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001 978-3-319-51951-7
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020 _a9783319519517
_9978-3-319-51951-7
024 7 _a10.1007/978-3-319-51951-7
_2doi
040 _aISI Library, Kolkata
050 4 _aQA440-699
072 7 _aPBM
_2bicssc
072 7 _aMAT012000
_2bisacsh
072 7 _aPBM
_2thema
082 0 4 _a516
_223
245 1 0 _aTensor Valuations and Their Applications in Stochastic Geometry and Imaging
_h[electronic resource] /
_cedited by Eva B. Vedel Jensen, Markus Kiderlen.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2017.
300 _aXIV, 462 p. 25 illus., 16 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2177
505 0 _a1 Valuations on Convex Bodies – the Classical Basic Facts: Rolf Schneider -- 2 Tensor Valuations and Their Local Versions: Daniel Hug and Rolf Schneider -- 3 Structures on Valuations: Semyon Alesker -- 4 Integral Geometry and Algebraic Structures for Tensor Valuations: Andreas Bernig and Daniel Hug -- 5 Crofton Formulae for Tensor-Valued Curvature Measures: Daniel Hug and Jan A. Weis -- 6 A Hadwiger-Type Theorem for General Tensor Valuations: Franz E. Schuster -- 7 Rotation Invariant Valuations: Eva B.Vedel Jensen and Markus Kiderlen -- 8 Valuations on Lattice Polytopes: Károly J. Böröczky and Monika Ludwig -- 9 Valuations and Curvature Measures on Complex Spaces: Andreas Bernig -- 10 Integral Geometric Regularity: Joseph H.G. Fu -- 11 Valuations and Boolean Models: Julia Hörrmann and Wolfgang Weil -- 12 Second Order Analysis of Geometric Functionals of Boolean Models: Daniel Hug, Michael A. Klatt, Günter Last and Matthias Schulte -- 13 Cell Shape Analysis of Random Tessellations Based on Minkowski Tensors: Michael A. Klatt, Günter Last, Klaus Mecke, Claudia Redenbach, Fabian M. Schaller, Gerd E. Schröder-Turk -- 14 Stereological Estimation of Mean Particle Volume Tensors in R3 from Vertical Sections: Astrid Kousholt, Johanna F. Ziegel, Markus Kiderlen -- 15 Valuations in Image Analysis: Anne Marie Svane.
520 _aThe purpose of this volume is to give an up-to-date introduction to tensor valuations and their applications. Starting with classical results concerning scalar-valued valuations on the families of convex bodies and convex polytopes, it proceeds to the modern theory of tensor valuations. Product and Fourier-type transforms are introduced and various integral formulae are derived. New and well-known results are presented, together with generalizations in several directions, including extensions to the non-Euclidean setting and to non-convex sets. A variety of applications of tensor valuations to models in stochastic geometry, to local stereology and to imaging are also discussed.
650 0 _aGeometry.
650 0 _aCell aggregation
_xMathematics.
650 0 _aDistribution (Probability theory.
650 1 4 _aGeometry.
_0http://scigraph.springernature.com/things/product-market-codes/M21006
650 2 4 _aManifolds and Cell Complexes (incl. Diff.Topology).
_0http://scigraph.springernature.com/things/product-market-codes/M28027
650 2 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
700 1 _aJensen, Eva B. Vedel.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
700 1 _aKiderlen, Markus.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319519500
776 0 8 _iPrinted edition:
_z9783319519524
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2177
856 4 0 _uhttps://doi.org/10.1007/978-3-319-51951-7
912 _aZDB-2-SMA
912 _aZDB-2-LNM
942 _cEB
950 _aMathematics and Statistics (Springer-11649)
999 _c427189
_d427189