Connectivity preserving digitization of blurred binary images in 2D and 3D

Connectivity and neighborhood are fundamental topological properties of objects in pictures. Since the input for any image analysis algorithm is a digital image, which does not need to have the same topological characteristics as the imaged real world, it is important to know, which shapes can be digitized without change of such topological properties. Most existing approaches do not take into account the unavoidable blurring in real image acquisition systems or use extremely simplified and thus unrealistic models of digitization with blurring. In some previous work we showed that certain shapes can be digitized topologically correctly with a square grid when some blurring with an arbitrary non-negative radially symmetric point spread function is involved. Now we extend this result to other common sampling grids in the two and even in the 3D space, including hexagonal, bcc and fcc grids.