Shape Preserving Digitization of Binary Images After Blurring

Topology is a fundamental property of shapes 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 topological changes. 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 case of the mostly used square grids we show which binary images can be digitized topologically correctly after blurring with an arbitrary non-negative radially symmetric point spread function, which is an important step forward to real digitization.