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008			220601s2017 sz | s |||| 0|eng d
020			_a9783031018190
024	7		_a10.1007/978-3-031-01819-0 _2doi
040			_aES-MaUEC _bspa _cES-MaUEC _dES-MaUEC
050		4	_aTA1637.5 _b2017 EB
100	1		_aJermyn, Ian H. _eautor _4aut _4http://id.loc.gov/vocabulary/relators/aut _9686121
245	1	0	_aElastic Shape Analysis of Three-Dimensional Objects _cby Ian H. Jermyn, Sebastian Kurtek, Hamid Laga, Anuj Srivastava
250			_a1st edition 2017
264		1	_aCham _bSpringer International Publishing _c2017
300			_a1 recurso en línea (XV, 169 páginas)
336			_atexto _btxt _2rdacontent
337			_aelectrónico _bc _2rdamedia
338			_arecurso electrónico _bcr _2rdacarrier
347			_aarchivo de texto _bPDF
490	0		_aSynthesis Lectures on Computer Vision _x2153-1064
505	0		_aPreface -- 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			_aStatistical 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 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.
988			_aSynthesis Collection of Technology_2017
650		7	_2embne _9675969 _aElastografía
650		7	_2embne _9686124 _aAnálisis elástico (Ingeniería)
700	1		_aKurtek, Sebastian, _eautor _4aut _4http://id.loc.gov/vocabulary/relators/aut _9686122 _d1985-
700	1		_aLaga, Hamid _eautor _4aut _4http://id.loc.gov/vocabulary/relators/aut _9686123
700	1		_aSrivastava, Anuj _eautor _4aut _4http://id.loc.gov/vocabulary/relators/aut
776	0	8	_iPrinted edition: _z9783031006913
776	0	8	_iPrinted edition: _z9783031029479
856	4	0	_uhttps://go.openathens.net/redirector/universidadeuropea.es?url=https://doi.org/10.1007/978-3-031-01819-0 _zAcceso a este recurso digital (usuarios Universidad Europea de Madrid)
942			_2lcc _cLE
998			_b01/2023 _dz _esc _zSI