A Blossoming Development Of Splines

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Blossoming Development of Splines

Author : Stephen Mann
Publisher : Springer Nature
ISBN 13 : 3031795164
Total Pages : 97 pages
Book Rating : 4.0/5 (317 download)

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Book Synopsis Blossoming Development of Splines by : Stephen Mann

Download or read book Blossoming Development of Splines written by Stephen Mann and published by Springer Nature. This book was released on 2022-05-31 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this lecture, we study Bézier and B-spline curves and surfaces, mathematical representations for free-form curves and surfaces that are common in CAD systems and are used to design aircraft and automobiles, as well as in modeling packages used by the computer animation industry. Bézier/B-splines represent polynomials and piecewise polynomials in a geometric manner using sets of control points that define the shape of the surface. The primary analysis tool used in this lecture is blossoming, which gives an elegant labeling of the control points that allows us to analyze their properties geometrically. Blossoming is used to explore both Bézier and B-spline curves, and in particular to investigate continuity properties, change of basis algorithms, forward differencing, B-spline knot multiplicity, and knot insertion algorithms. We also look at triangle diagrams (which are closely related to blossoming), direct manipulation of B-spline curves, NURBS curves, and triangular and tensor product surfaces.

A Blossoming Development of Splines

Author : Stephen Mann
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1598291165
Total Pages : 109 pages
Book Rating : 4.5/5 (982 download)

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Book Synopsis A Blossoming Development of Splines by : Stephen Mann

Download or read book A Blossoming Development of Splines written by Stephen Mann and published by Morgan & Claypool Publishers. This book was released on 2006 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this lecture, author Stephen Mann presents Bezier and B-spline curves and surfaces, mathematical representations for free-form curves and surfaces that are common in CAD systems. They are used to design aircraft and automobiles, as well as having uses in modeling packages used by the computer animation industry. Bezier/B-splines represent polynomials and piecewise polynomials in a geometric manner using sets of control points that define the shape of the surface.The primary analysis tool used in this lecture is blossoming, which gives an elegant labeling of the control points that allow us to analyze their properties geometrically. Blossoming is used to explore both Bezier and B-spline curves, and in particular to investigate continuity properties, change of basis algorithms, forward differencing, B-spline knot multiplicity, and knot insertion algorithms. We also look at triangle diagrams (which are closely related to blossoming), direct manipulation of B-spline curves, NURBS curves, and triangular and tensor product surfaces.

Pyramid Algorithms

Author : Ron Goldman
Publisher : Elsevier
ISBN 13 : 0080515479
Total Pages : 577 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Pyramid Algorithms by : Ron Goldman

Download or read book Pyramid Algorithms written by Ron Goldman and published by Elsevier. This book was released on 2002-07-16 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pyramid Algorithms presents a unique approach to understanding, analyzing, and computing the most common polynomial and spline curve and surface schemes used in computer-aided geometric design, employing a dynamic programming method based on recursive pyramids. The recursive pyramid approach offers the distinct advantage of revealing the entire structure of algorithms, as well as relationships between them, at a glance. This book-the only one built around this approach-is certain to change the way you think about CAGD and the way you perform it, and all it requires is a basic background in calculus and linear algebra, and simple programming skills.* Written by one of the world's most eminent CAGD researchers* Designed for use as both a professional reference and a textbook, and addressed to computer scientists, engineers, mathematicians, theoreticians, and students alike* Includes chapters on Bezier curves and surfaces, B-splines, blossoming, and multi-sided Bezier patches* Relies on an easily understood notation, and concludes each section with both practical and theoretical exercises that enhance and elaborate upon the discussion in the text* Foreword by Professor Helmut Pottmann, Vienna University of Technology

Heterogeneous Spatial Data

Author : Giuseppe Patanè
Publisher : Springer Nature
ISBN 13 : 303102589X
Total Pages : 129 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Heterogeneous Spatial Data by : Giuseppe Patanè

Download or read book Heterogeneous Spatial Data written by Giuseppe Patanè and published by Springer Nature. This book was released on 2022-05-31 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: New data acquisition techniques are emerging and are providing fast and efficient means for multidimensional spatial data collection. Airborne LIDAR surveys, SAR satellites, stereo-photogrammetry and mobile mapping systems are increasingly used for the digital reconstruction of the environment. All these systems provide extremely high volumes of raw data, often enriched with other sensor data (e.g., beam intensity). Improving methods to process and visually analyze this massive amount of geospatial and user-generated data is crucial to increase the efficiency of organizations and to better manage societal challenges. Within this context, this book proposes an up-to-date view of computational methods and tools for spatio-temporal data fusion, multivariate surface generation, and feature extraction, along with their main applications for surface approximation and rainfall analysis. The book is intended to attract interest from different fields, such as computer vision, computer graphics, geomatics, and remote sensing, working on the common goal of processing 3D data. To this end, it presents and compares methods that process and analyze the massive amount of geospatial data in order to support better management of societal challenges through more timely and better decision making, independent of a specific data modeling paradigm (e.g., 2D vector data, regular grids or 3D point clouds). We also show how current research is developing from the traditional layered approach, adopted by most GIS softwares, to intelligent methods for integrating existing data sets that might contain important information on a geographical area and environmental phenomenon. These services combine traditional map-oriented visualization with fully 3D visual decision support methods and exploit semantics-oriented information (e.g., a-priori knowledge, annotations, segmentations) when processing, merging, and integrating big pre-existing data sets.

Rethinking Quaternions

Author : Ron Goldman
Publisher : Springer Nature
ISBN 13 : 3031795490
Total Pages : 157 pages
Book Rating : 4.0/5 (317 download)

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Book Synopsis Rethinking Quaternions by : Ron Goldman

Download or read book Rethinking Quaternions written by Ron Goldman and published by Springer Nature. This book was released on 2022-05-31 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quaternion multiplication can be used to rotate vectors in three-dimensions. Therefore, in computer graphics, quaternions have three principal applications: to increase speed and reduce storage for calculations involving rotations, to avoid distortions arising from numerical inaccuracies caused by floating point computations with rotations, and to interpolate between two rotations for key frame animation. Yet while the formal algebra of quaternions is well-known in the graphics community, the derivations of the formulas for this algebra and the geometric principles underlying this algebra are not well understood. The goals of this monograph are to provide a fresh, geometric interpretation for quaternions, appropriate for contemporary computer graphics, based on mass-points; to present better ways to visualize quaternions, and the effect of quaternion multiplication on points and vectors in three dimensions using insights from the algebra and geometry of multiplication in the complex plane; to derive the formula for quaternion multiplication from first principles; to develop simple, intuitive proofs of the sandwiching formulas for rotation and reflection; to show how to apply sandwiching to compute perspective projections. In addition to these theoretical issues, we also address some computational questions. We develop straightforward formulas for converting back and forth between quaternion and matrix representations for rotations, reflections, and perspective projections, and we discuss the relative advantages and disadvantages of the quaternion and matrix representations for these transformations. Moreover, we show how to avoid distortions due to floating point computations with rotations by using unit quaternions to represent rotations. We also derive the formula for spherical linear interpolation, and we explain how to apply this formula to interpolate between two rotations for key frame animation. Finally, we explain the role of quaternions in low-dimensional Clifford algebras, and we show how to apply the Clifford algebra for R3 to model rotations, reflections, and perspective projections. To help the reader understand the concepts and formulas presented here, we have incorporated many exercises in order to clarify and elaborate some of the key points in the text. Table of Contents: Preface / Theory / Computation / Rethinking Quaternions and Clif ford Algebras / References / Further Reading / Author Biography

Introductory Tiling Theory for Computer Graphics

Author : Craig Kaplan
Publisher : Springer Nature
ISBN 13 : 3031795431
Total Pages : 103 pages
Book Rating : 4.0/5 (317 download)

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Book Synopsis Introductory Tiling Theory for Computer Graphics by : Craig Kaplan

Download or read book Introductory Tiling Theory for Computer Graphics written by Craig Kaplan and published by Springer Nature. This book was released on 2022-06-01 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tiling theory is an elegant branch of mathematics that has applications in several areas of computer science. The most immediate application area is graphics, where tiling theory has been used in the contexts of texture generation, sampling theory, remeshing, and of course the generation of decorative patterns. The combination of a solid theoretical base (complete with tantalizing open problems), practical algorithmic techniques, and exciting applications make tiling theory a worthwhile area of study for practitioners and students in computer science. This synthesis lecture introduces the mathematical and algorithmic foundations of tiling theory to a computer graphics audience. The goal is primarily to introduce concepts and terminology, clear up common misconceptions, and state and apply important results. The book also describes some of the algorithms and data structures that allow several aspects of tiling theory to be used in practice. Table of Contents: Introduction / Tiling Basics / Symmetry / Tilings by Polygons / Isohedral Tilings / Nonperiodic and Aperiodic Tilings / Survey

Mathematical Basics of Motion and Deformation in Computer Graphics, Second Edition

Author : Ken Anjyo
Publisher : Springer Nature
ISBN 13 : 303102592X
Total Pages : 79 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Mathematical Basics of Motion and Deformation in Computer Graphics, Second Edition by : Ken Anjyo

Download or read book Mathematical Basics of Motion and Deformation in Computer Graphics, Second Edition written by Ken Anjyo and published by Springer Nature. This book was released on 2022-06-01 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: This synthesis lecture presents an intuitive introduction to the mathematics of motion and deformation in computer graphics. Starting with familiar concepts in graphics, such as Euler angles, quaternions, and affine transformations, we illustrate that a mathematical theory behind these concepts enables us to develop the techniques for efficient/effective creation of computer animation. This book, therefore, serves as a good guidepost to mathematics (differential geometry and Lie theory) for students of geometric modeling and animation in computer graphics. Experienced developers and researchers will also benefit from this book, since it gives a comprehensive overview of mathematical approaches that are particularly useful in character modeling, deformation, and animation.

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.

Information Theory Tools for Image Processing

Author : Miquel Feixas
Publisher : Springer Nature
ISBN 13 : 3031795555
Total Pages : 148 pages
Book Rating : 4.0/5 (317 download)

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Book Synopsis Information Theory Tools for Image Processing by : Miquel Feixas

Download or read book Information Theory Tools for Image Processing written by Miquel Feixas and published by Springer Nature. This book was released on 2022-06-01 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Information Theory (IT) tools, widely used in many scientific fields such as engineering, physics, genetics, neuroscience, and many others, are also useful transversal tools in image processing. In this book, we present the basic concepts of IT and how they have been used in the image processing areas of registration, segmentation, video processing, and computational aesthetics. Some of the approaches presented, such as the application of mutual information to registration, are the state of the art in the field. All techniques presented in this book have been previously published in peer-reviewed conference proceedings or international journals. We have stressed here their common aspects, and presented them in an unified way, so to make clear to the reader which problems IT tools can help to solve, which specific tools to use, and how to apply them. The IT basics are presented so as to be self-contained in the book. The intended audiences are students and practitioners of image processing and related areas such as computer graphics and visualization. In addition, students and practitioners of IT will be interested in knowing about these applications. Table of Contents: Preface / Acknowledgments / Information Theory Basics / Image Registration / Image Segmentation / Video Key Frame Selection / Informational Aesthetics Measures / Bibliography / Authors' Biographies

Geometric and Discrete Path Planning for Interactive Virtual Worlds

Author : Marcelo Kallmann
Publisher : Springer Nature
ISBN 13 : 3031025881
Total Pages : 181 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Geometric and Discrete Path Planning for Interactive Virtual Worlds by : Marcelo Kallmann

Download or read book Geometric and Discrete Path Planning for Interactive Virtual Worlds written by Marcelo Kallmann and published by Springer Nature. This book was released on 2022-05-31 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: Path planning and navigation are indispensable components for controlling autonomous agents in interactive virtual worlds. Given the growing demands on the size and complexity of modern virtual worlds, a number of new techniques have been developed for achieving intelligent navigation for the next generation of interactive multi-agent simulations. This book reviews the evolution of several related techniques, starting from classical planning and computational geometry techniques and then gradually moving toward more advanced topics with focus on recent developments from the work of the authors. The covered topics range from discrete search and geometric representations to planning under different types of constraints and harnessing the power of graphics hardware in order to address Euclidean shortest paths and discrete search for multiple agents under limited time budgets. The use of planning algorithms beyond path planning is also discussed in the areas of crowd animation and whole-body motion planning for virtual characters.

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.

Virtual Crowds

Author : Nuria Palechano
Publisher : Springer Nature
ISBN 13 : 3031792424
Total Pages : 176 pages
Book Rating : 4.0/5 (317 download)

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Book Synopsis Virtual Crowds by : Nuria Palechano

Download or read book Virtual Crowds written by Nuria Palechano and published by Springer Nature. This book was released on 2022-05-31 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are many applications of computer animation and simulation where it is necessary to model virtual crowds of autonomous agents. Some of these applications include site planning, education, entertainment, training, and human factors analysis for building evacuation. Other applications include simulations of scenarios where masses of people gather, flow, and disperse, such as transportation centers, sporting events, and concerts. Most crowd simulations include only basic locomotive behaviors possibly coupled with a few stochastic actions. Our goal in this survey is to establish a baseline of techniques and requirements for simulating large-scale virtual human populations. Sometimes, these populations might be mutually engaged in a common activity such as evacuation from a building or area; other times they may be going about their individual and personal agenda of work, play, leisure, travel, or spectator. Computational methods to model one set of requirements may not mesh well with good approaches to another. By including both crowd and individual goals and constraints into a comprehensive computational model, we expect to simulate the visual texture and contextual behaviors of groups of seemingly sentient beings. Table of Contents: Introduction / Crowd Simulation Methodology Survey / Individual Differences in Crowds / Framework (HiDAC + MACES + CAROSA) / HiDAC: Local Motion / MACES: Wayfinding with Communication and Roles / CAROSA: Functional Crowds / Initializing a Scenario / Evaluating Crowds

Numerical Methods for Linear Complementarity Problems in Physics-Based Animation

Author : Sarah Niebe
Publisher : Springer Nature
ISBN 13 : 3031795644
Total Pages : 151 pages
Book Rating : 4.0/5 (317 download)

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Book Synopsis Numerical Methods for Linear Complementarity Problems in Physics-Based Animation by : Sarah Niebe

Download or read book Numerical Methods for Linear Complementarity Problems in Physics-Based Animation written by Sarah Niebe and published by Springer Nature. This book was released on 2022-05-31 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear complementarity problems (LCPs) have for many years been used in physics-based animation to model contact forces between rigid bodies in contact. More recently, LCPs have found their way into the realm of fluid dynamics. Here, LCPs are used to model boundary conditions with fluid-wall contacts. LCPs have also started to appear in deformable models and granular simulations. There is an increasing need for numerical methods to solve the resulting LCPs with all these new applications. This book provides a numerical foundation for such methods, especially suited for use in computer graphics. This book is mainly intended for a researcher/Ph.D. student/post-doc/professor who wants to study the algorithms and do more work/research in this area. Programmers might have to invest some time brushing up on math skills, for this we refer to Appendices A and B. The reader should be familiar with linear algebra and differential calculus. We provide pseudo code for all the numerical methods, which should be comprehensible by any computer scientist with rudimentary programming skills. The reader can find an online supplementary code repository, containing Matlab implementations of many of the core methods covered in these notes, as well as a few Python implementations [Erleben, 2011]. Table of Contents: Introduction / Numerical Methods / Guide for Software and Selecting Methods / Bibliography / Authors' Biographies

Gazing at Games

Author : Veronica Sundstedt
Publisher : Springer Nature
ISBN 13 : 3031795520
Total Pages : 95 pages
Book Rating : 4.0/5 (317 download)

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Book Synopsis Gazing at Games by : Veronica Sundstedt

Download or read book Gazing at Games written by Veronica Sundstedt and published by Springer Nature. This book was released on 2022-05-31 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eye tracking is a process that identifies a specific point in both space and time that is being looked at by the observer. This information can also be used in real-time to control applications using the eyes. Recent innovations in the video game industry include alternative input modalities to provide an enhanced, more immersive user experience. In particular, eye gaze control has recently been explored as an input modality in video games. This book is an introduction for those interested in using eye tracking to control or analyze video games and virtual environments. Key concepts are illustrated through three case studies in which gaze control and voice recognition have been used in combination to control virtual characters and applications. The lessons learned in the case studies are presented and issues relating to incorporating eye tracking in interactive applications are discussed. The reader will be given an introduction to human visual attention, eye movements and eye tracking technologies. Previous work in the field of studying fixation behavior in games and using eye tracking for video game interaction will also be presented. The final chapter discusses ideas for how this field can be developed further to create richer interaction for characters and crowds in virtual environments. Alternative means of interaction in video games are especially important for disabled users for whom traditional techniques, such as mouse and keyboard, may be far from ideal. This book is also relevant for those wishing to use gaze control in applications other than games. Table of Contents: Introduction / The Human Visual System / Eye Tracking / Eye Tracking in Video Games / Gaze and Voice Controlled Video Games: Case Study I and II / Gaze and Voice Controlled Drawing: Case Study III / Conclusion

Efficient Quadrature Rules for Illumination Integrals

Author : Ricardo Marques
Publisher : Springer Nature
ISBN 13 : 3031795679
Total Pages : 82 pages
Book Rating : 4.0/5 (317 download)

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Book Synopsis Efficient Quadrature Rules for Illumination Integrals by : Ricardo Marques

Download or read book Efficient Quadrature Rules for Illumination Integrals written by Ricardo Marques and published by Springer Nature. This book was released on 2022-06-01 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rendering photorealistic images is a costly process which can take up to several days in the case of high quality images. In most cases, the task of sampling the incident radiance function to evaluate the illumination integral is responsible for an important share of the computation time. Therefore, to reach acceptable rendering times, the illumination integral must be evaluated using a limited set of samples. Such a restriction raises the question of how to obtain the most accurate approximation possible with such a limited set of samples. One must thus ensure that sampling produces the highest amount of information possible by carefully placing and weighting the limited set of samples. Furthermore, the integral evaluation should take into account not only the information brought by sampling but also possible information available prior to sampling, such as the integrand smoothness. This idea of sparse information and the need to fully exploit the little information available is present throughout this book. The presented methods correspond to the state-of-the-art solutions in computer graphics, and take into account information which had so far been underexploited (or even neglected) by the previous approaches. The intended audiences are Ph.D. students and researchers in the field of realistic image synthesis or global illumination algorithms, or any person with a solid background in graphics and numerical techniques.

An Introduction to Verification of Visualization Techniques

Author : Tiago Etiene
Publisher : Springer Nature
ISBN 13 : 3031025873
Total Pages : 80 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis An Introduction to Verification of Visualization Techniques by : Tiago Etiene

Download or read book An Introduction to Verification of Visualization Techniques written by Tiago Etiene and published by Springer Nature. This book was released on 2022-06-01 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: As we increase our reliance on computer-generated information, often using it as part of our decision-making process, we must devise tools to assess the correctness of that information. Consider, for example, software embedded on vehicles, used for simulating aircraft performance, or used in medical imaging. In those cases, software correctness is of paramount importance as there's little room for error. Software verification is one of the tools available to attain such goals. Verification is a well known and widely studied subfield of computer science and computational science and the goal is to help us increase confidence in the software implementation by verifying that the software does what it is supposed to do. The goal of this book is to introduce the reader to software verification in the context of visualization. In the same way we became more dependent on commercial software, we have also increased our reliance on visualization software. The reason is simple: visualization is the lens through which users can understand complex data, and as such it must be verified. The explosion in our ability to amass data requires tools not only to store and analyze data, but also to visualize it. This book is comprised of six chapters. After an introduction to the goals of the book, we present a brief description of both worlds of visualization (Chapter 2) and verification (Chapter 3). We then proceed to illustrate the main steps of the verification pipeline for visualization algorithms. We focus on two classic volume visualization techniques, namely, Isosurface Extraction (Chapter 4) and Direct Volume Rendering (Chapter 5). We explain how to verify implementations of those techniques and report the latest results in the field of verification of visualization techniques. The last chapter 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 : 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.