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Discrete Fractional Calculus

Discrete Fractional Calculus Author Piotr Ostalczyk
ISBN-10 9789814725682
Release 2015-11-26
Pages 356
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The main subject of the monograph is the fractional calculus in the discrete version. The volume is divided into three main parts. Part one contains a theoretical introduction to the classical and fractional-order discrete calculus where the fundamental role is played by the backward difference and sum. In the second part, selected applications of the discrete fractional calculus in the discrete system control theory are presented. In the discrete system identification, analysis and synthesis, one can consider integer or fractional models based on the fractional-order difference equations. The third part of the book is devoted to digital image processing. Contents:Discrete-Variable Real FunctionsThe n-th Order Backward Difference/Sum of the Discrete-Variable FunctionFractional-Order Backward Differ-SumThe FOBD-S Graphical InterpretationThe FOBD/S Selected PropertiesThe FO Dynamic System DescriptionLinear FO System AnalysisThe Linear FO Discrete-Time Fundamental ElementsFO Discrete-Time System StructuresFractional Discrete-Time PID ControllerFOS Approximation ProblemsFractional PotentialFO Image Filtering and Edge DetectionAppendix A: Selected Linear Algebra Formulae and Discrete-Variable Special Functions Readership: Researchers, academics, professionals and graduate students in pattern recognition/image analysis, robotics and automated systems, systems engineering and mathematical modeling. Keywords:Fractional Calculus;Fractional-Order Backward-Difference;Fractional-Order Linear Difference Equation;Discrete-System;State-Space Equations



Non Integer Order Calculus and its Applications

Non Integer Order Calculus and its Applications Author Piotr Ostalczyk
ISBN-10 9783319784588
Release 2018-03-22
Pages 229
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This book focuses on fractional calculus, presenting novel advances in both the theory and applications of non-integer order systems. At the end of the twentieth century it was predicted that it would be the calculus of the twenty-first century, and that prophecy is confirmed year after year. Now this mathematical tool is successfully used in a variety of research areas, like engineering (e.g. electrical, mechanical, chemical), dynamical systems modeling, analysis and synthesis (e.g technical, biological, economical) as well as in multidisciplinary areas (e.g. biochemistry, electrochemistry).As well as the mathematical foundations the book concentrates on the technical applications of continuous-time and discrete-time fractional calculus, investigating the identification, analysis and control of electrical circuits and dynamical systems. It also presents the latest results.Although some scientific centers and scientists are skeptical and actively criticize the applicability of fractional calculus, it is worth breaking through the scientific and technological walls. Because the “fractional community” is growing rapidly there is a pressing need for the exchange of scientific results. The book includes papers presented at the 9th International Conference on Non-integer Order Calculus and Its Applications and is divided into three parts:• Mathematical foundations• Fractional systems analysis and synthesis• System modelingSeven papers discuss the mathematical foundations, twelve papers address fractional order analysis and synthesis and three focus on dynamical system modeling by the fractional order differential and difference equations. It is a useful resource for fractional calculus scientific community.



Automation 2018

Automation 2018 Author Roman Szewczyk
ISBN-10 9783319771793
Release 2018-03-07
Pages 795
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This book consists of papers presented at Automation 2018, an international conference held in Warsaw from March 21 to 23, 2018. It discusses the radical technological changes occurring due to the INDUSTRY 4.0, with a focus on offering a better understanding of the Fourth Industrial Revolution. Each chapter presents a detailed analysis of interdisciplinary knowledge, numerical modeling and simulation as well as the application of cyber-physical systems, where information technology and physical devices create synergic systems leading to unprecedented efficiency. The theoretical results, practical solutions and guidelines presented are valuable for both researchers working in the area of engineering sciences and practitioners looking for solutions to industrial problems.



Computer Vision And Robotics In Perioperative Process

Computer Vision And Robotics In Perioperative Process Author Xu Yi
ISBN-10 9789813233300
Release 2018-04-10
Pages 120
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This invaluable compendium highlights the challenges of perioperative process in hospitals today. It delves into the development of a multi-agent robotic system where a dirty-side robot that sorts instruments returned from a surgical room into different containers for easy scrubbing, a Traybot that navigates the environment and transports the instrument containers to different stations, a clean-side robot that picks up instruments and places them in surgical kits, and an orchestration software architecture that manages the cooperation between different robots. The book discusses the technical details of all the components, from system architecture to the details of the end-effector design. Readers will gain significant knowledge on how such a system was put together. Contents: Introduction Project Background Related Work Overall Robotic System Architecture Vision Based Instrument Singulation Dirty Side Robot Design Mobile Robot Architecture Clean Side Robot Design Experiments Conclusions and Future Work Readership: Researchers, academics, professionals and graduate students in machine perception /computer vision, pattern recognition/image analysis and robotics and automated systems software. Keywords: Computer Vision;Robotics;Mobile Robot;Bin-Picking;End-Effector;PerioperativeReview:0



Computer Vision in Robotics and Industrial Applications

Computer Vision in Robotics and Industrial Applications Author Dominik Sankowski
ISBN-10 9789814583732
Release 2014-06-26
Pages 580
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The book presents a collection of practical applications of image processing and analysis. Different vision systems are more often used among others in the automotive industry, pharmacy, military and police equipment, automated production and measurement systems. In each of these fields of technology, digital image processing and analysis module is a critical part of the process of building this type of system. The majority of books in the market deal with theoretical issues. However, this unique publication specially highlights industrial applications, especially industrial measurement applications. Along with its wide spectrum of image processing and analysis applications, this book is an interesting reference for both students and professionals. Contents:Theoretical Introduction to Image Reconstruction and Processing:Data Set Preparation for k-NN Classifier Using the Measure of Representativeness (Marcin Raniszewski)Segmentation Methods in the Selected Industrial Computer Vision Application (Anna Fabijanska and Dominik Sankowski)Line Fractional-Order Difference/Sum, Its Properties and an Application in Image Processing (Piotr Ostalczyk)Computer Vision in Robotics:Management Software for Distributed Mobile Robot System (Maciej Łaski, Sylwester Błaszczyk, Piotr Duch, Rafał Jachowicz, Adam Wulkiewicz, Dominik Sankowski and Piotr Ostalczyk)Advanced Vision Systems in Detection and Analysis of Characteristic Features of Objects (Adam Wulkiewicz, Rafał Jachowicz, Sylwester Błaszczyk, Piotr Duch, Maciej Łaski, Dominik Sankowski and Piotr Ostalczyk)Pattern Recognition Algorithms for the Navigation of Mobile Platform (Rafał Jachowicz, Sylwester Błaszczyk, Piotr Duch, Maciej Łaski, Adam Wulkiewicz, Dominik Sankowski and Piotr Ostalczyk)Partial Fractional-Order Difference in the Edge Detection (Piotr Duch, Rafał Jachowicz, Sylwester Błaszczyk, Maciej Łaski, Adam Wulkiewicz, Piotr Ostalczyk and Dominik Sankowski)Application of Fractional-Order Derivative for Edge Detection in Mobile Robot System (Sylwester Błaszczyk, Rafał Jachowicz, Piotr Duch, Maciej Łaski, Adam Wulkiewicz, Piotr Ostalczyk and Dominik Sankowski)Vision Based Human-Machine Interfaces: Visem Recognition (Krzysztof Ślot, Agnieszka Owczarek and Maria Janczyk)Industrial Applications of Computer Vision in Process Tomography, Material Science and Temperature Control:Hybrid Boundary Element Method Applied for Diffusion Tomography Problems (Jan Sikora, Maciej Pańczyk and Paweł Wieleba)Two-phase Gas-Liquid Flow Structures and Phase Distribution Determination Based on 3D Electrical Capacitance Tomography Visualization (Robert Banasiak, Radosław Wajman, Tomasz Jaworski, Paweł Fiderek, Jacek Nowakowski and Henryk Fidos)Tomographic Visualization of Dynamic Industrial Solid Transporting and Storage Systems (Zbigniew Chaniecki, Krzysztof Grudzień and Andrzej Romanowski)Tomography Data Processing for Multiphase Industrial Process Monitoring (Krzysztof Grudzień, Zbigniew Chaniecki, Andrzej Romanowski, Jacek Nowakowski and Dominik Sankowski)Dedicated 3D Image Processing Methods for the Analysis of X-Ray Tomography Data: Case Study of Materials Science (Laurent Babout and Marcin Janaszewski)Selected Algorithms of Quantitative Image Analysis for Measurements of Properties Characterizing Interfacial Interactions at High Temperatures (Krzysztof Strzecha, Anna Fabijańska, Tomasz Koszmider and Dominik Sankowski)Theoretical Introduction to Image Reconstruction for Capacitance Process Tomography (Radosław Wajman, Krzysztof Grudzien, Robert Banasiak, Andrzej Romanowski, Zbigniew Chaniecki and Dominik Sankowski)Infra-Red Thermovision in Surface Temperature Control System (Jacek Kucharski, Tomasz Jaworski, Andrzej Frączyk and Piotr Urbanek)Medical and Other Applications of Computer Vision:The Computer Evaluation of Surface Color Changes in Cultivated Plants Influence by Different Environmental Factors (Joanna Sekulska-Nalewajko and Jarosław Gocławski)Various Approaches to Processing and Analysis of Images Obtained from Immunoenzymatic Visualization of Secretory Activity with ELISPOT Method (Wojciech Bieniecki and Szymon Grabowski)Image Processing and Analysis Algorithms for Assessment and Diagnosis of Brain Diseases (Anna Fabijanska and Tomasz Węglinski)Computer Systems for Studying Dynamic Properties of Materials at High Temperatures (Marcin Bąkała, Rafał Wojciechowski and Dominik Sankowski) Readership: Researchers, professionals and academics in image analysis, machine perception/computer vision, software engineering and fuzzy logic. Keywords:Image Processing;Computer Vision;Robotics;Pattern Recognition;Fuzzy Logic;Process Tomography;Mobile Robots



Theory and Applications of Fractional Differential Equations

Theory and Applications of Fractional Differential Equations Author Anatoliĭ Aleksandrovich Kilbas
ISBN-10 0444518320
Release 2006
Pages 523
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This work aims to present, in a systematic manner, results including the existence and uniqueness of solutions for the Cauchy Type and Cauchy problems involving nonlinear ordinary fractional differential equations.



Sparse Coding and its Applications in Computer Vision

Sparse Coding and its Applications in Computer Vision Author Zhaowen Wang
ISBN-10 9789814725064
Release 2015-10-28
Pages 240
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This book provides a broader introduction to the theories and applications of sparse coding techniques in computer vision research. It introduces sparse coding in the context of representation learning, illustrates the fundamental concepts, and summarizes the most active research directions. A variety of applications of sparse coding are discussed, ranging from low-level image processing tasks such as super-resolution and de-blurring to high-level semantic understanding tasks such as image recognition, clustering and fusion. The book is suitable to be used as an introductory overview to this field, with its theoretical part being both easy and precious enough for quick understanding. It is also of great value to experienced researchers as it offers new perspective to the underlying mechanism of sparse coding, and points out potential future directions for different applications. Contents:IntroductionTheories of Sparse CodingImage Super-ResolutionImage DeblurringSensor FusionClusteringObject RecognitionHyper-Spectral Image ModelingConclusions Readership: Graduate students, researchers and professionals in the field of machine perception, pattern recognition, image analysis, artificial intelligence, machine learning. Key Features:Explanation of sparse coding from both theoretical and practical point of viewsA comprehensive review of the applications of sparse coding in both low-level and high-level vision problemsInvestigating future research directions of sparse coding by making connection with the current state-of-the-art feature learning models, including deep neural networksKeywords:Sparse Coding;Sparse Representation;Dictionary Learning;Super-Resolution;De-Blurring;Sensor Fusion;Image Classification;Hyper-Spectral Image



Local Fractional Integral Transforms and Their Applications

Local Fractional Integral Transforms and Their Applications Author Xiao Jun Yang
ISBN-10 9780128040324
Release 2015-10-22
Pages 262
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Local Fractional Integral Transforms and Their Applications provides information on how local fractional calculus has been successfully applied to describe the numerous widespread real-world phenomena in the fields of physical sciences and engineering sciences that involve non-differentiable behaviors. The methods of integral transforms via local fractional calculus have been used to solve various local fractional ordinary and local fractional partial differential equations and also to figure out the presence of the fractal phenomenon. The book presents the basics of the local fractional derivative operators and investigates some new results in the area of local integral transforms. Provides applications of local fractional Fourier Series Discusses definitions for local fractional Laplace transforms Explains local fractional Laplace transforms coupled with analytical methods



Emerging Topics in Computer Vision and Its Applications

Emerging Topics in Computer Vision and Its Applications Author C. H. Chen
ISBN-10 9789814343008
Release 2012
Pages 508
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This book gives a comprehensive overview of the most advanced theories, methodologies and applications in computer vision. Particularly, it gives an extensive coverage of 3D and robotic vision problems. Example chapters featured are Fourier methods for 3D surface modeling and analysis, use of constraints for calibration-free 3D Euclidean reconstruction, novel photogeometric methods for capturing static and dynamic objects, performance evaluation of robot localization methods in outdoor terrains, integrating 3D vision with force/tactile sensors, tracking via in-floor sensing, self-calibration of camera networks, etc. Some unique applications of computer vision in marine fishery, biomedical issues, driver assistance, are also highlighted.



New Trends in Nanotechnology and Fractional Calculus Applications

New Trends in Nanotechnology and Fractional Calculus Applications Author Dumitru Baleanu
ISBN-10 9048132932
Release 2010-03-14
Pages 531
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In recent years fractional calculus has played an important role in various fields such as mechanics, electricity, chemistry, biology, economics, modeling, identification, control theory and signal processing. The scope of this book is to present the state of the art in the study of fractional systems and the application of fractional differentiation. Furthermore, the manufacture of nanowires is important for the design of nanosensors and the development of high-yield thin films is vital in procuring clean solar energy. This wide range of applications is of interest to engineers, physicists and mathematicians.



Introduction to the Fractional Calculus of Variations

Introduction to the Fractional Calculus of Variations Author Agnieszka B Malinowska
ISBN-10 9781848169685
Release 2012-09-14
Pages 292
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This invaluable book provides a broad introduction to the fascinating and beautiful subject of Fractional Calculus of Variations (FCV). In 1996, FVC evolved in order to better describe non-conservative systems in mechanics. The inclusion of non-conservatism is extremely important from the point of view of applications. Forces that do not store energy are always present in real systems. They remove energy from the systems and, as a consequence, Noether's conservation laws cease to be valid. However, it is still possible to obtain the validity of Noether's principle using FCV. The new theory provides a more realistic approach to physics, allowing us to consider non-conservative systems in a natural way. The authors prove the necessary Euler–Lagrange conditions and corresponding Noether theorems for several types of fractional variational problems, with and without constraints, using Lagrangian and Hamiltonian formalisms. Sufficient optimality conditions are also obtained under convexity, and Leitmann's direct method is discussed within the framework of FCV. The book is self-contained and unified in presentation. It may be used as an advanced textbook by graduate students and ambitious undergraduates in mathematics and mechanics. It provides an opportunity for an introduction to FCV for experienced researchers. The explanations in the book are detailed, in order to capture the interest of the curious reader, and the book provides the necessary background material required to go further into the subject and explore the rich research literature.



Advanced Synchronization Control and Bifurcation of Chaotic Fractional Order Systems

Advanced Synchronization Control and Bifurcation of Chaotic Fractional Order Systems Author Boulkroune, Abdesselem
ISBN-10 9781522554196
Release 2018-05-11
Pages 539
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In the recent years, fractional-order systems have been studied by many researchers in the engineering field. It was found that many systems can be described more accurately by fractional differential equations than by integer-order models. Advanced Synchronization Control and Bifurcation of Chaotic Fractional-Order Systems is a scholarly publication that explores new developments related to novel chaotic fractional-order systems, control schemes, and their applications. Featuring coverage on a wide range of topics including chaos synchronization, nonlinear control, and cryptography, this publication is geared toward engineers, IT professionals, researchers, and upper-level graduate students seeking current research on chaotic fractional-order systems and their applications in engineering and computer science.



Computer Vision

Computer Vision Author Richard Szeliski
ISBN-10 1848829469
Release 2010-11-05
Pages 812
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Humans perceive the three-dimensional structure of the world with apparent ease. However, despite all of the recent advances in computer vision research, the dream of having a computer interpret an image at the same level as a two-year old remains elusive. Why is computer vision such a challenging problem and what is the current state of the art? Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images. It also describes challenging real-world applications where vision is being successfully used, both for specialized applications such as medical imaging, and for fun, consumer-level tasks such as image editing and stitching, which students can apply to their own personal photos and videos. More than just a source of “recipes,” this exceptionally authoritative and comprehensive textbook/reference also takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene. These problems are also analyzed using statistical models and solved using rigorous engineering techniques Topics and features: structured to support active curricula and project-oriented courses, with tips in the Introduction for using the book in a variety of customized courses; presents exercises at the end of each chapter with a heavy emphasis on testing algorithms and containing numerous suggestions for small mid-term projects; provides additional material and more detailed mathematical topics in the Appendices, which cover linear algebra, numerical techniques, and Bayesian estimation theory; suggests additional reading at the end of each chapter, including the latest research in each sub-field, in addition to a full Bibliography at the end of the book; supplies supplementary course material for students at the associated website, http://szeliski.org/Book/. Suitable for an upper-level undergraduate or graduate-level course in computer science or engineering, this textbook focuses on basic techniques that work under real-world conditions and encourages students to push their creative boundaries. Its design and exposition also make it eminently suitable as a unique reference to the fundamental techniques and current research literature in computer vision.



Advanced Methods in the Fractional Calculus of Variations

Advanced Methods in the Fractional Calculus of Variations Author Agnieszka B. Malinowska
ISBN-10 9783319147567
Release 2015-02-05
Pages 135
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This brief presents a general unifying perspective on the fractional calculus. It brings together results of several recent approaches in generalizing the least action principle and the Euler–Lagrange equations to include fractional derivatives. The dependence of Lagrangians on generalized fractional operators as well as on classical derivatives is considered along with still more general problems in which integer-order integrals are replaced by fractional integrals. General theorems are obtained for several types of variational problems for which recent results developed in the literature can be obtained as special cases. In particular, the authors offer necessary optimality conditions of Euler–Lagrange type for the fundamental and isoperimetric problems, transversality conditions, and Noether symmetry theorems. The existence of solutions is demonstrated under Tonelli type conditions. The results are used to prove the existence of eigenvalues and corresponding orthogonal eigenfunctions of fractional Sturm–Liouville problems. Advanced Methods in the Fractional Calculus of Variations is a self-contained text which will be useful for graduate students wishing to learn about fractional-order systems. The detailed explanations will interest researchers with backgrounds in applied mathematics, control and optimization as well as in certain areas of physics and engineering.



Mathematical Techniques of Fractional Order Systems

Mathematical Techniques of Fractional Order Systems Author Ahmad Taher Azar
ISBN-10 0128135921
Release 2018-06
Pages 500
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Mathematical Techniques of Fractional Order Systems illustrates advances in linear and nonlinear fractional-order systems relating to many interdisciplinary applications, including biomedical, control, circuits, electromagnetics and security. The book covers the mathematical background and literature survey of fractional-order calculus and generalized fractional-order circuit theorems from different perspectives in design, analysis and realizations, nonlinear fractional-order circuits and systems, the fractional-order memristive circuits and systems in design, analysis, emulators, simulation and experimental results. It is primarily meant for researchers from academia and industry, and for those working in areas such as control engineering, electrical engineering, computer science and information technology. This book is ideal for researchers working in the area of both continuous-time and discrete-time dynamics and chaotic systems. Discusses multidisciplinary applications with new fundamentals, modeling, analysis, design, realization and experimental results Includes circuits and systems based on new nonlinear elements Covers most of the linear and nonlinear fractional-order theorems that will solve many scientific issues for researchers Closes the gap between theoretical approaches and real-world applications Provides MATLAB(R) and Simulink code for many applications in the book



Fractional order Systems and Controls

Fractional order Systems and Controls Author Concepción A. Monje
ISBN-10 1849963355
Release 2010-09-28
Pages 415
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Fractional-order Systems and Controls details the use of fractional calculus in the description and modeling of systems, and in a range of control design and practical applications. It is largely self-contained, covering the fundamentals of fractional calculus together with some analytical and numerical techniques and providing MATLAB® codes for the simulation of fractional-order control (FOC) systems. Many different FOC schemes are presented for control and dynamic systems problems. Practical material relating to a wide variety of applications is also provided. All the control schemes and applications are presented in the monograph with either system simulation results or real experimental results, or both. Fractional-order Systems and Controls provides readers with a basic understanding of FOC concepts and methods, so they can extend their use of FOC in other industrial system applications, thereby expanding their range of disciplines by exploiting this versatile new set of control techniques.



The Essential Guide to Image Processing

The Essential Guide to Image Processing Author Alan C. Bovik
ISBN-10 0080922511
Release 2009-07-08
Pages 672
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A complete introduction to the basic and intermediate concepts of image processing from the leading people in the field Up-to-date content, including statistical modeling of natural, anistropic diffusion, image quality and the latest developments in JPEG 2000 This comprehensive and state-of-the art approach to image processing gives engineers and students a thorough introduction, and includes full coverage of key applications: image watermarking, fingerprint recognition, face recognition and iris recognition and medical imaging. "This book combines basic image processing techniques with some of the most advanced procedures. Introductory chapters dedicated to general principles are presented alongside detailed application-orientated ones. As a result it is suitably adapted for different classes of readers, ranging from Master to PhD students and beyond." – Prof. Jean-Philippe Thiran, EPFL, Lausanne, Switzerland "Al Bovik’s compendium proceeds systematically from fundamentals to today’s research frontiers. Professor Bovik, himself a highly respected leader in the field, has invited an all-star team of contributors. Students, researchers, and practitioners of image processing alike should benefit from the Essential Guide." – Prof. Bernd Girod, Stanford University, USA "This book is informative, easy to read with plenty of examples, and allows great flexibility in tailoring a course on image processing or analysis." – Prof. Pamela Cosman, University of California, San Diego, USA A complete and modern introduction to the basic and intermediate concepts of image processing – edited and written by the leading people in the field An essential reference for all types of engineers working on image processing applications Up-to-date content, including statistical modelling of natural, anisotropic diffusion, image quality and the latest developments in JPEG 2000