000 | 04289nam a22005175i 4500 | ||
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001 | 978-3-031-02544-0 | ||
003 | DE-He213 | ||
005 | 20240730164724.0 | ||
007 | cr nn 008mamaa | ||
008 | 220601s2021 sz | s |||| 0|eng d | ||
020 |
_a9783031025440 _9978-3-031-02544-0 |
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024 | 7 |
_a10.1007/978-3-031-02544-0 _2doi |
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050 | 4 | _aT1-995 | |
072 | 7 |
_aTBC _2bicssc |
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_aTEC000000 _2bisacsh |
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072 | 7 |
_aTBC _2thema |
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082 | 0 | 4 |
_a620 _223 |
100 | 1 |
_aKanatani, Kenichi. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _985811 |
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245 | 1 | 0 |
_aLinear Algebra for Pattern Processing _h[electronic resource] : _bProjection, Singular Value Decomposition, and Pseudoinverse / _cby Kenichi Kanatani. |
250 | _a1st ed. 2021. | ||
264 | 1 |
_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2021. |
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300 |
_aXIV, 141 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 Signal Processing, _x1932-1694 |
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505 | 0 | _aPreface -- Introduction -- Linear Space and Projection -- Eigenvalues and Spectral Decomposition -- Singular Values and Singular Value Decomposition -- Pseudoinverse -- Least-Squares Solution of Linear Equations -- Probability Distribution of Vectors -- Fitting Spaces -- Matrix Factorization -- Triangulation from Three Views -- Bibliography -- Author's Biography -- Index. | |
520 | _aLinear algebra is one of the most basic foundations of a wide range of scientific domains, and most textbooks of linear algebra are written by mathematicians. However, this book is specifically intended to students and researchers of pattern information processing, analyzing signals such as images and exploring computer vision and computer graphics applications. The author himself is a researcher of this domain. Such pattern information processing deals with a large amount of data, which are represented by high-dimensional vectors and matrices. There, the role of linear algebra is not merely numerical computation of large-scale vectors and matrices. In fact, data processing is usually accompanied with "geometric interpretation." For example, we can think of one data set being "orthogonal" to another and define a "distance" between them or invoke geometric relationships such as "projecting" some data onto some space. Such geometric concepts not only help us mentally visualize abstracthigh-dimensional spaces in intuitive terms but also lead us to find what kind of processing is appropriate for what kind of goals. First, we take up the concept of "projection" of linear spaces and describe "spectral decomposition," "singular value decomposition," and "pseudoinverse" in terms of projection. As their applications, we discuss least-squares solutions of simultaneous linear equations and covariance matrices of probability distributions of vector random variables that are not necessarily positive definite. We also discuss fitting subspaces to point data and factorizing matrices in high dimensions in relation to motion image analysis. Finally, we introduce a computer vision application of reconstructing the 3D location of a point from three camera views to illustrate the role of linear algebra in dealing with data with noise. This book is expected to help students and researchers of pattern information processing deepen the geometric understanding of linear algebra. | ||
650 | 0 |
_aEngineering. _99405 |
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650 | 0 |
_aElectrical engineering. _985812 |
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650 | 0 |
_aSignal processing. _94052 |
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650 | 1 | 4 |
_aTechnology and Engineering. _985813 |
650 | 2 | 4 |
_aElectrical and Electronic Engineering. _985814 |
650 | 2 | 4 |
_aSignal, Speech and Image Processing. _931566 |
710 | 2 |
_aSpringerLink (Online service) _985817 |
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773 | 0 | _tSpringer Nature eBook | |
776 | 0 | 8 |
_iPrinted edition: _z9783031003370 |
776 | 0 | 8 |
_iPrinted edition: _z9783031014161 |
776 | 0 | 8 |
_iPrinted edition: _z9783031036729 |
830 | 0 |
_aSynthesis Lectures on Signal Processing, _x1932-1694 _985819 |
|
856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-031-02544-0 |
912 | _aZDB-2-SXSC | ||
942 | _cEBK | ||
999 |
_c85861 _d85861 |