000			04371nam a22004935i 4500
001			978-1-4419-9961-0
003			DE-He213
005			20140220083731.0
007			cr nn 008mamaa
008			110603s2011 xxu| s |||| 0|eng d
020			_a9781441999610 _9978-1-4419-9961-0
024	7		_a10.1007/978-1-4419-9961-0 _2doi
050		4	_aQA440-699
072		7	_aPBM _2bicssc
072		7	_aMAT012000 _2bisacsh
082	0	4	_a516 _223
100	1		_aGallier, Jean. _eauthor.
245	1	0	_aGeometric Methods and Applications _h[electronic resource] : _bFor Computer Science and Engineering / _cby Jean Gallier.
264		1	_aNew York, NY : _bSpringer New York, _c2011.
300			_aXXVIII, 680 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aTexts in Applied Mathematics, _x0939-2475 ; _v38
505	0		_aIntroduction -- Basics of Affine Geometry --  Basic Properties of Convex Sets -- Embedding an Affine Space in a Vector Space -- Basics of Projective Geometry -- Basics of Euclidean Geometry -- Separating and Supporting Hyperplanes; Polar Duality -- Polytopes and Polyhedra -- The Cartan–Dieudonn´e Theorem -- The Quaternions and the Spaces S3, SU(2), SO(3), and RP3 --  Dirichlet–Voronoi Diagrams -- Basics of Hermitian Geometry -- Spectral Theorems --  Singular Value Decomposition (SVD) and Polar Form -- Applications of SVD and Pseudo-Inverses -- Quadratic Optimization Problems -- Schur Complements and Applications -- Quadratic Optimization and Contour Grouping -- Basics of Manifolds and Classical Lie Groups -- Basics of the Differential Geometry of Curves -- Basics of the Differential Geometry of Surfaces -- Appendix -- References -- Symbol Index -- IndexAppendix -- References -- Symbol Index -- Index.
520			_aThis book is an introduction to the fundamental concepts and tools needed for solving problems of a geometric nature using a computer. It attempts to fill the gap between standard geometry books, which are primarily theoretical, and applied books on computer graphics, computer vision, robotics, or machine learning.  This book covers the following topics: affine geometry, projective geometry, Euclidean geometry, convex sets, SVD and principal component analysis, manifolds and Lie groups, quadratic optimization, basics of differential geometry, and a glimpse of computational geometry (Voronoi diagrams and Delaunay triangulations). Some practical applications of the concepts presented in this book include computer vision, more specifically contour grouping, motion interpolation, and robot kinematics.   In this extensively updated second edition, more material on convex sets, Farkas’s lemma, quadratic optimization and the Schur complement have been added. The chapter on SVD has been greatly expanded and now includes a presentation of PCA.  The book is well illustrated and has chapter summaries and a large number of exercises throughout. It will be of interest to a wide audience including computer scientists, mathematicians, and engineers.  Reviews of first edition: "Gallier's book will be a useful source for anyone interested in applications of geometrical methods to solve problems that arise in various branches of engineering. It may help to develop the sophisticated concepts from the more advanced parts of geometry into useful tools for applications." (Mathematical Reviews, 2001) "...it will be useful as a reference book for postgraduates wishing to find the connection between their current problem and the underlying geometry." (The Australian Mathematical Society, 2001)
650		0	_aMathematics.
650		0	_aComputer vision.
650		0	_aGeometry.
650		0	_aMathematical optimization.
650	1	4	_aMathematics.
650	2	4	_aGeometry.
650	2	4	_aComputer Imaging, Vision, Pattern Recognition and Graphics.
650	2	4	_aControl, Robotics, Mechatronics.
650	2	4	_aOptimization.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781441999603
830		0	_aTexts in Applied Mathematics, _x0939-2475 ; _v38
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4419-9961-0
912			_aZDB-2-SMA
999			_c106164 _d106164