Discrete Images, Objects, and Functions in Zn [Paperback]

Content.- 1 Neighborhood Structures.- 1.1 Finite Graphs.- 1.1.1 Historical Remarks.- 1.1.2 Elementary Theory of Sets and Relations.- 1.1.3 Elementary Graph Theory.- 1.2 Neighborhood Graphs.- 1.2.1 Graph Theory and Image Processing.- 1.2.2 Points, Edges, Paths, and Regions.- 1.2.3 Matrices of Adjacency.- 1.2.4 Graph Distances.- 1.3 Components in Neighborhood Structures.- 1.3.1 Search in Graphs and Labyrinths.- 1.3.2 Neighborhood Search.- 1.3.3 Graph Search in Images.- 1.3.4 Neighbored Sets and Separated Sets.- 1.3.5 Component Labeling.- 1.4 Dilatation and Erosion.- 1.4.1 Metric Spaces.- 1.4.2 Boundaries and Cores in Neighborhood Structures.- 1.4.3 Set Operations and Set Operators.- 1.4.4 Dilatation and Erosion.- 1.4.5 Opening and Closing.- 2 Incidence Structures.- 2.1 Homogeneous Incidence Structures.- 2.1.1 Topological Problems.- 2.1.2 Cellular Complexes.- 2.1.3 Incidence Structures.- 2.1.4 Homogeneous Incidence Structures.- 2.1.5 Zn as Incidence Structure.- 2.2 Oriented Neighborhood Structures.- 2.2.1 Orientation of a Neighborhood Structure.- 2.2.2 Euler Characteristic of a Neighborhood Structure.- 2.2.3 Border Meshes and Separation Theorem.- 2.2.4 Search in Oriented Neighborhood Structures.- 2.2.5 Coloring in Oriented Neighborhood Structures.- 2.3 Homogeneous Oriented Neighborhood Structures.- 2.3.1 Homogeneity in Neighborhood Structures.- 2.3.2 Toroidal Nets.- 2.3.3 Curvature of Border Meshes in Toroidal Nets.- 2.3.4 Planar Semi-Homogeneous Graphs.- 2.4 Objects in N-Dimensional Incidence Structures.- 2.4.1 Three-Dimensional Homogeneous Incidence Structures.- 2.4.2 Objects in Zn.- 2.4.3 Similarity of Objects.- 2.4.4 General Surface Formulas.- 2.4.5 Interpretation of Object Characteristics.- 3 Topological Laws and Properties.- 3.1 Objects and Surfaces.- 3.1.1 Surfaces in Discrete Spaces.- 3.1.2 Contur Following as Two-Dimensional Boundary Detection.- 3.1.3 Three-Dimensional Surface Detection.- 3.1.4 Curvature of Conturs and Surfaces.- 3.2 Motions and Intersections.l£Ù