Discrete Images, Objects, and Functions in Zn

Voss' book which deals with theoretical problems of digital image processing is an indispensable source of information for all those who are involved in the design, implementation, and application of mathematically sound algorithms in image processing; it is written for engineers, mathematicians, and computer scientists. The author, who is a well-known expert in the field of digital image processing, presents important new research which generalizes the currently used two-dimensional theory to n dimensions.

Texte du rabat

This book treats theoretical problems of digital image pro-cessing. Voss uses the discrete nature of digital images asthe basis for contructing appropriate mathematical modelslike n-dimensional incidence structures, lattices, and dis-crete functions. Presenting the results from this point ofview has the important advantage that they can be used di-rectly in practical image processing.Voss presents the results of his own research and has col-lected other relevant and up-to-date material from the jour-nals in this field. His treatment of n-dimensional incidencestructures is a generalisation of the currently used two-di-mensional theory in image processing. There are numerous newresults e.g. on similarity of digital objects, n-dimensionalsurfacedetection, and inversion of convolution equations.Voss' book is an indispensable source of information to allthose who are involved in the design, implementation, andapplication of mathematically sound algorithms in image pro-cessing; it is written for engineers, mathematicians, andcomputer scientists.

Contenu
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.