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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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The generalized H2 controller synthesis problem of sampled-data systems

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AUTOMATICA 2022年 142卷

作者： Kim, Jung Hoon Hagiwara, Tomomichi Pohang Univ Sci & Technol POSTECH Dept Elect Engn Pohang 37673 South Korea Yonsei Univ Inst Convergence & Educ Technol Incheon 21893 South Korea Kyoto Univ Dept Elect Engn Kyoto 6158510 Japan

This paper tackles the generalized H-2 controller synthesis problem of sampled-data systems, which is associated with the controller minimizing the induced norm from L-2 to L-infinity. To alleviate the difficulty of the linear periodically time-varying (LPTV) nature of sampled-data systems, we first take an operatorbased approach to sampled-data systems via the lifting treatment. We next develop a framework for piecewise constant approximation in the context of the generalized H-2 controller synthesis problem after further applying the so-called fast-lifting treatment. An optimal controller for the approximate treatment is also shown to achieve the generalized H-2 performance for the sampled-data system that is close enough to its optimal generalized H-2 performance, if the fast-lifting parameter N is large enough. This is established by deriving, in a fashion suitable for controller synthesis, upper and lower bounds on the resulting sampled-data generalized H-2 performance, where their gap tends to 0 at the rate of 1/N. We further introduce a discretization method of the continuous-time plant, with which the controller synthesis in the approximate fashion can actually be carried out through an equivalent discrete-time counterpart of the generalized H-2 controller synthesis problem. Finally, numerical examples are given to validate the overall arguments. (C) 2022 Elsevier Ltd. All rights reserved.

关键词： Sampled-data systems Generalized H-2 norms Operator approximation piecewise constant approximation

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Optimal approximation order of piecewise constants on convex partitions

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JOURNAL OF COMPLEXITY 2020年 58卷 101444-101444页

作者： Davydov, Oleg Kozynenko, Oleksandr Skorokhodov, Dmytro Justus Liebig Univ Dept Math Arndtstr 2 D-35392 Giessen Germany Oles Honchar Dnipro Natl Univ Dept Mech & Math Pr Gagarina 72 UA-49010 Dnipro Ukraine

We prove that the error of the best nonlinear L-p-approximation by piecewise constants on convex partitions is O(N-2d+1), where N is the number of cells, for all functions in the Sobolev space W-q(2) (Omega) on a cube Omega subset of R-d, d >= 2, as soon as 2/d+1 + 1p - 1q >= 0. The approximation order O (N-2d+1) is achieved on a polyhedral partition obtained by anisotropic refinement of an adaptive dyadic partition. Further estimates of the approximation order from the above and below are given for various Sobolev and Sobolev-Slobodeckij spaces W-q(r) (Omega) embedded in L-p(Omega), some of which also improve the standard estimate O(N-1d) known to be optimal on isotropic partitions. (C) 2019 Elsevier Inc. All rights reserved.

关键词： piecewise constant approximation Nonlinear approximation Saturation order Sobolev space Sobolev-Slobodeckij space Anisotropic partitions

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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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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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Finite element approximations for second-order stochastic differential equation driven by fractional Brownian motion

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IMA JOURNAL OF NUMERICAL ANALYSIS 2018年第1期38卷 184-197页

作者： Cao, Yanzhao Hong, Jialin Liu, Zhihui Auburn Univ Dept Math & Stat Auburn AL 36849 USA Chinese Acad Sci Acad Math & Syst Sci Beijing 100190 Peoples R China

We consider finite element approximations for a one-dimensional second-order stochastic differential equation of boundary value type driven by a fractional Brownian motion with Hurst index H <= 1/2. We make use of a sequence of approximate solutions with the fractional noise replaced by its piecewise constant approximations to construct the finite element approximations for the equation. The error estimate of the approximations is derived through rigorous convergence analysis.

关键词： stochastic differential equation of boundary value type fractional Brownian motion piecewise constant approximation finite element approximation

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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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Image Segmentation Improvement by Reversible Segment Merging

Image Segmentation Improvement by Reversible Segment Merging

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International Conference on Soft Computing and its Engineering Applications (icSoftComp)

作者： Khanykov, Igor G. Kharinov, Mikhail V. Patel, Chirag RAS Inst Informat & Automat Appl Informat Lab 3914th Line St Petersburg 199178 Russia Smt Chandaben Mohanbhai Patel Inst Comp Applicat Fac Comp Sci & Applicat Changa 388421 Gujarat India

ISBN: (纸本)9781538620533

The paper focuses on image segmentation by means of approaching by piecewise-constant approximations. The objective is the improvement of the segmented image, expressed in the noticeable drop of image approximation error (total squared error). The proposed method involves segment dividing into two in some image part and merge of a pair of adjacent segments in another image part, keeping a total segment number constant. For further enhancement of the segmentation, the proposed method is used in combination with advanced K-means method. The steep decline of the approximation error is provided along with obvious increase of perceptual quality of image segmentation. The effect is achieved owing to binary adaptive hierarchy of nested segments, generated for each segment. The segmentation improvement method is usable for the advancement of the computer vision systems using conventional segmentation by partitioning image into connected segments.

关键词： image segments piecewise constant approximation segmentation quality estimation standard deviation reversible computing

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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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