| 000 | 05270nam a22005535i 4500 | ||
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| 001 | 978-3-031-01819-0 | ||
| 003 | DE-He213 | ||
| 005 | 20240730163434.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 220601s2017 sz | s |||| 0|eng d | ||
| 020 |
_a9783031018190 _9978-3-031-01819-0 |
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| 024 | 7 |
_a10.1007/978-3-031-01819-0 _2doi |
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| 050 | 4 | _aTA1501-1820 | |
| 050 | 4 | _aTA1634 | |
| 072 | 7 |
_aUYT _2bicssc |
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_aCOM016000 _2bisacsh |
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| 072 | 7 |
_aUYT _2thema |
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| 082 | 0 | 4 |
_a006 _223 |
| 100 | 1 |
_aJermyn, Ian H. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _978529 |
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| 245 | 1 | 0 |
_aElastic Shape Analysis of Three-Dimensional Objects _h[electronic resource] / _cby Ian H. Jermyn, Sebastian Kurtek, Hamid Laga, Anuj Srivastava. |
| 250 | _a1st ed. 2017. | ||
| 264 | 1 |
_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2017. |
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| 300 |
_aXV, 169 p. _bonline resource. |
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| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 347 |
_atext file _bPDF _2rda |
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| 490 | 1 |
_aSynthesis Lectures on Computer Vision, _x2153-1064 |
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| 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 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 |
_aImage processing _xDigital techniques. _94145 |
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| 650 | 0 |
_aComputer vision. _978530 |
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| 650 | 0 |
_aPattern recognition systems. _93953 |
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| 650 | 1 | 4 |
_aComputer Imaging, Vision, Pattern Recognition and Graphics. _931569 |
| 650 | 2 | 4 |
_aComputer Vision. _978531 |
| 650 | 2 | 4 |
_aAutomated Pattern Recognition. _931568 |
| 700 | 1 |
_aKurtek, Sebastian. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _978532 |
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| 700 | 1 |
_aLaga, Hamid. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _978533 |
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| 700 | 1 |
_aSrivastava, Anuj. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _978534 |
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| 710 | 2 |
_aSpringerLink (Online service) _978535 |
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| 773 | 0 | _tSpringer Nature eBook | |
| 776 | 0 | 8 |
_iPrinted edition: _z9783031006913 |
| 776 | 0 | 8 |
_iPrinted edition: _z9783031029479 |
| 830 | 0 |
_aSynthesis Lectures on Computer Vision, _x2153-1064 _978536 |
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| 856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-031-01819-0 |
| 912 | _aZDB-2-SXSC | ||
| 942 | _cEBK | ||
| 999 |
_c84605 _d84605 |
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