Shape preserving digitization of ideal and blurred binary images

Abstract

In order to make image analysis methods more reliable it is important to analyse to what extend shape information is preserved during image digitization. Most existing approaches to this problem consider topology preservation and are restricted to ideal binary images. We extend these results in two ways. First, we characterize the set of binary images which can be correctly digitized by both regular and irregular sampling grids, such that not only topology is preserved but also the Hausdorff distance between the original image and the reconstruction is bounded. Second, we prove an analogous theorem for gray scale images that arise from blurring of binary images with a certain filter type. These results are steps towards a theory of shape digitization applicable to real optical systems. © Springer-Verlag Berlin Heidelberg 2003.