Discrete Images, Objects, and Functions in Zn

the long version

This book treats theoretical problems of digital image pro- cessing. Voss uses the discrete nature of digital images as the basis for contructing appropriate mathematical models like n-dimensional incidence structures, lattices, and dis- crete functions. Presenting the results from this point of view 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 incidence structures is a generalisation of the currently used two-di- mensional theory in image processing. There are numerous new results e.g. on similarity of digital objects, n-dimensional surfacedetection, and inversion of convolution equations. Voss' book is an indispensable source of information to all those who are involved in the design, implementation, and application of mathematically sound algorithms in image pro- cessing; it is written for engineers, mathematicians, and computer scientists.