Mathematics Of Shapes And Applications

Author : Sergey Kushnarev,Anqi Qiu,Laurent Younes
Publisher : World Scientific
Page : 220 pages
File Size : 50,5 Mb
Release : 2019-11-20
Category : Mathematics
ISBN : 9789811200144

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Mathematics Of Shapes And Applications by Sergey Kushnarev,Anqi Qiu,Laurent Younes Pdf

Understanding how a single shape can incur a complex range of transformations, while defining the same perceptually obvious figure, entails a rich and challenging collection of problems, at the interface between applied mathematics, statistics and computer science. The program on Mathematics of Shapes and Applications, was held at the Institute for Mathematical Sciences at the National University of Singapore in 2016. It provided discussions on theoretical developments and numerous applications in computer vision, object recognition and medical imaging.The analysis of shapes is an example of a mathematical problem directly connected with applications while offering deep open challenges to theoretical mathematicians. It has grown, over the past decades, into an interdisciplinary area in which researchers studying infinite-dimensional Riemannian manifolds (global analysis) interact with applied mathematicians, statisticians, computer scientists and biomedical engineers on a variety of problems involving shapes.The volume illustrates this wealth of subjects by providing new contributions on the metric structure of diffeomorphism groups and shape spaces, recent developments on deterministic and stochastic models of shape evolution, new computational methods manipulating shapes, and new statistical tools to analyze shape datasets. In addition to these contributions, applications of shape analysis to medical imaging and computational anatomy are discussed, leading, in particular, to improved understanding of the impact of cognitive diseases on the geometry of the brain.

Author : D. G. Kendall,D. Barden,T. K. Carne,H. Le
Publisher : John Wiley & Sons
Page : 318 pages
File Size : 53,6 Mb
Release : 2009-09-25
Category : Mathematics
ISBN : 9780470317846

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Shape and Shape Theory by D. G. Kendall,D. Barden,T. K. Carne,H. Le Pdf

Shape and Shape Theory D. G. Kendall Churchill College, University of Cambridge, UK D. Barden Girton College, University of Cambridge, UK T. K. Carne King's College, University of Cambridge, UK H. Le University of Nottingham, UK The statistical theory of shape is a relatively new topic and is generating a great deal of interest and comment by statisticians, engineers and computer scientists. Mathematically, 'shape' is the geometrical information required to describe an object when location, scale and rotational effects are removed. The theory was pioneered by Professor David Kendall to solve practical problems concerning shape. This text presents an elegant account of the theory of shape that has evolved from Kendall's work. Features include: * A comprehensive account of Kendall's shape spaces * A variety of topological and geometric invariants of these spaces * Emphasis on the mathematical aspects of shape analysis * Coverage of the mathematical issues for a wide range of applications The early chapters provide all the necessary background information, including the history and applications of shape theory. The authors then go on to analyse the topic, in brilliant detail, in a variety of different shape spaces. Kendall's own procedures for visualising distributions of shapes and shape processes are covered at length. Implications from other branches of mathematics are explored, along with more advanced applications, incorporating statistics and stochastic analysis. Applied statisticians, applied mathematicians, engineers and computer scientists working and researching in the fields of archaeology, astronomy, biology, geography and physical chemistry will find this book of great benefit. The theories presented are used today in a wide range of subjects from archaeology through to physics, and will provide fascinating reading to anyone engaged in such research. Visit our web page! http://www.wiley.com/

Author : Ying-Lie O,Alexander Toet,David Foster,Henk J.A.M. Heijmans,Peter Meer
Publisher : Springer Science & Business Media
Page : 685 pages
File Size : 44,9 Mb
Release : 2013-04-17
Category : Computers
ISBN : 9783662030394

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Shape in Picture by Ying-Lie O,Alexander Toet,David Foster,Henk J.A.M. Heijmans,Peter Meer Pdf

The fields of image analysis, computer vision, and artificial intelligence all make use of descriptions of shape in grey-level images. Most existing algorithms for the automatic recognition and classification of particular shapes have been devel oped for specific purposes, with the result that these methods are often restricted in their application. The use of advanced and theoretically well-founded math ematical methods should lead to the construction of robust shape descriptors having more general application. Shape description can be regarded as a meeting point of vision research, mathematics, computing science, and the application fields of image analy sis, computer vision, and artificial intelligence. The NATO Advanced Research Workshop "Shape in Picture" was organised with a twofold objective: first, it should provide all participants with an overview of relevant developments in these different disciplines; second, it should stimulate researchers to exchange original results and ideas across the boundaries of these disciplines. This book comprises a widely drawn selection of papers presented at the workshop, and many contributions have been revised to reflect further progress in the field. The focus of this collection is on mathematical approaches to the construction of shape descriptions from grey-level images. The book is divided into five parts, each devoted to a different discipline. Each part contains papers that have tutorial sections; these are intended to assist the reader in becoming acquainted with the variety of approaches to the problem.

Author : Laurent Younes
Publisher : Springer Science & Business Media
Page : 438 pages
File Size : 42,7 Mb
Release : 2010-05-17
Category : Mathematics
ISBN : 9783642120558

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Shapes and Diffeomorphisms by Laurent Younes Pdf

Shapes are complex objects to apprehend, as mathematical entities, in terms that also are suitable for computerized analysis and interpretation. This volume provides the background that is required for this purpose, including different approaches that can be used to model shapes, and algorithms that are available to analyze them. It explores, in particular, the interesting connections between shapes and the objects that naturally act on them, diffeomorphisms. The book is, as far as possible, self-contained, with an appendix that describes a series of classical topics in mathematics (Hilbert spaces, differential equations, Riemannian manifolds) and sections that represent the state of the art in the analysis of shapes and their deformations. A direct application of what is presented in the book is a branch of the computerized analysis of medical images, called computational anatomy.

Author : Eric A. Lord,C. B. Wilson
Publisher : Unknown
Page : 260 pages
File Size : 51,8 Mb
Release : 1984
Category : Geometry
ISBN : 0853127220

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The Mathematical Description of Shape and Form by Eric A. Lord,C. B. Wilson Pdf

Author : Laurent Younes
Publisher : Springer
Page : 558 pages
File Size : 41,6 Mb
Release : 2019-05-17
Category : Mathematics
ISBN : 9783662584965

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Shapes and Diffeomorphisms by Laurent Younes Pdf

This book covers mathematical foundations and methods for the computerized analysis of shapes, providing the requisite background in geometry and functional analysis and introducing various algorithms and approaches to shape modeling, with a special focus on the interesting connections between shapes and their transformations by diffeomorphisms. A direct application is to computational anatomy, for which techniques such as large‒deformation diffeomorphic metric mapping and metamorphosis, among others, are presented. The appendices detail a series of classical topics (Hilbert spaces, differential equations, Riemannian manifolds, optimal control). The intended audience is applied mathematicians and mathematically inclined engineers interested in the topic of shape analysis and its possible applications in computer vision or medical imaging. The first part can be used for an advanced undergraduate course on differential geometry with a focus on applications while the later chapters are suitable for a graduate course on shape analysis through the action of diffeomorphisms. Several significant additions appear in the 2nd edition, most notably a new chapter on shape datasets, and a discussion of optimal control theory in an infinite-dimensional framework, which is then used to enrich the presentation of diffeomorphic matching.

Author : Akcayir, Gokce,Demmans Epp, Carrie
Publisher : IGI Global
Page : 404 pages
File Size : 48,9 Mb
Release : 2020-10-23
Category : Education
ISBN : 9781799850441

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Designing, Deploying, and Evaluating Virtual and Augmented Reality in Education by Akcayir, Gokce,Demmans Epp, Carrie Pdf

Augmented reality (AR) and virtual reality (VR) provide flexibility in education and have become widely used for the promotion of multimedia learning. This use coincides with mobile devices becoming prevalent, VR devices becoming more affordable, and the creation of user-friendly software that allows the development of AR/VR applications by non-experts. However, because the integration of AR and VR into education is a fairly new practice that is only in its initial stage, these processes and outcomes need to be improved. Designing, Deploying, and Evaluating Virtual and Augmented Reality in Education is an essential research book that presents current practices and procedures from different technology-implementation stages (design, deployment, and evaluation) to help educators use AR/VR applications in their own teaching practices. The book provides comprehensive information on AR and VR applications in different educational settings from various perspectives including but not limited to mobile learning, formal/informal learning, and integration strategies with practical and/or theoretical implications. Barriers and challenges to their implementation that are currently faced by educators are also addressed. This book is ideal for academicians, instructors, curriculum designers, policymakers, instructional designers, researchers, education professionals, practitioners, and students.

Author : Moira Anderson
Publisher : Teacher Created Materials
Page : 18 pages
File Size : 54,8 Mb
Release : 2008-10-10
Category : Education
ISBN : 9781433391484

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Shapes in Our World by Moira Anderson Pdf

Three-dimensional (3-D) shapes have three dimensions--length, width, and height. These shapes are solids that are found in buildings and structures as well as in nature. Some 3-D shapes are prisms, cylinders, cones, pyramids, and spheres.

Author : M. C. Delfour,J.-P. Zolesio
Publisher : SIAM
Page : 637 pages
File Size : 40,8 Mb
Release : 2011-01-01
Category : Mathematics
ISBN : 9780898719369

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Shapes and Geometries by M. C. Delfour,J.-P. Zolesio Pdf

Presents the latest groundbreaking theoretical foundation to shape optimization in a form accessible to mathematicians, scientists and engineers.

Author : Michael Breuß,Alfred Bruckstein,Petros Maragos
Publisher : Springer Science & Business Media
Page : 510 pages
File Size : 49,6 Mb
Release : 2013-04-04
Category : Mathematics
ISBN : 9783642341410

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Innovations for Shape Analysis by Michael Breuß,Alfred Bruckstein,Petros Maragos Pdf

The concept of 'shape' is at the heart of image processing and computer vision, yet researchers still have some way to go to replicate the human brain's ability to extrapolate meaning from the most basic of outlines. This volume reflects the advances of the last decade, which have also opened up tough new challenges in image processing. Today's applications require flexible models as well as efficient, mathematically justified algorithms that allow data processing within an acceptable timeframe. Examining important topics in continuous-scale and discrete modeling, as well as in modern algorithms, the book is the product of a key seminar focused on innovations in the field. It is a thorough introduction to the latest technology, especially given the tutorial style of a number of chapters. It also succeeds in identifying promising avenues for future research. The topics covered include mathematical morphology, skeletonization, statistical shape modeling, continuous-scale shape models such as partial differential equations and the theory of discrete shape descriptors. Some authors highlight new areas of enquiry such as partite skeletons, multi-component shapes, deformable shape models, and the use of distance fields. Combining the latest theoretical analysis with cutting-edge applications, this book will attract both academics and engineers.

Author : Hamid Krim,Anthony Yezzi
Publisher : Springer Science & Business Media
Page : 396 pages
File Size : 53,9 Mb
Release : 2007-12-31
Category : Mathematics
ISBN : 9780817644819

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Statistics and Analysis of Shapes by Hamid Krim,Anthony Yezzi Pdf

The subject of pattern analysis and recognition pervades many aspects of our daily lives, including user authentication in banking, object retrieval from databases in the consumer sector, and the omnipresent surveillance and security measures around sensitive areas. Shape analysis, a fundamental building block in many approaches to these applications, is also used in statistics, biomedical applications (Magnetic Resonance Imaging), and many other related disciplines. With contributions from some of the leading experts and pioneers in the field, this self-contained, unified volume is the first comprehensive treatment of theory, methods, and algorithms available in a single resource. Developments are discussed from a rapidly increasing number of research papers in diverse fields, including the mathematical and physical sciences, engineering, and medicine.

Author : Jing Hua,Zichun Zhong
Publisher : Academic Press
Page : 152 pages
File Size : 44,8 Mb
Release : 2020-01-15
Category : Computers
ISBN : 9780128138427

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Spectral Geometry of Shapes by Jing Hua,Zichun Zhong Pdf

Spectral Geometry of Shapes presents unique shape analysis approaches based on shape spectrum in differential geometry. It provides insights on how to develop geometry-based methods for 3D shape analysis. The book is an ideal learning resource for graduate students and researchers in computer science, computer engineering and applied mathematics who have an interest in 3D shape analysis, shape motion analysis, image analysis, medical image analysis, computer vision and computer graphics. Due to the rapid advancement of 3D acquisition technologies there has been a big increase in 3D shape data that requires a variety of shape analysis methods, hence the need for this comprehensive resource. Presents the latest advances in spectral geometric processing for 3D shape analysis applications, such as shape classification, shape matching, medical imaging, etc. Provides intuitive links between fundamental geometric theories and real-world applications, thus bridging the gap between theory and practice Describes new theoretical breakthroughs in applying spectral methods for non-isometric motion analysis Gives insights for developing spectral geometry-based approaches for 3D shape analysis and deep learning of shape geometry

Author : Pijush K. Ghosh,Koichiro Deguchi
Publisher : John Wiley & Sons
Page : 272 pages
File Size : 51,5 Mb
Release : 2009-03-04
Category : Technology & Engineering
ISBN : 9780470823088

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Mathematics of Shape Description by Pijush K. Ghosh,Koichiro Deguchi Pdf

Image processing problems are often not well defined because real images are contaminated with noise and other uncertain factors. In Mathematics of Shape Description, the authors take a mathematical approach to address these problems using the morphological and set-theoretic approach to image processing and computer graphics by presenting a simple shape model using two basic shape operators called Minkowski addition and decomposition. This book is ideal for professional researchers and engineers in Information Processing, Image Measurement, Shape Description, Shape Representation and Computer Graphics. Post-graduate and advanced undergraduate students in pure and applied mathematics, computer sciences, robotics and engineering will also benefit from this book. Key Features Explains the fundamental and advanced relationships between algebraic system and shape description through the set-theoretic approach Promotes interaction of image processing geochronology and mathematics in the field of algebraic geometry Provides a shape description scheme that is a notational system for the shape of objects Offers a thorough and detailed discussion on the mathematical characteristics and significance of the Minkowski operators

Author : Tor Dokken,Georg Muntingh
Publisher : Springer
Page : 323 pages
File Size : 51,8 Mb
Release : 2014-10-24
Category : Mathematics
ISBN : 9783319086354

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SAGA – Advances in ShApes, Geometry, and Algebra by Tor Dokken,Georg Muntingh Pdf

This book summarizes research carried out in workshops of the SAGA project, an Initial Training Network exploring the interplay of Shapes, Algebra, Geometry and Algorithms. Written by a combination of young and experienced researchers, the book introduces new ideas in an established context. Among the central topics are approximate and sparse implicitization and surface parametrization; algebraic tools for geometric computing; algebraic geometry for computer aided design applications and problems with industrial applications. Readers will encounter new methods for the (approximate) transition between the implicit and parametric representation; new algebraic tools for geometric computing; new applications of isogeometric analysis and will gain insight into the emerging research field situated between algebraic geometry and computer aided geometric design.

Author : Karl Kunisch,Günther Of,Olaf Steinbach
Publisher : Springer Science & Business Media
Page : 825 pages
File Size : 48,5 Mb
Release : 2008-09-19
Category : Mathematics
ISBN : 9783540697770

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Numerical Mathematics and Advanced Applications by Karl Kunisch,Günther Of,Olaf Steinbach Pdf

The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) is a series of conferences held every two years to provide a forum for discussion on recent aspects of numerical mathematics and their applications. The ?rst ENUMATH conference was held in Paris (1995), and the series continued by the one in Heidelberg (1997), Jyvaskyla (1999), Ischia (2001), Prague (2003), and Santiago de Compostela (2005). This volume contains a selection of invited plenary lectures, papers presented in minisymposia, and contributed papers of ENUMATH 2007, held in Graz, Austria, September 10–14, 2007. We are happy that so many people have shown their interest in this conference. In addition to the ten invited presentations and the public lecture, we had more than 240 talks in nine minisymposia and ?fty four sessions of contributed talks, and about 316 participants from all over the world, specially from Europe. A total of 98 contributions appear in these proceedings. Topics include theoretical aspects of new numerical techniques and algorithms, as well as to applications in engineering and science. The book will be useful for a wide range of readers, giving them an excellent overview of the most modern methods, techniques, algorithms and results in numerical mathematics, scienti?c computing and their applications. We would like to thank all the participants for the attendance and for their va- ablecontributionsanddiscussionsduringtheconference.Specialthanksgothe m- isymposium organizers, who made a large contribution to the conference, the chair persons, and all speakers.