First Order Quasi-Linear PDEs with BV Boundary Data and Applications to Image Inpainting

First Order Quasi-Linear PDEs with BV Boundary Data and Applications to Image Inpainting

Author: Thomas März

Publisher: Logos Verlag Berlin GmbH

Published: 2010

Total Pages: 194

ISBN-13: 3832526390

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This book investigates the well-posedness of the mathematical model behind the method "Image Inpainting Based on Coherence Transport". Image inpainting methods serve the purpose of touching up damaged or unwanted elements of a digital picture. The model behind the mentioned method is a Dirichlet problem for a first order quasi-linear hyperbolic functional partial differential equation where all points of the boundary are inflow points. The main concern of this thesis is to proof the existence and the uniqueness of a solution to such kind of problems as well as the solutions's continuous dependence on the data. The general theory finally is used to obtain the well-posedness of the inpainting model.


Partial Differential Equation Methods for Image Inpainting

Partial Differential Equation Methods for Image Inpainting

Author: Carola-Bibiane Schönlieb

Publisher: Cambridge University Press

Published: 2015-10-26

Total Pages: 265

ISBN-13: 1316404587

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This book is concerned with digital image processing techniques that use partial differential equations (PDEs) for the task of image 'inpainting', an artistic term for virtual image restoration or interpolation, whereby missing or occluded parts in images are completed based on information provided by intact parts. Computer graphic designers, artists and photographers have long used manual inpainting to restore damaged paintings or manipulate photographs. Today, mathematicians apply powerful methods based on PDEs to automate this task. This book introduces the mathematical concept of PDEs for virtual image restoration. It gives the full picture, from the first modelling steps originating in Gestalt theory and arts restoration to the analysis of resulting PDE models, numerical realisation and real-world application. This broad approach also gives insight into functional analysis, variational calculus, optimisation and numerical analysis and will appeal to researchers and graduate students in mathematics with an interest in image processing and mathematical analysis.


Image Processing and Analysis

Image Processing and Analysis

Author: Tony F. Chan

Publisher: SIAM

Published: 2005-09-01

Total Pages: 414

ISBN-13: 089871589X

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This book develops the mathematical foundation of modern image processing and low-level computer vision, bridging contemporary mathematics with state-of-the-art methodologies in modern image processing, whilst organizing contemporary literature into a coherent and logical structure. The authors have integrated the diversity of modern image processing approaches by revealing the few common threads that connect them to Fourier and spectral analysis, the machinery that image processing has been traditionally built on. The text is systematic and well organized: the geometric, functional, and atomic structures of images are investigated, before moving to a rigorous development and analysis of several image processors. The book is comprehensive and integrative, covering the four most powerful classes of mathematical tools in contemporary image analysis and processing while exploring their intrinsic connections and integration. The material is balanced in theory and computation, following a solid theoretical analysis of model building and performance with computational implementation and numerical examples.


Partial Differential Equation Methods for Image Inpainting

Partial Differential Equation Methods for Image Inpainting

Author: Carola-Bibiane Schönlieb

Publisher: Cambridge University Press

Published: 2015-10-26

Total Pages: 265

ISBN-13: 1107001005

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This book introduces the mathematical concept of partial differential equations (PDE) for virtual image restoration. It provides insight in mathematical modelling, partial differential equations, functional analysis, variational calculus, optimisation and numerical analysis. It is addressed towards generally informed mathematicians and graduate students in mathematics with an interest in image processing and mathematical analysis.


Level Set Methods and Dynamic Implicit Surfaces

Level Set Methods and Dynamic Implicit Surfaces

Author: Stanley Osher

Publisher: Springer Science & Business Media

Published: 2006-04-06

Total Pages: 292

ISBN-13: 0387227466

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Very hot area with a wide range of applications; Gives complete numerical analysis and recipes, which will enable readers to quickly apply the techniques to real problems; Includes two new techniques pioneered by Osher and Fedkiw; Osher and Fedkiw are internationally well-known researchers in this area


Applied Partial Differential Equations:

Applied Partial Differential Equations:

Author: Peter Markowich

Publisher: Springer Science & Business Media

Published: 2007-08-06

Total Pages: 210

ISBN-13: 3540346465

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This book presents topics of science and engineering which occur in nature or are part of daily life. It describes phenomena which are modelled by partial differential equations, relating to physical variables like mass, velocity and energy, etc. to their spatial and temporal variations. The author has chosen topics representing his career-long interests, including the flow of fluids and gases, granular flows, biological processes like pattern formation on animal skins, kinetics of rarified gases and semiconductor devices. Each topic is presented in its scientific or engineering context, followed by an introduction of applicable mathematical models in the form of partial differential equations.


Framelets and Wavelets

Framelets and Wavelets

Author: Bin Han

Publisher: Springer

Published: 2018-01-04

Total Pages: 750

ISBN-13: 3319685309

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Marking a distinct departure from the perspectives of frame theory and discrete transforms, this book provides a comprehensive mathematical and algorithmic introduction to wavelet theory. As such, it can be used as either a textbook or reference guide. As a textbook for graduate mathematics students and beginning researchers, it offers detailed information on the basic theory of framelets and wavelets, complemented by self-contained elementary proofs, illustrative examples/figures, and supplementary exercises. Further, as an advanced reference guide for experienced researchers and practitioners in mathematics, physics, and engineering, the book addresses in detail a wide range of basic and advanced topics (such as multiwavelets/multiframelets in Sobolev spaces and directional framelets) in wavelet theory, together with systematic mathematical analysis, concrete algorithms, and recent developments in and applications of framelets and wavelets. Lastly, the book can also be used to teach on or study selected special topics in approximation theory, Fourier analysis, applied harmonic analysis, functional analysis, and wavelet-based signal/image processing.


Image and Signal Processing

Image and Signal Processing

Author: Abderrahim El Moataz

Publisher: Springer Nature

Published: 2020-07-08

Total Pages: 388

ISBN-13: 303051935X

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This volume constitutes the refereed proceedings of the 9th International Conference on Image and Signal Processing, ICISP 2020, which was due to be held in Marrakesh, Morocco, in June 2020. The conference was cancelled due to the COVID-19 pandemic. The 40 revised full papers were carefully reviewed and selected from 84 submissions. The contributions presented in this volume were organized in the following topical sections: digital cultural heritage & color and spectral imaging; data and image processing for precision agriculture; machine learning application and innovation; biomedical imaging; deep learning and applications; pattern recognition; segmentation and retrieval; mathematical imaging & signal processing.


Digital Signal Processing with Matlab Examples, Volume 3

Digital Signal Processing with Matlab Examples, Volume 3

Author: Jose Maria Giron-Sierra

Publisher: Springer

Published: 2016-11-21

Total Pages: 443

ISBN-13: 9811025401

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This is the third volume in a trilogy on modern Signal Processing. The three books provide a concise exposition of signal processing topics, and a guide to support individual practical exploration based on MATLAB programs. This book includes MATLAB codes to illustrate each of the main steps of the theory, offering a self-contained guide suitable for independent study. The code is embedded in the text, helping readers to put into practice the ideas and methods discussed. The book primarily focuses on filter banks, wavelets, and images. While the Fourier transform is adequate for periodic signals, wavelets are more suitable for other cases, such as short-duration signals: bursts, spikes, tweets, lung sounds, etc. Both Fourier and wavelet transforms decompose signals into components. Further, both are also invertible, so the original signals can be recovered from their components. Compressed sensing has emerged as a promising idea. One of the intended applications is networked devices or sensors, which are now becoming a reality; accordingly, this topic is also addressed. A selection of experiments that demonstrate image denoising applications are also included. In the interest of reader-friendliness, the longer programs have been grouped in an appendix; further, a second appendix on optimization has been added to supplement the content of the last chapter.


Advances in Smart System Technologies

Advances in Smart System Technologies

Author: P. Suresh

Publisher: Springer Nature

Published: 2020-08-29

Total Pages: 823

ISBN-13: 9811550298

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This book presents select peer-reviewed proceedings of the International Conference on Frontiers in Smart Systems Technologies (ICFSST 2019). It focuses on latest research and cutting-edge technologies in smart systems and intelligent autonomous systems with advanced functionality. Comprising topics related to diverse aspects of smart technologies such as high security, reliability, miniaturization, energy consumption, and intelligent data processing, the book contains contributions from academics as well as industry. Given the range of the topics covered, this book will prove useful for students, researchers, and professionals alike.