Shape and Shape Theory

Shape and Shape Theory

Author: D. G. Kendall

Publisher: John Wiley & Sons

Published: 2009-09-25

Total Pages: 318

ISBN-13: 0470317841

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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/


Book Synopsis Shape and Shape Theory by : D. G. Kendall

Download or read book Shape and Shape Theory written by D. G. Kendall and published by John Wiley & Sons. This book was released on 2009-09-25 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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/

The Statistical Theory of Shape

The Statistical Theory of Shape

Author: Christopher G. Small

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 237

ISBN-13: 1461240328

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In general terms, the shape of an object, data set, or image can be de fined as the total of all information that is invariant under translations, rotations, and isotropic rescalings. Thus two objects can be said to have the same shape if they are similar in the sense of Euclidean geometry. For example, all equilateral triangles have the same shape, and so do all cubes. In applications, bodies rarely have exactly the same shape within measure ment error. In such cases the variation in shape can often be the subject of statistical analysis. The last decade has seen a considerable growth in interest in the statis tical theory of shape. This has been the result of a synthesis of a number of different areas and a recognition that there is considerable common ground among these areas in their study of shape variation. Despite this synthesis of disciplines, there are several different schools of statistical shape analysis. One of these, the Kendall school of shape analysis, uses a variety of mathe matical tools from differential geometry and probability, and is the subject of this book. The book does not assume a particularly strong background by the reader in these subjects, and so a brief introduction is provided to each of these topics. Anyone who is unfamiliar with this material is advised to consult a more complete reference. As the literature on these subjects is vast, the introductory sections can be used as a brief guide to the literature.


Book Synopsis The Statistical Theory of Shape by : Christopher G. Small

Download or read book The Statistical Theory of Shape written by Christopher G. Small and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: In general terms, the shape of an object, data set, or image can be de fined as the total of all information that is invariant under translations, rotations, and isotropic rescalings. Thus two objects can be said to have the same shape if they are similar in the sense of Euclidean geometry. For example, all equilateral triangles have the same shape, and so do all cubes. In applications, bodies rarely have exactly the same shape within measure ment error. In such cases the variation in shape can often be the subject of statistical analysis. The last decade has seen a considerable growth in interest in the statis tical theory of shape. This has been the result of a synthesis of a number of different areas and a recognition that there is considerable common ground among these areas in their study of shape variation. Despite this synthesis of disciplines, there are several different schools of statistical shape analysis. One of these, the Kendall school of shape analysis, uses a variety of mathe matical tools from differential geometry and probability, and is the subject of this book. The book does not assume a particularly strong background by the reader in these subjects, and so a brief introduction is provided to each of these topics. Anyone who is unfamiliar with this material is advised to consult a more complete reference. As the literature on these subjects is vast, the introductory sections can be used as a brief guide to the literature.

A Theory of Shape Identification

A Theory of Shape Identification

Author: Frédéric Cao

Publisher: Springer

Published: 2008-08-17

Total Pages: 260

ISBN-13: 3540684816

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Recent years have seen dramatic progress in shape recognition algorithms applied to ever-growing image databases. They have been applied to image stitching, stereo vision, image mosaics, solid object recognition and video or web image retrieval. More fundamentally, the ability of humans and animals to detect and recognize shapes is one of the enigmas of perception. The book describes a complete method that starts from a query image and an image database and yields a list of the images in the database containing shapes present in the query image. A false alarm number is associated to each detection. Many experiments will show that familiar simple shapes or images can reliably be identified with false alarm numbers ranging from 10-5 to less than 10-300. Technically speaking, there are two main issues. The first is extracting invariant shape descriptors from digital images. Indeed, a shape can be seen from various angles and distances and in various lights.


Book Synopsis A Theory of Shape Identification by : Frédéric Cao

Download or read book A Theory of Shape Identification written by Frédéric Cao and published by Springer. This book was released on 2008-08-17 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent years have seen dramatic progress in shape recognition algorithms applied to ever-growing image databases. They have been applied to image stitching, stereo vision, image mosaics, solid object recognition and video or web image retrieval. More fundamentally, the ability of humans and animals to detect and recognize shapes is one of the enigmas of perception. The book describes a complete method that starts from a query image and an image database and yields a list of the images in the database containing shapes present in the query image. A false alarm number is associated to each detection. Many experiments will show that familiar simple shapes or images can reliably be identified with false alarm numbers ranging from 10-5 to less than 10-300. Technically speaking, there are two main issues. The first is extracting invariant shape descriptors from digital images. Indeed, a shape can be seen from various angles and distances and in various lights.

How Things Shape the Mind

How Things Shape the Mind

Author: Lambros Malafouris

Publisher: MIT Press

Published: 2016-02-12

Total Pages: 321

ISBN-13: 0262528924

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An account of the different ways in which things have become cognitive extensions of the human body, from prehistory to the present. An increasingly influential school of thought in cognitive science views the mind as embodied, extended, and distributed rather than brain-bound or “all in the head.” This shift in perspective raises important questions about the relationship between cognition and material culture, posing major challenges for philosophy, cognitive science, archaeology, and anthropology. In How Things Shape the Mind, Lambros Malafouris proposes a cross-disciplinary analytical framework for investigating the ways in which things have become cognitive extensions of the human body. Using a variety of examples and case studies, he considers how those ways might have changed from earliest prehistory to the present. Malafouris's Material Engagement Theory definitively adds materiality—the world of things, artifacts, and material signs—into the cognitive equation. His account not only questions conventional intuitions about the boundaries and location of the human mind but also suggests that we rethink classical archaeological assumptions about human cognitive evolution.


Book Synopsis How Things Shape the Mind by : Lambros Malafouris

Download or read book How Things Shape the Mind written by Lambros Malafouris and published by MIT Press. This book was released on 2016-02-12 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: An account of the different ways in which things have become cognitive extensions of the human body, from prehistory to the present. An increasingly influential school of thought in cognitive science views the mind as embodied, extended, and distributed rather than brain-bound or “all in the head.” This shift in perspective raises important questions about the relationship between cognition and material culture, posing major challenges for philosophy, cognitive science, archaeology, and anthropology. In How Things Shape the Mind, Lambros Malafouris proposes a cross-disciplinary analytical framework for investigating the ways in which things have become cognitive extensions of the human body. Using a variety of examples and case studies, he considers how those ways might have changed from earliest prehistory to the present. Malafouris's Material Engagement Theory definitively adds materiality—the world of things, artifacts, and material signs—into the cognitive equation. His account not only questions conventional intuitions about the boundaries and location of the human mind but also suggests that we rethink classical archaeological assumptions about human cognitive evolution.

Number, Shape, & Symmetry

Number, Shape, & Symmetry

Author: Diane L. Herrmann

Publisher: CRC Press

Published: 2012-10-18

Total Pages: 446

ISBN-13: 1466554649

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Through a careful treatment of number theory and geometry, Number, Shape, & Symmetry: An Introduction to Number Theory, Geometry, and Group Theory helps readers understand serious mathematical ideas and proofs. Classroom-tested, the book draws on the authors’ successful work with undergraduate students at the University of Chicago, seventh to tenth grade mathematically talented students in the University of Chicago’s Young Scholars Program, and elementary public school teachers in the Seminars for Endorsement in Science and Mathematics Education (SESAME). The first half of the book focuses on number theory, beginning with the rules of arithmetic (axioms for the integers). The authors then present all the basic ideas and applications of divisibility, primes, and modular arithmetic. They also introduce the abstract notion of a group and include numerous examples. The final topics on number theory consist of rational numbers, real numbers, and ideas about infinity. Moving on to geometry, the text covers polygons and polyhedra, including the construction of regular polygons and regular polyhedra. It studies tessellation by looking at patterns in the plane, especially those made by regular polygons or sets of regular polygons. The text also determines the symmetry groups of these figures and patterns, demonstrating how groups arise in both geometry and number theory. The book is suitable for pre-service or in-service training for elementary school teachers, general education mathematics or math for liberal arts undergraduate-level courses, and enrichment activities for high school students or math clubs.


Book Synopsis Number, Shape, & Symmetry by : Diane L. Herrmann

Download or read book Number, Shape, & Symmetry written by Diane L. Herrmann and published by CRC Press. This book was released on 2012-10-18 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through a careful treatment of number theory and geometry, Number, Shape, & Symmetry: An Introduction to Number Theory, Geometry, and Group Theory helps readers understand serious mathematical ideas and proofs. Classroom-tested, the book draws on the authors’ successful work with undergraduate students at the University of Chicago, seventh to tenth grade mathematically talented students in the University of Chicago’s Young Scholars Program, and elementary public school teachers in the Seminars for Endorsement in Science and Mathematics Education (SESAME). The first half of the book focuses on number theory, beginning with the rules of arithmetic (axioms for the integers). The authors then present all the basic ideas and applications of divisibility, primes, and modular arithmetic. They also introduce the abstract notion of a group and include numerous examples. The final topics on number theory consist of rational numbers, real numbers, and ideas about infinity. Moving on to geometry, the text covers polygons and polyhedra, including the construction of regular polygons and regular polyhedra. It studies tessellation by looking at patterns in the plane, especially those made by regular polygons or sets of regular polygons. The text also determines the symmetry groups of these figures and patterns, demonstrating how groups arise in both geometry and number theory. The book is suitable for pre-service or in-service training for elementary school teachers, general education mathematics or math for liberal arts undergraduate-level courses, and enrichment activities for high school students or math clubs.

Shape Theory

Shape Theory

Author: J. Dydak

Publisher: Springer

Published: 2006-11-15

Total Pages: 156

ISBN-13: 3540356843

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Book Synopsis Shape Theory by : J. Dydak

Download or read book Shape Theory written by J. Dydak and published by Springer. This book was released on 2006-11-15 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Shape Theory

Shape Theory

Author: Sibe Mardešić

Publisher: North Holland

Published: 1982

Total Pages: 404

ISBN-13:

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Book Synopsis Shape Theory by : Sibe Mardešić

Download or read book Shape Theory written by Sibe Mardešić and published by North Holland. This book was released on 1982 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Shape Theory

Shape Theory

Author: J. M. Cordier

Publisher: Courier Corporation

Published: 2013-12-01

Total Pages: 212

ISBN-13: 0486783472

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This in-depth treatment uses shape theory as a "case study" to illustrate situations common to many areas of mathematics, including the use of archetypal models as a basis for systems of approximations. It offers students a unified and consolidated presentation of extensive research from category theory, shape theory, and the study of topological algebras. A short introduction to geometric shape explains specifics of the construction of the shape category and relates it to an abstract definition of shape theory. Upon returning to the geometric base, the text considers simplical complexes and numerable covers, in addition to Morita's form of shape theory. Subsequent chapters explore Bénabou's theory of distributors, the theory of exact squares, Kan extensions, the notion of a stable object, and stability in an Abelian context. The text concludes with a brief description of derived functors of the limit functor theory—the concept that leads to movability and strong movability of systems—and illustrations of the equivalence of strong movability and stability in many contexts.


Book Synopsis Shape Theory by : J. M. Cordier

Download or read book Shape Theory written by J. M. Cordier and published by Courier Corporation. This book was released on 2013-12-01 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This in-depth treatment uses shape theory as a "case study" to illustrate situations common to many areas of mathematics, including the use of archetypal models as a basis for systems of approximations. It offers students a unified and consolidated presentation of extensive research from category theory, shape theory, and the study of topological algebras. A short introduction to geometric shape explains specifics of the construction of the shape category and relates it to an abstract definition of shape theory. Upon returning to the geometric base, the text considers simplical complexes and numerable covers, in addition to Morita's form of shape theory. Subsequent chapters explore Bénabou's theory of distributors, the theory of exact squares, Kan extensions, the notion of a stable object, and stability in an Abelian context. The text concludes with a brief description of derived functors of the limit functor theory—the concept that leads to movability and strong movability of systems—and illustrations of the equivalence of strong movability and stability in many contexts.

Theory of the Earth's Shape

Theory of the Earth's Shape

Author: V.C. Dragomir

Publisher: Elsevier

Published: 2017-01-31

Total Pages: 705

ISBN-13: 1483291898

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Theory of the Earth's Shape considers the physical-mathematical problems raised by the determination of the form of the planet, thereby making a significant contribution to the technological scientific literature in this field. This book is organized into six parts encompassing 29 chapters. The first part, entitled Physical Geodesy, presents the theory of the determination of the gravitational field, in the definition of which preference was given to the method of expansion in spherical harmonics recommended by the International Union of Geodesy and Geophysics in establishing the international "Geodetic Reference System 1967". Part II deals with the principal aspects of Ellipsoidal Geodesy, such as the methods of solving the geodetic problems on the reference ellipsoid. Part III considers the main problems associated with Astro-geodetic Triangulation, particularly with the conception of materialization and the necessary measurements as the required adjustment procedures. This part also provides approaches regarding the controlled analysis of angular measurements and the description of some original calculation and measurement methods. Part IV concerns one of the methods of determining the spatial coordinates of the geodetic points in a unitary system, such as the three-dimensional geodesy, which has had more concrete applications since the launching of the Earth's first artificial satellites. Part V describes the methods for determining the terrestrial ellipsoid and the geoid, as well as the conventional methods and the methods of Dynamical Geodesy. Part VI discusses the geodetic methods for the determination of the movements of the Earth's crust, along with an overall examination of the theoretical and practical aspects which in principle constitute the object of such activities.


Book Synopsis Theory of the Earth's Shape by : V.C. Dragomir

Download or read book Theory of the Earth's Shape written by V.C. Dragomir and published by Elsevier. This book was released on 2017-01-31 with total page 705 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory of the Earth's Shape considers the physical-mathematical problems raised by the determination of the form of the planet, thereby making a significant contribution to the technological scientific literature in this field. This book is organized into six parts encompassing 29 chapters. The first part, entitled Physical Geodesy, presents the theory of the determination of the gravitational field, in the definition of which preference was given to the method of expansion in spherical harmonics recommended by the International Union of Geodesy and Geophysics in establishing the international "Geodetic Reference System 1967". Part II deals with the principal aspects of Ellipsoidal Geodesy, such as the methods of solving the geodetic problems on the reference ellipsoid. Part III considers the main problems associated with Astro-geodetic Triangulation, particularly with the conception of materialization and the necessary measurements as the required adjustment procedures. This part also provides approaches regarding the controlled analysis of angular measurements and the description of some original calculation and measurement methods. Part IV concerns one of the methods of determining the spatial coordinates of the geodetic points in a unitary system, such as the three-dimensional geodesy, which has had more concrete applications since the launching of the Earth's first artificial satellites. Part V describes the methods for determining the terrestrial ellipsoid and the geoid, as well as the conventional methods and the methods of Dynamical Geodesy. Part VI discusses the geodetic methods for the determination of the movements of the Earth's crust, along with an overall examination of the theoretical and practical aspects which in principle constitute the object of such activities.

The Shape of Inner Space

The Shape of Inner Space

Author: Shing-Tung Yau

Publisher: Il Saggiatore

Published: 2010-09-07

Total Pages: 398

ISBN-13: 0465020232

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The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations.


Book Synopsis The Shape of Inner Space by : Shing-Tung Yau

Download or read book The Shape of Inner Space written by Shing-Tung Yau and published by Il Saggiatore. This book was released on 2010-09-07 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations.