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The Resource Digital geometry : geometric methods for digital picture analysis, Reinhard Klette, Azriel Rosenfeld, (electronic resource)
Digital geometry : geometric methods for digital picture analysis, Reinhard Klette, Azriel Rosenfeld, (electronic resource)
Resource Information
The item Digital geometry : geometric methods for digital picture analysis, Reinhard Klette, Azriel Rosenfeld, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Digital geometry : geometric methods for digital picture analysis, Reinhard Klette, Azriel Rosenfeld, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary
 Digital geometry is about deriving geometric information from digital pictures. The field emerged from its mathematical roots some fortyyears ago through work in computerbased 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
 Language

 eng
 eng
 Edition
 1st edition
 Extent
 1 online resource (675 p.)
 Note
 Description based upon print version of record
 Contents

 Preface; 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
 1.2.11 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 Gridintersection digitization
 2.3.4 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 IntegerValued 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
 3.2.2 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 Valueweighted 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
 4.1.2 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
 5.1 Incidence Structures
 Isbn
 9781281010124
 Label
 Digital geometry : geometric methods for digital picture analysis
 Title
 Digital geometry
 Title remainder
 geometric methods for digital picture analysis
 Statement of responsibility
 Reinhard Klette, Azriel Rosenfeld
 Language

 eng
 eng
 Summary
 Digital geometry is about deriving geometric information from digital pictures. The field emerged from its mathematical roots some fortyyears ago through work in computerbased 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
 Cataloging source
 MiAaPQ
 http://library.link/vocab/creatorName
 Klette, Reinhard
 Dewey number

 006.6
 621.367
 621.36701561
 Illustrations
 illustrations
 Index
 index present
 Language note
 English
 LC call number
 TA1637
 LC item number
 .K54 2004
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorDate
 1931
 http://library.link/vocab/relatedWorkOrContributorName
 Rosenfeld, Azriel
 Series statement
 The Morgan Kaufmann series in computer graphics and geometric modeling
 http://library.link/vocab/subjectName

 Image processing
 Geometry
 Image analysis
 Computer graphics
 Algorithms
 Label
 Digital geometry : geometric methods for digital picture analysis, Reinhard Klette, Azriel Rosenfeld, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Content category
 text
 Content type code

 txt
 Contents

 Preface; 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
 1.2.11 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 Gridintersection digitization
 2.3.4 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 IntegerValued 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
 3.2.2 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 Valueweighted 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
 4.1.2 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
 5.1 Incidence Structures
 Dimensions
 unknown
 Edition
 1st edition
 Extent
 1 online resource (675 p.)
 Form of item
 online
 Isbn
 9781281010124
 Media category
 computer
 Media type code

 c
 Specific material designation
 remote
 System control number

 (EBL)226738
 (OCoLC)701840317
 (SSID)ssj0000139074
 (PQKBManifestationID)11146826
 (PQKBTitleCode)TC0000139074
 (PQKBWorkID)10017276
 (PQKB)10862813
 (MiAaPQ)EBC226738
 (CaSebORM)9781558608610
 (EXLCZ)991000000000341407
 Label
 Digital geometry : geometric methods for digital picture analysis, Reinhard Klette, Azriel Rosenfeld, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Content category
 text
 Content type code

 txt
 Contents

 Preface; 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
 1.2.11 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 Gridintersection digitization
 2.3.4 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 IntegerValued 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
 3.2.2 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 Valueweighted 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
 4.1.2 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
 5.1 Incidence Structures
 Dimensions
 unknown
 Edition
 1st edition
 Extent
 1 online resource (675 p.)
 Form of item
 online
 Isbn
 9781281010124
 Media category
 computer
 Media type code

 c
 Specific material designation
 remote
 System control number

 (EBL)226738
 (OCoLC)701840317
 (SSID)ssj0000139074
 (PQKBManifestationID)11146826
 (PQKBTitleCode)TC0000139074
 (PQKBWorkID)10017276
 (PQKB)10862813
 (MiAaPQ)EBC226738
 (CaSebORM)9781558608610
 (EXLCZ)991000000000341407
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