Image Digitization and its Influence on Shape Properties in Finite Dimensions
This work addresses the problem of shape preserving digitization in finite dimensional spaces. The book gives an overview of existing approaches for sampling and reconstructing objects without changing certain topological properties and extends these results in various ways. First, the previously often used object class of r-regular sets is generalized to more realistic shapes. Second, a detailed overview about different sampling grids and sampling methods is given, including sampling under the influence of noise and blurring effects. It follows an analysis of different common reconstruction methods regarding their geometrical and topological properties. Finally, several new sampling theorems are derived from a deep investigation of the different combinations of shapes, samplings and reconstruction methods. Wherever possible, the results are proved for objects of arbitrary dimension.