Elastic Shape Analysis of Three-Dimensional Objects (Record no. 84605)
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| 000 -LEADER | |
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| fixed length control field | 05270nam a22005535i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-3-031-01819-0 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240730163434.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 220601s2017 sz | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9783031018190 |
| -- | 978-3-031-01819-0 |
| 082 04 - CLASSIFICATION NUMBER | |
| Call Number | 006 |
| 100 1# - AUTHOR NAME | |
| Author | Jermyn, Ian H. |
| 245 10 - TITLE STATEMENT | |
| Title | Elastic Shape Analysis of Three-Dimensional Objects |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. 2017. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | XV, 169 p. |
| 490 1# - SERIES STATEMENT | |
| Series statement | Synthesis Lectures on Computer Vision, |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Remark 2 | Preface -- Acknowledgments -- Problem Introduction and Motivation -- Elastic Shape Analysis: Metrics and Representations -- Computing Geometrical Quantities -- Statistical Analysis of Shapes -- Case Studies Using Human Body and Anatomical Shapes -- Landmark-driven Elastic Shape Analysis -- Bibliography -- Authors' Biographies . |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | 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 #x211D;, 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 frameworkis 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. |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| General subdivision | Digital techniques. |
| 700 1# - AUTHOR 2 | |
| Author 2 | Kurtek, Sebastian. |
| 700 1# - AUTHOR 2 | |
| Author 2 | Laga, Hamid. |
| 700 1# - AUTHOR 2 | |
| Author 2 | Srivastava, Anuj. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | https://doi.org/10.1007/978-3-031-01819-0 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | eBooks |
| 264 #1 - | |
| -- | Cham : |
| -- | Springer International Publishing : |
| -- | Imprint: Springer, |
| -- | 2017. |
| 336 ## - | |
| -- | text |
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| -- | rdacontent |
| 337 ## - | |
| -- | computer |
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| -- | rdamedia |
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| -- | online resource |
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| 347 ## - | |
| -- | text file |
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| -- | rda |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Image processing |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Computer vision. |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Pattern recognition systems. |
| 650 14 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Computer Imaging, Vision, Pattern Recognition and Graphics. |
| 650 24 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Computer Vision. |
| 650 24 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Automated Pattern Recognition. |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| -- | 2153-1064 |
| 912 ## - | |
| -- | ZDB-2-SXSC |
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