Applied Mathematics Working With Shapes In Three Dimensions
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Applied Mathematics Working With Shapes In Three Dimensions
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Author : Center for Occupational Research and Development (U.S.)
language : en
Publisher:
Release Date : 1988
Applied Mathematics Working With Shapes In Three Dimensions written by Center for Occupational Research and Development (U.S.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
36 units on applied math.
Applied Mathematics Unit 8
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Author : Center for Occupational Research and Development Staff
language : en
Publisher:
Release Date : 1989
Applied Mathematics Unit 8 written by Center for Occupational Research and Development Staff and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with categories.
Working With Shapes In Three Dimensions
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Author : Center for Occupational Research and Development (U.S.)
language : en
Publisher:
Release Date : 1988
Working With Shapes In Three Dimensions written by Center for Occupational Research and Development (U.S.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
Working With Shapes In Three Dimensions Student Text
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Author : Center for Occupational Research and Development (U.S.)
language : en
Publisher:
Release Date : 1988
Working With Shapes In Three Dimensions Student Text written by Center for Occupational Research and Development (U.S.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
Elastic Shape Analysis Of Three Dimensional Objects
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Author : Ian H. Jermyn
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2017-09-15
Elastic Shape Analysis Of Three Dimensional Objects written by Ian H. Jermyn and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-15 with Computers categories.
Statistical analysis of shapes of 3D objects is an important problem with a wide range of applications. This analysis is difficult for many reasons, including the fact that objects differ in both geometry and topology. In this manuscript, we narrow the problem by focusing on objects with fixed topology, say objects that are diffeomorphic to unit spheres, and develop tools for analyzing their geometries. The main challenges in this problem are to register points across objects and to perform analysis while being invariant to certain shape-preserving transformations. We develop a comprehensive framework for analyzing shapes of spherical objects, i.e., objects that are embeddings of a unit sphere in R, including tools for: quantifying shape differences, optimally deforming shapes into each other, summarizing shape samples, extracting principal modes of shape variability, and modeling shape variability associated with populations. An important strength of this framework is that it is elastic: it performs alignment, registration, and comparison in a single unified framework, while being invariant to shape-preserving transformations. The approach is essentially Riemannian in the following sense. We specify natural mathematical representations of surfaces of interest, and impose Riemannian metrics that are invariant to the actions of the shape-preserving transformations. In particular, they are invariant to reparameterizations of surfaces. While these metrics are too complicated to allow broad usage in practical applications, we introduce a novel representation, termed square-root normal fields (SRNFs), that transform a particular invariant elastic metric into the standard L2 metric. As a result, one can use standard techniques from functional data analysis for registering, comparing, and summarizing shapes. Specifically, this results in: pairwise registration of surfaces; computation of geodesic paths encoding optimal deformations; computation of Karcher means and covariances under the shape metric; tangent Principal Component Analysis (PCA) and extraction of dominant modes of variability; and finally, modeling of shape variability using wrapped normal densities. These ideas are demonstrated using two case studies: the analysis of surfaces denoting human bodies in terms of shape and pose variability; and the clustering and classification of the shapes of subcortical brain structures for use in medical diagnosis. This book develops these ideas without assuming advanced knowledge in differential geometry and statistics. We summarize some basic tools from differential geometry in the appendices, and introduce additional concepts and terminology as needed in the individual chapters.
Cord Applied Mathematics Metric Version Unit 8
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Author : Center for Occupational Research and Development Staff
language : en
Publisher:
Release Date : 1994-01-01
Cord Applied Mathematics Metric Version Unit 8 written by Center for Occupational Research and Development Staff and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-01 with categories.
The Shape Of Space
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Author : Jeffrey R. Weeks
language : en
Publisher: CRC Press
Release Date : 2001-12-12
The Shape Of Space written by Jeffrey R. Weeks and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-12-12 with Mathematics categories.
Maintaining the standard of excellence set by the previous edition, this textbook covers the basic geometry of two- and three-dimensional spaces Written by a master expositor, leading researcher in the field, and MacArthur Fellow, it includes experiments to determine the true shape of the universe and contains illustrated examples and engaging exercises that teach mind-expanding ideas in an intuitive and informal way. Bridging the gap from geometry to the latest work in observational cosmology, the book illustrates the connection between geometry and the behavior of the physical universe and explains how radiation remaining from the big bang may reveal the actual shape of the universe.
The Shape Of Space
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Author : Jeffrey R. Weeks
language : en
Publisher: Marcel Dekker
Release Date : 1985
The Shape Of Space written by Jeffrey R. Weeks and has been published by Marcel Dekker this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.
The Shape of Space brings topology to the general reader by showing how to visualize manifolds directly ... complements existing textbooks, which often deal only in abstractions, by offering a wealth of concrete examples ... includes the first elementary exposition of William P. Thurston's revolutionary discoveries ... applies topology to cosmology ... gives the first simple pictorial exposition of the Gauss-Bonnet formula ... builds intuition with more than 140 hands-on exercises, all with complete solutions ... and offers over 170 illustrations. An annotated bibliography lists useful references for further study on specific topics.
The Shape Of Space
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Author : Jeffrey R. Weeks
language : en
Publisher:
Release Date : 1985
The Shape Of Space written by Jeffrey R. Weeks and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with categories.
Applied Mathematics Working With Shapes In Two Dimensions
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Author : Center for Occupational Research and Development (U.S.)
language : en
Publisher:
Release Date : 1988
Applied Mathematics Working With Shapes In Two Dimensions written by Center for Occupational Research and Development (U.S.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
36 units on applied math.