. Numerical examples and an application to a single-species logistic growth model with density-dependence harvesting are given to show the effectiveness of our theoretical results. (C) 2012 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

关键词： DIFFERENTIAL equations STABILITY theory piecewise constant approximation LYAPUNOV functions NONLINEAR differential equations -- Numerical solutions COMPARATIVE studies

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Development of a Novel Continuum Robotic System for Maxillary Sinus Surgery

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IEEE-ASME TRANSACTIONS ON MECHATRONICS 2018年第3期23卷 1226-1237页

作者： Hong, Wuzhou Xie, Le Liu, Jiahui Sun, Yajing Li, Keyong Wang, Hesheng Shanghai Jiao Tong Univ Inst Forming Technol & Equipment Shanghai 200030 Peoples R China Shanghai Jiao Tong Univ Inst Rehabil Engn Shanghai 200030 Peoples R China Shanghai Jiao Tong Univ Shanghai Gen Hosp Dept Otorhinolaryngol Head & Neck Surg Sch Med Shanghai Peoples R China Shanghai Jiao Tong Univ Dept Automat Shanghai 200240 Peoples R China

Lesions in the maxillary sinus area are usually treated with endoscopic interventional surgery. However, target lesions are often hardly accessible with conventional surgical tools. A new continuum module is proposed with a bending manipulator to perform maxillary sinus surgery. The developed manipulator has a NiTiNol tube embedded in its continuum module. It has a diameter of 4 mm and can be bent up to 270 degrees to reach the target position flexibly. In this paper, a kinematic model of the continuum module is presented. An external loading analysis of the robot was formulated to analyze payload capacity and tensions, by taking into account friction, actuation, elastic effects, and external loadings. Some experiments were carried out to validate the kinematics and to test the robot capabilities of scissoring, payload, and manipulation.

关键词： Dexterous manipulators flexible structures piecewise constant approximation robot kinematics

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Transient performance analysis of smart grid with dynamic power distribution

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INFORMATION SCIENCES 2018年 422卷 98-109页

作者： Chang, Xiaolin Martinez, Jose M. Trivedi, Kishor S. Beijing Jiaotong Univ Beijing Key Lab Secur & Privacy Intelligent Trans Beijing Peoples R China Beijing Jiaotong Univ Sch Comp & Informat Technol Beijing Peoples R China Duke Univ Dept Elect & Comp Engn Durham NC USA

Transient performance analysis of power distribution network (PDN) after a failure occurrence could facilitate the better design of smart grid. Researchers have proposed analytical models and the numerical solutions to analyze the PDN's transient behaviors by applying homogeneous continuous-time Markov chain (CTMC). However, the PDN system may be time-varying during a failure recovery. Then, the system restoration process evolves as a non-homogeneous CTMC (NHCTMC) on a finite state space. This paper seeks to analyze the transient performance of such a time-varying system from a failure occurrence until the system's full restoration. This restoration process consists of multiple phases which are sequential or in parallel. We apply piecewise constant approximation method to derive the formulas for computing state transient probabilities and then derive the computation formulas for the metrics of interest. A case study is conducted to apply the proposed approach to analyze the transient performance of a simple distribution automation network. This network was derived from a real power distribution network. (C) 2017 Elsevier Inc. All rights reserved.

关键词： Non-homogeneous continuous time Markov Chain Smart grid Transient analysis piecewise constant approximation

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A new active contour remote sensing river image segmentation algorithm inspired from the cross entropy

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DIGITAL SIGNAL PROCESSING 2016年 48卷 322-332页

作者： Song Yu Wu Yiquan Dai Yimian Nanjing Univ Aeronaut & Astronaut Sch Elect & Informat Engn Nanjing 210016 Jiangsu Peoples R China Minist Water Resources Yellow River Sediment Key Lab Zhenzhou 450003 Peoples R China Yangtse River Water Conservancy Comm Key Lab Rivers & Lakes Governance & Flood Protect Wuhan 430010 Peoples R China State Key Lab Urban Water Resource & Environm Harbin 150090 Peoples R China

The CV (Chan-Vese) model is a piecewise constant approximation of the Mumford and Shah model. It assumes that the original image can be segmented into two regions such that each region can be represented as constant grayscale value. In fact, the objective functional of the CV model actually finds a segmentation of the image such that the within-class variance is minimized. This is equivalent to the Otsu image thresholding algorithm which also aims to minimize the within-class variance. Similarly to the Otsu image thresholding algorithm, cross entropy is another widely used image thresholding algorithm and it finds a segmentation such that the cross entropy of the segmented image and the original image is minimized. Inspired from the cross entropy, a new active contour image segmentation algorithm is proposed. The region term in the new objective functional is the integral of the logarithm of the ratio between the grayscale of the original image and the mean value computed from the segmented image weighted by the grayscale of the original image. The new objective functional can be solved by the level set evolution method. A distance regularized term is added to the level set evolution equation so the level set need not be reinitialized periodically. A fast global minimization algorithm of the objective functional is also proposed which incorporates the edge term originated from the geodesic active contour model. Experimental results show that, the algorithm proposed can segment images more accurately than the CV model and the implementation speed of the fast global minimization algorithm is fast. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Image segmentation piecewise constant approximation CV model Minimum within-class variance Cross entropy Distance regularized term

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Numerical analysis of the factorization method for EIT with a piecewise constant uncertain background

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INVERSE PROBLEMS 2013年第6期29卷 065009-065037页

作者： Haddar, Houssem Migliorati, Giovanni INRIA Saclay Ile France F-91128 Palaiseau France Ecole Polytech CMAP F-91128 Palaiseau France Politecn Milan Dipartimento Matemat I-20133 Milan Italy

We extend the factorization method for electrical impedance tomography to the case of background featuring uncertainty. We first describe the algorithm for the known but inhomogeneous backgrounds and indicate expected accuracy from the inversion method through some numerical tests. Then we develop three methodologies to apply the factorization method to the more difficult case of a piecewise constant but uncertain background. The first one is based on a recovery of the background through an optimization scheme and is well adapted to relatively low-dimensional random variables describing the background. The second one is based on a weighted combination of the indicator functions provided by the factorization method for different realizations of the random variables describing the uncertain background. We show through numerical experiments that this procedure is well suited to the case where many realizations of the measurement operators are available. The third strategy is a variant of the previous one when measurements for the inclusion-free background are available. In this case, a single pair ofmeasurements is sufficient to achieve comparable accuracy to the deterministic case.

关键词： FACTORIZATION (Mathematics) RESEARCH NUMERICAL analysis ELECTRICAL impedance tomography piecewise constant approximation DETERMINISTIC algorithms

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Computing the L_∞-induced norm of linear time-invariant systems via Kernel approximation and its comparison with input approximation

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IET CONTROL THEORY AND APPLICATIONS 2015年第5期9卷 700-709页

作者： Kim, Jung Hoon Hagiwara, Tomomichi Kyoto Univ Dept Elect Engn Nishikyo Ku Kyoto 6158510 Japan

This study deals with the L-1 analysis of stable finite-dimensional linear time-invariant (LTI) systems, by which the authors mean the computation of the L-infinity-induced norm of these systems. To compute this norm, they need to integrate the absolute value of the impulse response of the given system, which corresponds to the kernel function in the convolution formula for the input/output relation. However, it is very difficult to compute this integral exactly or even approximately with an explicit upper bound and lower bound. They first review an approach named input approximation, in which the input of the LTI system is approximated by a staircase or piecewise linear function and computation methods for an upper bound and lower bound of the L-infinity-induced norm are given. They further develop another approach using an idea of kernel approximation, in which the kernel function in the convolution is approximated by a staircase or piecewise linear function. These approaches are introduced through fast-lifting, by which the interval [0, h) with a sufficiently large h is divided into M subintervals with an equal width. It is then shown that the approximation errors in staircase or piecewise linear approximation are ensured to be reciprocally proportional to M or M-2, respectively. The effectiveness of the proposed methods is demonstrated through numerical examples.

关键词： LINEAR time invariant systems RESEARCH KERNEL functions piecewise constant approximation CONVOLUTIONS (Mathematics) LINEAR systems

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A scalable dynamic programming scheme for the computation of optimal k-segments for ordered data

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INFORMATION SYSTEMS 2017年 70卷 2-17页

作者： Mahlknecht, Giovanni Dignos, Anton Gamper, Johann Free Univ Bozen Bolzano Fac Comp Sci Bolzano Italy

The optimal k-segments of an ordered dataset of size n consists of k tuples that are obtained by merging consecutive tuples such that a given error metric is minimized. The problem is general and has been studied in various flavors, e.g., piecewise-constant approximation, parsimonious temporal aggregation, and v-optimal histograms. A well-known computation scheme for the optimal k-segments is based on dynamic programming, which computes a k x n error matrix E and a corresponding split point matrix J of the same size. This yields O(n.k) space and O(n(2).k) runtime complexity. In this paper, we propose three optimization techniques for the runtime complexity and one for the space complexity. First, diagonal pruning identifies regions of the error matrix E that need not to be computed since they cannot lead to a valid solution. Second, for those cells in E that are computed, we provide a heuristic to determine a better seed value, which in turn leads to a tighter lower bound for the potential split points to be considered for the calculation of the minimal error. Third, we show how the algorithm can be effectively parallelized. The space complexity is dominated by the split point matrix J, which needs to be kept till the end. To tackle this problem, we replace the split point matrix by a dynamic split point graph, which eliminates entries that are not needed to retrieve the optimal solution. A detailed experimental evaluation shows the effectiveness of the proposed solutions. Our optimization techniques significantly improve the runtime of state-of-the-art matrix implementations, and they guarantee a comparable performance of an implementation that uses the split point graph. The split point graph reduces the memory consumption up to two orders of magnitude and allows us to process large datasets for which the memory explodes if the matrix is used. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Optimal k-segments Dynamic programming Parsimonious temporal aggregation piecewise constant approximation v-optimal histograms Data approximation

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approximations with piecewise constant fluxes for diffusion equations on polyhedral meshes: algorithms and applications

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RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING 2012年第4期27卷 339-368页

作者： Boyarkin, O. Kikinzon, E. Kuznetsov, Yu. A. Prokopenko, A. Univ Augsburg Inst Math D-86135 Augsburg Germany Univ Houston Dept Math Houston TX 77204 USA

In this paper we consider implementation algorithms and applications of the discretization method for diffusion equations on polygonal (2D) and polyhedral (3D) meshes recently proposed by one of the authors in [11]. The discretization method is based on the approximation of fluxes in the mixed finite element method by appropriate piecewise constant vector functions inside the mesh cells. The new piecewise constant fluxes are discontinuous inside the mesh cells but their normal components are continuous on the interfaces between neighbouring cells. Numerical results are given for test problems relevant to applications in reservoir simulation and basin modelling.

关键词： approximation theory piecewise constant approximation BURGERS' equation POLYHEDRAL functions COMPUTER algorithms NUMERICAL analysis

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