Stochastic Partial Differential Equations For Computer Vision With Uncertain Data

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Stochastic Partial Differential Equations for Computer Vision with Uncertain Data

Author : Tobias Preusser
Publisher : Springer Nature
ISBN 13 : 3031025946
Total Pages : 150 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Stochastic Partial Differential Equations for Computer Vision with Uncertain Data by : Tobias Preusser

Download or read book Stochastic Partial Differential Equations for Computer Vision with Uncertain Data written by Tobias Preusser and published by Springer Nature. This book was released on 2022-06-01 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: In image processing and computer vision applications such as medical or scientific image data analysis, as well as in industrial scenarios, images are used as input measurement data. It is good scientific practice that proper measurements must be equipped with error and uncertainty estimates. For many applications, not only the measured values but also their errors and uncertainties, should be—and more and more frequently are—taken into account for further processing. This error and uncertainty propagation must be done for every processing step such that the final result comes with a reliable precision estimate. The goal of this book is to introduce the reader to the recent advances from the field of uncertainty quantification and error propagation for computer vision, image processing, and image analysis that are based on partial differential equations (PDEs). It presents a concept with which error propagation and sensitivity analysis can be formulated with a set of basic operations. The approach discussed in this book has the potential for application in all areas of quantitative computer vision, image processing, and image analysis. In particular, it might help medical imaging finally become a scientific discipline that is characterized by the classical paradigms of observation, measurement, and error awareness. This book is comprised of eight chapters. After an introduction to the goals of the book (Chapter 1), we present a brief review of PDEs and their numerical treatment (Chapter 2), PDE-based image processing (Chapter 3), and the numerics of stochastic PDEs (Chapter 4). We then proceed to define the concept of stochastic images (Chapter 5), describe how to accomplish image processing and computer vision with stochastic images (Chapter 6), and demonstrate the use of these principles for accomplishing sensitivity analysis (Chapter 7). Chapter 8 concludes the book and highlights new research topics for the future.

Stochastic Partial Differential Equations for Computer Vision with Uncertain Data

Author : Tobias Preusser
Publisher : Morgan & Claypool
ISBN 13 : 9781681731438
Total Pages : 0 pages
Book Rating : 4.7/5 (314 download)

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Book Synopsis Stochastic Partial Differential Equations for Computer Vision with Uncertain Data by : Tobias Preusser

Download or read book Stochastic Partial Differential Equations for Computer Vision with Uncertain Data written by Tobias Preusser and published by Morgan & Claypool. This book was released on 2017-07-13 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In image processing and computer vision applications such as medical or scientific image data analysis, as well as in industrial scenarios, images are used as input measurement data. It is good scientific practice that proper measurements must be equipped with error and uncertainty estimates. For many applications, not only the measured values but also their errors and uncertainties, should be--and more and more frequently are--taken into account for further processing. This error and uncertainty propagation must be done for every processing step such that the final result comes with a reliable precision estimate. The goal of this book is to introduce the reader to the recent advances from the field of uncertainty quantification and error propagation for computer vision, image processing, and image analysis that are based on partial differential equations (PDEs). It presents a concept with which error propagation and sensitivity analysis can be formulated with a set of basic operations. The approach discussed in this book has the potential for application in all areas of quantitative computer vision, image processing, and image analysis. In particular, it might help medical imaging finally become a scientific discipline that is characterized by the classical paradigms of observation, measurement, and error awareness. This book is comprised of eight chapters. After an introduction to the goals of the book (Chapter 1), we present a brief review of PDEs and their numerical treatment (Chapter 2), PDE-based image processing (Chapter 3), and the numerics of stochastic PDEs (Chapter 4). We then proceed to define the concept of stochastic images (Chapter 5), describe how to accomplish image processing and computer vision with stochastic images (Chapter 6), and demonstrate the use of these principles for accomplishing sensitivity analysis (Chapter 7). Chapter 8 concludes the book and highlights new research topics for the future.

Mathematical Methods in Computer Vision

Author : Peter J. Olver
Publisher : Springer Science & Business Media
ISBN 13 : 9780387004976
Total Pages : 176 pages
Book Rating : 4.0/5 (49 download)

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Book Synopsis Mathematical Methods in Computer Vision by : Peter J. Olver

Download or read book Mathematical Methods in Computer Vision written by Peter J. Olver and published by Springer Science & Business Media. This book was released on 2003-10 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Comprises some of the key work presented at two IMA Wokshops on Computer Vision during fall of 2000."--Pref.

Mathematical Problems in Image Processing

Author : Gilles Aubert
Publisher : Springer Science & Business Media
ISBN 13 : 0387217665
Total Pages : 288 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Mathematical Problems in Image Processing by : Gilles Aubert

Download or read book Mathematical Problems in Image Processing written by Gilles Aubert and published by Springer Science & Business Media. This book was released on 2008-04-06 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Partial differential equations and variational methods were introduced into image processing about 15 years ago, and intensive research has been carried out since then. The main goal of this work is to present the variety of image analysis applications and the precise mathematics involved. It is intended for two audiences. The first is the mathematical community, to show the contribution of mathematics to this domain and to highlight some unresolved theoretical questions. The second is the computer vision community, to present a clear, self-contained, and global overview of the mathematics involved in image processing problems. The book is divided into five main parts. Chapter 1 is a detailed overview. Chapter 2 describes and illustrates most of the mathematical notions found throughout the work. Chapters 3 and 4 examine how PDEs and variational methods can be successfully applied in image restoration and segmentation processes. Chapter 5, which is more applied, describes some challenging computer vision problems, such as sequence analysis or classification. This book will be useful to researchers and graduate students in mathematics and computer vision.

Mathematical Methods in Computer Vision

Author : Peter J. Olver
Publisher : Springer
ISBN 13 : 9781475741278
Total Pages : 0 pages
Book Rating : 4.7/5 (412 download)

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Book Synopsis Mathematical Methods in Computer Vision by : Peter J. Olver

Download or read book Mathematical Methods in Computer Vision written by Peter J. Olver and published by Springer. This book was released on 2010-11-16 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises some of the key work presented at two IMA Workshops on Computer Vision during fall of 2000. Recent years have seen significant advances in the application of sophisticated mathematical theories to the problems arising in image processing. Basic issues include image smoothing and denoising, image enhancement, morphology, image compression, and segmentation (determining boundaries of objects-including problems of camera distortion and partial occlusion). Several mathematical approaches have emerged, including methods based on nonlinear partial differential equations, stochastic and statistical methods, and signal processing techniques, including wavelets and other transform theories. Shape theory is of fundamental importance since it is the bottleneck between high and low level vision, and formed the bridge between the two workshops on vision. The recent geometric partial differential equation methods have been essential in throwing new light on this very difficult problem area. Further, stochastic processes, including Markov random fields, have been used in a Bayesian framework to incorporate prior constraints on smoothness and the regularities of discontinuities into algorithms for image restoration and reconstruction. A number of applications are considered including optical character and handwriting recognizers, printed-circuit board inspection systems and quality control devices, motion detection, robotic control by visual feedback, reconstruction of objects from stereoscopic view and/or motion, autonomous road vehicles, and many others.

Virtual Material Acquisition and Representation for Computer Graphics

Author : Dar'ya Guarnera
Publisher : Springer Nature
ISBN 13 : 3031025954
Total Pages : 93 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Virtual Material Acquisition and Representation for Computer Graphics by : Dar'ya Guarnera

Download or read book Virtual Material Acquisition and Representation for Computer Graphics written by Dar'ya Guarnera and published by Springer Nature. This book was released on 2022-05-31 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides beginners in computer graphics and related fields a guide to the concepts, models, and technologies for realistic rendering of material appearance. It provides a complete and thorough overview of reflectance models and acquisition setups, along with providing a selection of the available tools to explore, visualize, and render the reflectance data. Reflectance models are under continuous development, since there is still no straightforward solution for general material representations. Every reflectance model is specific to a class of materials. Hence, each has strengths and weaknesses, which the book highlights in order to help the reader choose the most suitable model for any purpose. The overview of the acquisition setups will provide guidance to a reader who needs to acquire virtual materials and will help them to understand which measurement setup can be useful for a particular purpose, while taking into account the performance and the expected cost derived from the required components. The book also describes several recent open source software solutions, useful for visualizing and manipulating a wide variety of reflectance models and data.

Geometric Partial Differential Equations and Image Analysis

Author : Guillermo Sapiro
Publisher : Cambridge University Press
ISBN 13 : 1139936514
Total Pages : 510 pages
Book Rating : 4.1/5 (399 download)

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Book Synopsis Geometric Partial Differential Equations and Image Analysis by : Guillermo Sapiro

Download or read book Geometric Partial Differential Equations and Image Analysis written by Guillermo Sapiro and published by Cambridge University Press. This book was released on 2006-02-13 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Cloth Simulation for Computer Graphics

Author : Tuur Stuyck
Publisher : Springer Nature
ISBN 13 : 3031025970
Total Pages : 110 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Cloth Simulation for Computer Graphics by : Tuur Stuyck

Download or read book Cloth Simulation for Computer Graphics written by Tuur Stuyck and published by Springer Nature. This book was released on 2022-06-01 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: Physics-based animation is commonplace in animated feature films and even special effects for live-action movies. Think about a recent movie and there will be some sort of special effects such as explosions or virtual worlds. Cloth simulation is no different and is ubiquitous because most virtual characters (hopefully!) wear some sort of clothing. The focus of this book is physics-based cloth simulation. We start by providing background information and discuss a range of applications. This book provides explanations of multiple cloth simulation techniques. More specifically, we start with the most simple explicitly integrated mass-spring model and gradually work our way up to more complex and commonly used implicitly integrated continuum techniques in state-of-the-art implementations. We give an intuitive explanation of the techniques and give additional information on how to efficiently implement them on a computer. This book discusses explicit and implicit integration schemes for cloth simulation modeled with mass-spring systems. In addition to this simple model, we explain the more advanced continuum-inspired cloth model introduced in the seminal work of Baraff and Witkin [1998]. This method is commonly used in industry. We also explain recent work by Liu et al. [2013] that provides a technique to obtain fast simulations. In addition to these simulation approaches, we discuss how cloth simulations can be art directed for stylized animations based on the work of Wojan et al. [2016]. Controllability is an essential component of a feature animation film production pipeline. We conclude by pointing the reader to more advanced techniques.

Computer Vision -- ECCV 2010

Author : Kostas Daniilidis
Publisher : Springer
ISBN 13 : 3642155553
Total Pages : 828 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Computer Vision -- ECCV 2010 by : Kostas Daniilidis

Download or read book Computer Vision -- ECCV 2010 written by Kostas Daniilidis and published by Springer. This book was released on 2010-09-08 with total page 828 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 2010 edition of the European Conference on Computer Vision was held in Heraklion, Crete. The call for papers attracted an absolute record of 1,174 submissions. We describe here the selection of the accepted papers: Thirty-eight area chairs were selected coming from Europe (18), USA and Canada (16), and Asia (4). Their selection was based on the following criteria: (1) Researchers who had served at least two times as Area Chairs within the past two years at major vision conferences were excluded; (2) Researchers who served as Area Chairs at the 2010 Computer Vision and Pattern Recognition were also excluded (exception: ECCV 2012 Program Chairs); (3) Minimization of overlap introduced by Area Chairs being former student and advisors; (4) 20% of the Area Chairs had never served before in a major conference; (5) The Area Chair selection process made all possible efforts to achieve a reasonable geographic distribution between countries, thematic areas and trends in computer vision. Each Area Chair was assigned by the Program Chairs between 28–32 papers. Based on paper content, the Area Chair recommended up to seven potential reviewers per paper. Such assignment was made using all reviewers in the database including the conflicting ones. The Program Chairs manually entered the missing conflict domains of approximately 300 reviewers. Based on the recommendation of the Area Chairs, three reviewers were selected per paper (with at least one being of the top three suggestions), with 99.

An Introduction to Laplacian Spectral Distances and Kernels

Author : Giuseppe Patanè
Publisher : Springer Nature
ISBN 13 : 3031025938
Total Pages : 120 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis An Introduction to Laplacian Spectral Distances and Kernels by : Giuseppe Patanè

Download or read book An Introduction to Laplacian Spectral Distances and Kernels written by Giuseppe Patanè and published by Springer Nature. This book was released on 2022-05-31 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: In geometry processing and shape analysis, several applications have been addressed through the properties of the Laplacian spectral kernels and distances, such as commute time, biharmonic, diffusion, and wave distances. Within this context, this book is intended to provide a common background on the definition and computation of the Laplacian spectral kernels and distances for geometry processing and shape analysis. To this end, we define a unified representation of the isotropic and anisotropic discrete Laplacian operator on surfaces and volumes; then, we introduce the associated differential equations, i.e., the harmonic equation, the Laplacian eigenproblem, and the heat equation. Filtering the Laplacian spectrum, we introduce the Laplacian spectral distances, which generalize the commute-time, biharmonic, diffusion, and wave distances, and their discretization in terms of the Laplacian spectrum. As main applications, we discuss the design of smooth functions and the Laplacian smoothing of noisy scalar functions. All the reviewed numerical schemes are discussed and compared in terms of robustness, approximation accuracy, and computational cost, thus supporting the reader in the selection of the most appropriate with respect to shape representation, computational resources, and target application.

Sound Synthesis, Propagation, and Rendering

Author : Shiguang Liu
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1636393217
Total Pages : 110 pages
Book Rating : 4.6/5 (363 download)

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Book Synopsis Sound Synthesis, Propagation, and Rendering by : Shiguang Liu

Download or read book Sound Synthesis, Propagation, and Rendering written by Shiguang Liu and published by Morgan & Claypool Publishers. This book was released on 2022-03-24 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a broad overview of research on sound simulation driven by a variety of applications. Vibrating objects produce sound, which then propagates through a medium such as air or water before finally being heard by a listener. As a crucial sensory channel, sound plays a vital role in many applications. There is a well-established research community in acoustics that has studied the problems related to sound simulation for six decades. Some of the earliest work was motivated by the design of concert halls, theaters, or lecture rooms with good acoustic characteristics. These problems also have been investigated in other applications, including noise control and sound design for urban planning, building construction, and automotive applications. Moreover, plausible or realistic sound effects can improve the sense of presence in a virtual environment or a game. In these applications, sound can provide important clues such as source directionality and spatial size. The book first surveys various sound synthesis methods, including harmonic synthesis, texture synthesis, spectral analysis, and physics-based synthesis. Next, it provides an overview of sound propagation techniques, including wave-based methods, geometric-based methods, and hybrid methods. The book also summarizes various techniques for sound rendering. Finally, it surveys some recent trends, including the use of machine learning methods to accelerate sound simulation and the use of sound simulation techniques for other applications such as speech recognition, source localization, and computer-aided design.

GPU Ray Tracing in Non-Euclidean Spaces

Author : Tiago Novello
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1636393276
Total Pages : 129 pages
Book Rating : 4.6/5 (363 download)

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Book Synopsis GPU Ray Tracing in Non-Euclidean Spaces by : Tiago Novello

Download or read book GPU Ray Tracing in Non-Euclidean Spaces written by Tiago Novello and published by Morgan & Claypool Publishers. This book was released on 2022-03-21 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the visualization of three-dimensional non-Euclidean spaces using raytracing techniques in Graphics Processing Unit (GPU). This is a trending topic in mathematical visualization that combines the mathematics areas of geometry and topology, with visualization concepts of computer graphics. Several conditions made this a special moment for such topic. On one hand, the development of mathematical research, computer graphics, and algorithms have provided the necessary theoretical framework. On the other hand, the evolution of the technologies and media allows us to be immersed in three-dimensional spaces using Virtual Reality. The content of this book serves both experts in the areas and students. Although this is a short book, it is self-contained since it considers all the ideas, motivations, references, and intuitive explanations of the required fundamental concepts.

Design, Representations, and Processing for Additive Manufacturing

Author : Marco Attene
Publisher : Springer Nature
ISBN 13 : 3031025962
Total Pages : 136 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Design, Representations, and Processing for Additive Manufacturing by : Marco Attene

Download or read book Design, Representations, and Processing for Additive Manufacturing written by Marco Attene and published by Springer Nature. This book was released on 2022-06-01 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: The wide diffusion of 3D printing technologies continuously calls for effective solutions for designing and fabricating objects of increasing complexity. The so called "computational fabrication" pipeline comprises all the steps necessary to turn a design idea into a physical object, and this book describes the most recent advancements in the two fundamental phases along this pipeline: design and process planning. We examine recent systems in the computer graphics community that allow us to take a design idea from conception to a digital model, and classify algorithms that are necessary to turn such a digital model into an appropriate sequence of machining instructions.

Image Processing and Analysis

Author : Tony F. Chan
Publisher : SIAM
ISBN 13 : 089871589X
Total Pages : 414 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Image Processing and Analysis by : Tony F. Chan

Download or read book Image Processing and Analysis written by Tony F. Chan and published by SIAM. This book was released on 2005-09-01 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Image Processing Based on Partial Differential Equations

Author : Xue-Cheng Tai
Publisher : Springer Science & Business Media
ISBN 13 : 3540332677
Total Pages : 440 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Image Processing Based on Partial Differential Equations by : Xue-Cheng Tai

Download or read book Image Processing Based on Partial Differential Equations written by Xue-Cheng Tai and published by Springer Science & Business Media. This book was released on 2006-11-22 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book publishes a collection of original scientific research articles that address the state-of-art in using partial differential equations for image and signal processing. Coverage includes: level set methods for image segmentation and construction, denoising techniques, digital image inpainting, image dejittering, image registration, and fast numerical algorithms for solving these problems.

Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

Author : Ke Chen
Publisher : Springer Nature
ISBN 13 : 3030986616
Total Pages : 1981 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging by : Ke Chen

Download or read book Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging written by Ke Chen and published by Springer Nature. This book was released on 2023-02-24 with total page 1981 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook gathers together the state of the art on mathematical models and algorithms for imaging and vision. Its emphasis lies on rigorous mathematical methods, which represent the optimal solutions to a class of imaging and vision problems, and on effective algorithms, which are necessary for the methods to be translated to practical use in various applications. Viewing discrete images as data sampled from functional surfaces enables the use of advanced tools from calculus, functions and calculus of variations, and nonlinear optimization, and provides the basis of high-resolution imaging through geometry and variational models. Besides, optimization naturally connects traditional model-driven approaches to the emerging data-driven approaches of machine and deep learning. No other framework can provide comparable accuracy and precision to imaging and vision. Written by leading researchers in imaging and vision, the chapters in this handbook all start with gentle introductions, which make this work accessible to graduate students. For newcomers to the field, the book provides a comprehensive and fast-track introduction to the content, to save time and get on with tackling new and emerging challenges. For researchers, exposure to the state of the art of research works leads to an overall view of the entire field so as to guide new research directions and avoid pitfalls in moving the field forward and looking into the next decades of imaging and information services. This work can greatly benefit graduate students, researchers, and practitioners in imaging and vision; applied mathematicians; medical imagers; engineers; and computer scientists.

Geometric Partial Differential Equations and Image Analysis

Author : Guillermo Sapiro
Publisher :
ISBN 13 : 9780521790758
Total Pages : 385 pages
Book Rating : 4.7/5 (97 download)

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Book Synopsis Geometric Partial Differential Equations and Image Analysis by : Guillermo Sapiro

Download or read book Geometric Partial Differential Equations and Image Analysis written by Guillermo Sapiro and published by . This book was released on 2001-01-01 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.