Digital geometry geometric methods for digital picture analysis
Digital 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...
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| Formato: | Libro electrónico |
| Idioma: | Inglés |
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Amsterdam ; Boston :
Elsevier : Morgan Kaufman Publishers
c2004.
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| Edición: | 1st edition |
| Colección: | Morgan Kaufmann series in computer graphics and geometric modeling.
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| Ver en Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009627813706719 |
Tabla de Contenidos:
- 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 Grid-intersection 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 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
- 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 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
- 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
