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020 _a9783031025440
_9978-3-031-02544-0
024 7 _a10.1007/978-3-031-02544-0
_2doi
050 4 _aT1-995
072 7 _aTBC
_2bicssc
072 7 _aTEC000000
_2bisacsh
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082 0 4 _a620
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100 1 _aKanatani, Kenichi.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_985811
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.
300 _aXIV, 141 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSynthesis Lectures on Signal Processing,
_x1932-1694
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
650 0 _aElectrical engineering.
_985812
650 0 _aSignal processing.
_94052
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
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