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Man wird dem einzelnen nicht gerecht, wenn man es gesondert ins Auge jaftt, ohne seinen Zusammenhang mit dem Ganzen zu beachten und dem Beziehungssystem Rechnung zu tragen, in dem es steht. Thomas Mann Science in general, as well as in each of its individual fields, is a part of human culture. In that sense, this book aims to contribute to uncovering a small part of the connections and relationships which bind image processing, categorized in informatics and technology, with the knowledge accumulated over the years on discrete structures. How does one consider problems, models, mathematical methods and prac tical applications? How does the search for ideas and the endeavour for know ledge in the original work of scientists find expression? Is there something to be learnt from science to date for future developments? Such questions have shaped the content and style of this book. Substantial impetus to the discrete theory of image processing was afforded by the work of Rosenfeld and colleagues. Other fruitful sources of ideas con sidered here are number theoretical problems (GauB, Minkowski) and integral geometric investigations (Blaschke, Santalo). Since the beginning of the 1980s I have strived to build upon these ideas a unified mathematical representation of discrete image processing working together with R.K1ette and P.Hufnagl.
Inhaltsverzeichnis
Content.- 1 Neighborhood Structures.- 1.1 Finite Graphs.- 1.2 Neighborhood Graphs.- 1.3 Components in Neighborhood Structures.- 1.4 Dilatation and Erosion.- 2 Incidence Structures.- 2.1 Homogeneous Incidence Structures.- 2.2 Oriented Neighborhood Structures.- 2.3 Homogeneous Oriented Neighborhood Structures.- 2.4 Objects in N-Dimensional Incidence Structures.- 3 Topological Laws and Properties.- 3.1 Objects and Surfaces.- 3.2 Motions and Intersections.- 3.3 Topology Preserving Operations.- 4 Geometrical Laws and Properties.- 4.1 Discrete Geometry.- 4.2 Straight Lines.- 4.3 Convexity.- 4.4 Approximative Motions.- 5 Discrete Functions.- 5.1 One-Dimensional Periodical Discrete Functions.- 5.2 Algebraic Theory of Discrete Functions.- 5.3 Orthogonal Convolution Bases.- 5.4 Inversion of Convolutions.- 5.5 Differences and Sums of Functions.- 6 Summary and Symbols.- 7 References.- 8 Index.
