LEADER 05826nam 2200781Ia 450 001 9910784236603321 005 20200520144314.0 010 $a1-281-01012-X 010 $a9786611010126 010 $a0-08-047726-7 035 $a(CKB)1000000000341407 035 $a(EBL)226738 035 $a(OCoLC)701840317 035 $a(SSID)ssj0000139074 035 $a(PQKBManifestationID)11146826 035 $a(PQKBTitleCode)TC0000139074 035 $a(PQKBWorkID)10017276 035 $a(PQKB)10862813 035 $a(Au-PeEL)EBL226738 035 $a(CaPaEBR)ebr10254611 035 $a(CaONFJC)MIL101012 035 $a(CaSebORM)9781558608610 035 $a(MiAaPQ)EBC226738 035 $a(PPN)150196237 035 $a(EXLCZ)991000000000341407 100 $a20041228d2004 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDigital geometry$b[electronic resource] $egeometric methods for digital picture analysis /$fReinhard Klette, Azriel Rosenfeld 205 $a1st edition 210 $aAmsterdam ;$aBoston $cElsevier $cMorgan Kaufman Publishers$dc2004 215 $a1 online resource (675 p.) 225 1 $aThe Morgan Kaufmann series in computer graphics and geometric modeling 300 $aDescription based upon print version of record. 311 $a1-4933-0372-4 311 $a1-55860-861-3 320 $aIncludes bibliographical references and index. 327 $aPreface; Structure of this Book; Contents; 1. Introduction; 1.1 Pictures; 1.1.1 Pixels, voxels, and their values; 1.1.2 Picture resolution and picture size; 1.1.3 Scan orders; 1.1.4 Adjacency and connectedness; 1.2 Digital Geometry and Related Disciplines; 1.2.1 Coordinates and metric spaces; 1.2.2 Euclidean, similarity, and affine geometry; 1.2.3 Projective geometry; 1.2.4 Vector and geometric algebra; 1.2.5 Graph theory; 1.2.6 Topology; 1.2.7 Approximation and estimation; 1.2.8 Combinatorial geometry; 1.2.9 Computational geometry; 1.2.10 Fuzzy geometry 327 $a1.2.11 Integral geometry, isoperimetry, stereology, and tomography1.2.12 Mathematic morphology; 1.3 Exercises; 1.4 Commented Bibliography; 2. Grids and Digitization; 2.1 The Grid Point and Grid Cell Models; 2.1.1 Grid points and grid cells; 2.1.2 Variable grid resolution; 2.1.3 Adjacencies in 2D grids; 2.1.4 Adjacencies in 3D grids; 2.1.5 Grid cell incidence; 2.2 Connected Components; 2.2.1 Connectedness and components; 2.2.2 Counting connected sets; 2.2.3 Component labeling; 2.3 Digitization Models; 2.3.1 Gauss digitization; 2.3.2 Jordan digitization; 2.3.3 Grid-intersection digitization 327 $a2.3.4 Types of digital sets2.3.5 Domain digitizations; 2.4 Property Estimation; 2.4.1 Content estimation; 2.4.2 Convergent 2D area estimates; 2.4.3 Multigrid convergence; 2.5 Exercises; 2.6 Commented Bibliography; 3. Metrics; 3.1 Basics About Metrics; 3.1.1 The Euclidean metric; 3.1.2 Norms and Minkowski metrics; 3.1.3 Scalar products and angles; 3.1.4 Integer-Valued metrics; 3.1.5 Restricting and combining metrics; 3.1.6 Boundedness; 3.1.7 The topology induced by a metric; 3.1.8 Distances between sets; 3.2 Grid Point Metrics; 3.2.1 Basic grid point metrics 327 $a3.2.2 Neighborhoods and degrees of closeness3.2.3 Approximations to the Euclidean metric; 3.2.4 Paths, geodesics, and intrinsic distances; 3.2.5 Distances between sets; 3.3 Grid Cell Metrics; 3.3.1 Basic grid cell metrics; 3.3.2 Seminorms; 3.3.3 Scalar products and angles; 3.4 Metrics on Pictures; 3.4.1 Value-weighted distance; 3.4.2 Distance transforms; 3.4.3 The Euclidean distance transform; 3.4.4 Medial axes; 3.5 Exercises; 3.6 Commented Bibliography; 4. Adjacency Graphs; 4.1 Graphs, Adjacency Structures, and Adjacency Graphs; 4.1.1 Graphs and adjacency structures 327 $a4.1.2 Connectedness with respect to a subgraph4.1.3 Adjacency graphs; 4.1.4 Types of nodes; region adjacencies; 4.2 Some Basics of Graph Theory; 4.2.1 Nodes, paths, and distances; 4.2.2 Special types of nodes, edges, and graphs; 4.3 Oriented Adjacency Graphs; 4.3.1 Local circular orders; 4.3.2 The Euler characteristic and planarity; 4.3.3 Atomic and border cycles; 4.3.4 The separation theorem; 4.3.5 Holes; 4.3.6 Boundaries; 4.3.7 Some combinatorial results; 4.4 Combinatorial Maps; 4.4.1 2D maps; 4.4.2 3D maps; 4.5 Exercises; 4.6 Commented Bibliography; 5. Incidence Pseudographs 327 $a5.1 Incidence Structures 330 $aDigital geometry is about deriving geometric information from digital pictures. The field emerged from its mathematical roots some forty-years ago through work in computer-based imaging, and it is used today in many fields, such as digital image processing and analysis (with applications in medical imaging, pattern recognition, and robotics) and of course computer graphics. Digital Geometry is the first book to detail the concepts, algorithms, and practices of the discipline. This comphrehensive text and reference provides an introduction to the mathematical foundations of digital geome 410 0$aMorgan Kaufmann series in computer graphics and geometric modeling. 606 $aImage processing$xDigital techniques 606 $aGeometry$xData processing 606 $aImage analysis 606 $aComputer graphics 606 $aAlgorithms 615 0$aImage processing$xDigital techniques. 615 0$aGeometry$xData processing. 615 0$aImage analysis. 615 0$aComputer graphics. 615 0$aAlgorithms. 676 $a006.6 700 $aKlette$b Reinhard$0725642 701 $aRosenfeld$b Azriel$f1931-$011948 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910784236603321 996 $aDigital geometry$91425814 997 $aUNINA