Mathematics Of Shape Description

Author : Pijush K. Ghosh,Koichiro Deguchi
Publisher : John Wiley & Sons
Page : 272 pages
File Size : 50,9 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 : Eric A. Lord,C. B. Wilson
Publisher : Unknown
Page : 260 pages
File Size : 50,8 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 : Ying-Lie O,Alexander Toet,David Foster,Henk J.A.M. Heijmans,Peter Meer
Publisher : Springer Science & Business Media
Page : 685 pages
File Size : 50,7 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 : Jordan Ellenberg
Publisher : Penguin
Page : 481 pages
File Size : 40,9 Mb
Release : 2021-05-25
Category : Mathematics
ISBN : 9781984879066

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Shape by Jordan Ellenberg Pdf

An instant New York Times Bestseller! “Unreasonably entertaining . . . reveals how geometric thinking can allow for everything from fairer American elections to better pandemic planning.” —The New York Times From the New York Times-bestselling author of How Not to Be Wrong—himself a world-class geometer—a far-ranging exploration of the power of geometry, which turns out to help us think better about practically everything. How should a democracy choose its representatives? How can you stop a pandemic from sweeping the world? How do computers learn to play Go, and why is learning Go so much easier for them than learning to read a sentence? Can ancient Greek proportions predict the stock market? (Sorry, no.) What should your kids learn in school if they really want to learn to think? All these are questions about geometry. For real. If you're like most people, geometry is a sterile and dimly remembered exercise you gladly left behind in the dust of ninth grade, along with your braces and active romantic interest in pop singers. If you recall any of it, it's plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place. That's not geometry. Okay, it is geometry, but only a tiny part, which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel. Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face. Geometry asks: Where are things? Which things are near each other? How can you get from one thing to another thing? Those are important questions. The word "geometry"comes from the Greek for "measuring the world." If anything, that's an undersell. Geometry doesn't just measure the world—it explains it. Shape shows us how.

Author : Moira Anderson
Publisher : Teacher Created Materials
Page : 32 pages
File Size : 52,8 Mb
Release : 2008-10-10
Category : Juvenile Nonfiction
ISBN : 074390897X

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Shapes in Our World by Moira Anderson Pdf

Identify three-dimensional shapes all around the world! This vibrant title gives readers practice identifying familiar shapes like cones, cylinders, pentagons, polygons, and prisms, while familiarizing them with STEM themes and more advanced geometry concepts. Children will learn more about vertices, symmetry, and bases. With each shape, this book gives readers information about an example of the shape, be it a building, a honeycomb, or a tree trunk! With an accessible glossary, clear mathematical diagrams, practical examples, and easy-to-read text, readers will have all the tools they need to improve their geometry skills and find shapes on their own!

Author : Anonim
Publisher : Remedia Publications
Page : 28 pages
File Size : 50,8 Mb
Release : 2006
Category : Mathematics
ISBN : 1596398558

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Multiplication Word Problems by Anonim Pdf

Author : Silvia Biasotti,Bianca Falcidieno,Daniela Giorgi,Michela Spagnuolo
Publisher : Springer Nature
Page : 124 pages
File Size : 50,6 Mb
Release : 2022-06-01
Category : Mathematics
ISBN : 9783031795589

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Mathematical Tools for Shape Analysis and Description by Silvia Biasotti,Bianca Falcidieno,Daniela Giorgi,Michela Spagnuolo Pdf

This book is a guide for researchers and practitioners to the new frontiers of 3D shape analysis and the complex mathematical tools most methods rely on. The target reader includes students, researchers and professionals with an undergraduate mathematics background, who wish to understand the mathematics behind shape analysis. The authors begin with a quick review of basic concepts in geometry, topology, differential geometry, and proceed to advanced notions of algebraic topology, always keeping an eye on the application of the theory, through examples of shape analysis methods such as 3D segmentation, correspondence, and retrieval. A number of research solutions in the field come from advances in pure and applied mathematics, as well as from the re-reading of classical theories and their adaptation to the discrete setting. In a world where disciplines (fortunately) have blurred boundaries, the authors believe that this guide will help to bridge the distance between theory and practice. Table of Contents: Acknowledgments / Figure Credits / About this Book / 3D Shape Analysis in a Nutshell / Geometry, Topology, and Shape Representation / Differential Geometry and Shape Analysis / Spectral Methods for Shape Analysis / Maps and Distances between Spaces / Algebraic Topology and Topology Invariants / Differential Topology and Shape Analysis / Reeb Graphs / Morse and Morse-Smale Complexes / Topological Persistence / Beyond Geometry and Topology / Resources / Bibliography / Authors' Biographies

Author : Lorraine Harrison
Publisher : The Rosen Publishing Group, Inc
Page : 18 pages
File Size : 40,6 Mb
Release : 2013-08-01
Category : Juvenile Nonfiction
ISBN : 9781477716168

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Flat Shapes, Solid Shapes by Lorraine Harrison Pdf

Our first encounters with math usually come through shapes. Geometry skills are learned from an early age, and readers build upon those first geometry lessons with topics like describing objects using the names of shapes, identifying both two-dimensional and three-dimensional shapes, and composing shapes. Readers are able to explore these essential concepts independently through accessible text and colorful images of both new and familiar shapes. Common two-dimensional and three-dimensional shapes are introduced in this volume, which adheres to standard K.G.A.3 of the Common Core State Standards for Mathematics. This book should be paired with "Is It Flat or Is It Solid?" (9781477720004) from the InfoMax Math Readers Program to provide the alternative point of view on the same topic.

Author : Shawn W. Walker
Publisher : SIAM
Page : 152 pages
File Size : 49,6 Mb
Release : 2015-06-25
Category : Mathematics
ISBN : 9781611973969

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The Shapes of Things by Shawn W. Walker Pdf

Many things around us have properties that depend on their shape--for example, the drag characteristics of a rigid body in a flow. This self-contained overview of differential geometry explains how to differentiate a function (in the calculus sense) with respect to a "shape variable." This approach, which is useful for understanding mathematical models containing geometric partial differential equations (PDEs), allows readers to obtain formulas for geometric quantities (such as curvature) that are clearer than those usually offered in differential geometry texts. Readers will learn how to compute sensitivities with respect to geometry by developing basic calculus tools on surfaces and combining them with the calculus of variations. Several applications that utilize shape derivatives and many illustrations that help build intuition are included.

Author : L.Christine Kinsey,Teresa E. Moore
Publisher : Springer Science & Business Media
Page : 524 pages
File Size : 45,5 Mb
Release : 2006-05-09
Category : Mathematics
ISBN : 1930190093

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Symmetry, Shape and Space by L.Christine Kinsey,Teresa E. Moore Pdf

This book will appeal to at least three groups of readers: prospective high school teachers, liberal arts students, and parents whose children are studying high school or college math. It is modern in its selection of topics, and in the learning models used by the authors. The book covers some exciting but non-traditional topics from the subject area of geometry. It is also intended for undergraduates and tries to engage their interest in mathematics. Many innovative pedagogical modes are used throughout.

Author : Chandler Davis,Marjorie Senechal,Jan Zwicky
Publisher : A K Peters/CRC Press
Page : 0 pages
File Size : 47,9 Mb
Release : 2008-10-28
Category : Mathematics
ISBN : 1568814445

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The Shape of Content by Chandler Davis,Marjorie Senechal,Jan Zwicky Pdf

This book is a collection of creative pieces—poems, short stories, essays, play excerpts—that give shape to mathematical and scientific content. This book portrays by example how various people work creatively with ideas from mathematics and other sciences. Creative writing about the content of mathematics and science is rare, and creative writing about the activity of mathematical and scientific creation is even rarer. And yet, when it occurs, it can be extremely popular, as well known plays like Proof and Copenhagen and biographies like A Beautiful Mind and The Man Who Loved Only Numbers attest. What draws the public to these works? And why, given that something does, are there so few examples of literature that engages these themes? Mathematics and science are part of world culture, part of the human spirit, fit subjects for art of all kinds.

Author : Jennifer Boothroyd,Lerner Publications Company
Publisher : LernerClassroom
Page : 16 pages
File Size : 44,6 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 9780822591986

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Solid Shapes by Jennifer Boothroyd,Lerner Publications Company Pdf

SOLID SHAPES TEACHING GUIDE

Author : OECD
Publisher : OECD Publishing
Page : 228 pages
File Size : 42,6 Mb
Release : 2004-03-02
Category : Electronic
ISBN : 9789264101739

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PISA The PISA 2003 Assessment Framework Mathematics, Reading, Science and Problem Solving Knowledge and Skills by OECD Pdf

The PISA 2003 Assessment Framework presents the conceptual underpinning of the PISA 2003 assessments. Within each assessment area, the volume defines the content that students need to acquire, the processes that need to be performed and the contexts in which knowledge and skills are applied.

Author : Mary Rosenberg
Publisher : Classroom Complete Press
Page : 35 pages
File Size : 52,5 Mb
Release : 2009-09-01
Category : Education
ISBN : 9781553198000

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Geometry - Task Sheets Gr. PK-2 by Mary Rosenberg Pdf

For grades PK-2, our State Standards-based resource meets the geometry concepts addressed by the NCTM standards and encourages the students to learn and review the concepts in unique ways. Each task sheet is organized around a central problem taken from real-life experiences of the students. The pages of this resource contain a variety in terms of levels of difficulty and content so as to provide students with a variety of differentiated learning opportunities. Included in our resource are activities on two- and three-dimensional shapes, fractions, coordinate points, and composing and decomposing shapes. The task sheets offer space for reflection, and opportunity for the appropriate use of technology. Also contained are assessment and standards rubrics, review sheets, test prep, color activity posters and bonus worksheets. All of our content is aligned to your State Standards and are written to Bloom's Taxonomy, STEM, and NCTM standards.

Author : J. M. Cordier,T. Porter
Publisher : Courier Corporation
Page : 212 pages
File Size : 42,6 Mb
Release : 2013-12-01
Category : Science
ISBN : 9780486783475

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Shape Theory by J. M. Cordier,T. Porter Pdf

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.