Shape Theory

Author : D. G. Kendall
Publisher : John Wiley & Sons
ISBN 13 : 0470317841
Total Pages : 318 pages
Book Rating : 4.46/5 ( download)

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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/

Author : Christopher G. Small
Publisher : Springer Science & Business Media
ISBN 13 : 1461240328
Total Pages : 237 pages
Book Rating : 4.27/5 ( download)

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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.

Author : Lambros Malafouris
Publisher : MIT Press
ISBN 13 : 0262528924
Total Pages : 321 pages
Book Rating : 4.24/5 ( download)

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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.

Author : Frédéric Cao
Publisher : Springer
ISBN 13 : 3540684816
Total Pages : 260 pages
Book Rating : 4.17/5 ( download)

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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.

Author : Diane L. Herrmann
Publisher : CRC Press
ISBN 13 : 1466554649
Total Pages : 446 pages
Book Rating : 4.41/5 ( download)

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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.

Author : Luciano da Fontoura Costa
Publisher : CRC Press
ISBN 13 : 9781420037555
Total Pages : 688 pages
Book Rating : 4.52/5 ( download)

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Download or read book Shape Analysis and Classification written by Luciano da Fontoura Costa and published by CRC Press. This book was released on 2010-12-12 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in shape analysis impact a wide range of disciplines, from mathematics and engineering to medicine, archeology, and art. Anyone just entering the field, however, may find the few existing books on shape analysis too specific or advanced, and for students interested in the specific problem of shape recognition and characterization, traditio

Author : Shing-Tung Yau
Publisher : Il Saggiatore
ISBN 13 : 0465020232
Total Pages : 398 pages
Book Rating : 4.32/5 ( download)

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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.

Author : Jonathan Dancy
Publisher : Oxford University Press
ISBN 13 : 0192528017
Total Pages : 160 pages
Book Rating : 4.18/5 ( download)

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Download or read book Practical Shape written by Jonathan Dancy and published by Oxford University Press. This book was released on 2018-06-21 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Everyone allows that we can reason to a new belief from beliefs that we already have. Aristotle thought that we could also reason from beliefs to action. Practical Shape: A Theory of Practical Reasoning establishes this possibility of reasoning to action, in a way that allows also for reasoning to intention, hope, fear, and doubt. While many philosophers have found little sense in Aristotle's claim, Dancy offers a general theory of reasoning that is sensitive to current debates but still Aristotelian in spirit. The text clearly sets out the similarities between reasoning to action and reasoning to belief, which are far more striking than any dissimilarities. Its detailed account of practical reasoning, a topic inadequately covered in current literature, is presented in such a way as to be intelligible to a variety of readers, making it an ideal resource for students of philosophy but also of interest to academics in related disciplines.

Author : Michael Leyton
Publisher : Walter de Gruyter
ISBN 13 : 3764378123
Total Pages : 93 pages
Book Rating : 4.27/5 ( download)

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Download or read book Shape as Memory written by Michael Leyton and published by Walter de Gruyter. This book was released on 2006-05-19 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: How do buildings store information and experience in their shape and form? Michael Leyton has attracted considerable attention with his interpretation of geometrical form as a medium for the storage of information and memory. In this publication he draws specific conclusions for the field of architecture and construction, attaching fundamental importance to the complex relationship between symmetry and asymmetry. Wie können Gebäudeformen Erfahrungen und Inhalte speichern? Leyton hat eine viel beachtete neue Theorie der geometrischen Form entwickelt. Er interpretiert die geometrische Form – im Gegensatz zur gesamten Tradition – als Informations- und Gedächtnisträger. In vorliegender Darstellung zieht er die spezifischen Konsequenzen davon für den Bereich der Architektur und des Bauens.

Author : Sibe Mardešić
Publisher : North Holland
ISBN 13 :
Total Pages : 404 pages
Book Rating : 4.28/5 ( download)

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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: