Special Issue on Partial Differential Equations and Geometry-driven Diffusion in Image Processing and Analysis PDF Download
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Author:
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ISBN:
Category : Differential equations, Partial
Languages : en
Pages : 205
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Author:
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ISBN:
Category : Differential equations, Partial
Languages : en
Pages : 205
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Author: Vicent Caselles
Publisher:
ISBN:
Category :
Languages : en
Pages : 205
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Languages : en
Pages : 0
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We first describe results on shape-base image contrast enhancement. This work shows how to perform local contrast enhancement while preserving the shapes in the image. We have transferred this software to Dr. Szymczak from Physical Acoustics at the Naval Research Laboratory for testing on underwater laser images (LIDAR). We then show a novel approach to anisotropic diffusion. This approach is based on robust statistics, and in particular, in the theory of influence functions. This technique is, for example, of particular significance for image denoising prior to segmentation. We conclude this document with a description of a novel technique of incorporating prior information in anisotropic diffusion. The idea is to use Bayes rule to compute posterior distributions, and then, regularize those distributions via partial differential equations before the MAP is computed. Although a number of results have already been obtained in these areas, the work described in this document is still in progress. As was mentioned above, we want to extend the work on shape-preserving contrast enhancement to include additional definitions of shape and adapt it to specific applications. We are also planing to extend the robust framework for anisotropic diffusion to vector-valued data, and investigate fast implementations. We plan to further investigate the underlying theory of the posterior diffusion work, and to apply it to additional problems. The work described in this document opens a number of theoretical questions that we plan to address as well.
Author: Carola-Bibiane Schönlieb
Publisher: Cambridge University Press
ISBN: 1316404587
Category : Mathematics
Languages : en
Pages : 265
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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.
Author: Ky Fan
Publisher:
ISBN:
Category :
Languages : en
Pages : 237
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Author: Shiing-shen Chern
Publisher: Nankai Institute of Mathematics, Tianjin, P.R. China
ISBN:
Category : Mathematics
Languages : en
Pages : 308
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The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.
Author: Fouad Sabry
Publisher: One Billion Knowledgeable
ISBN:
Category : Computers
Languages : en
Pages : 165
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Book Description
What is Anisotropic Diffusion In image processing and computer vision, anisotropic diffusion, also called Perona-Malik diffusion, is a technique aiming at reducing image noise without removing significant parts of the image content, typically edges, lines or other details that are important for the interpretation of the image. Anisotropic diffusion resembles the process that creates a scale space, where an image generates a parameterized family of successively more and more blurred images based on a diffusion process. Each of the resulting images in this family are given as a convolution between the image and a 2D isotropic Gaussian filter, where the width of the filter increases with the parameter. This diffusion process is a linear and space-invariant transformation of the original image. Anisotropic diffusion is a generalization of this diffusion process: it produces a family of parameterized images, but each resulting image is a combination between the original image and a filter that depends on the local content of the original image. As a consequence, anisotropic diffusion is a non-linear and space-variant transformation of the original image. How you will benefit (I) Insights, and validations about the following topics: Chapter 1: Anisotropic diffusion Chapter 2: Fick's laws of diffusion Chapter 3: Diffusion equation Chapter 4: Heat equation Chapter 5: Navier-Stokes equations Chapter 6: Total variation Chapter 7: Divergence Chapter 8: Laplace operator Chapter 9: Curl (mathematics) Chapter 10: Divergence theorem (II) Answering the public top questions about anisotropic diffusion. (III) Real world examples for the usage of anisotropic diffusion in many fields. Who this book is for Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of Anisotropic Diffusion.
Author: Guillermo Sapiro
Publisher: Cambridge University Press
ISBN: 1139936514
Category : Mathematics
Languages : en
Pages : 391
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Book Description
This book provides an introduction to the use of geometric partial differential equations in image processing and computer vision. This research area brings a number of new concepts into the field, providing a very fundamental and formal approach to image processing. State-of-the-art practical results in a large number of real problems are achieved with the techniques described in this book. Applications covered include image segmentation, shape analysis, image enhancement, and tracking. This book will be a useful resource for researchers and practitioners. It is intended to provide information for people investigating new solutions to image processing problems as well as for people searching for existent advanced solutions.
Author:
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ISBN:
Category :
Languages : en
Pages : 580
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Author: Habib Ammari
Publisher:
ISBN: 9781470429324
Category : Differential equations, Partial
Languages : en
Pages :
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