Downsampling of Binary Images Using Adaptive Crossing Numbers

A downsampling method for binary images is presented, which aims at preserving the topology of the image. It uses a general reference sampling structure. The reference image is computed through the analysis of the connected components of the neighborhood of each pixel. The resulting downsampling operator is auto-dual, which ensures that white and black structures are treated in the same way. Experiments show that the image topology is indeed preserved, when there is enough space, satisfactorily.